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Comprehensive exergy analysis of the dynamic process of compressed air energy storage system with low-temperature thermal energy storage
Applied Thermal Engineering 147 (2019) 684–693
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Comprehensive exergy analysis of the dynamic process of compressed air energy storage system with low-temperature thermal energy storage
T
Cong Guoa, Yujie Xua,b, Huan Guoa, Xinjing Zhanga,b, Xipeng Lina, Liang Wanga,b, Yi Zhanga,b, ⁎ Haisheng Chena,b, a b
Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China University of Chinese Academy of Sciences, Beijing 100049, China
H I GH L IG H T S
process of CAES system with low-temperature TES was modeled. • Dynamic destructions for each component in dynamic process were presented. • Exergy • Influence of ambient factors on multi-cycle performance was revealed.
A R T I C LE I N FO
A B S T R A C T
Keywords: CAES Dynamic modeling Exergy analysis Electrical energy storage
Compressed air energy storage (CAES) system with low-temperature thermal energy storage (TES) has advantages of profitability and start-up characteristics in the field of electrical energy storage, and many CAES pilot plants have been built in China. However, CAES systems face challenge of different working conditions in operation process due to changing pressure of air storage, influence of components’ thermal mass and other boundary conditions. In this paper, we simulated a dynamic CAES system in which part-load operation regularities of compressors and expanders, thermal inertia of components, volumetric effects of pipes and heat exchange between system and environment were taken into consideration. Based on this, exergy analysis of whole energy storage process and influence of ambient factors on multi-cycle performances have been conducted. The results indicate detailed features of the dynamic charging and discharging processes including system performance at start-up stage and entire process, which are beneficial to a comprehensive understanding of operation process and can be a reference in design and operation of CAES plants.
1. Introduction Global electricity production increased steadily over the past few decades and has reached 25,592 TWh by the end of 2017. With rapid development of hydro power, solar power and wind power etc., the proportion of renewable energy in all energy sources rises year by year, achieving 24.8% in 2017 [1]. However, due to the intrinsic intermittence and fluctuation, renewable energy cannot replace all traditional fossil fuels [2]. Electrical energy storage (EES) can store electricity when it is abundant and release it when necessary, therefore, EES is identified as one of the most prospective technologies for balancing power in time scale [3–5]. EES includes pumped hydro energy storage (PHES), compressed air energy storage (CAES), battery, flywheel and super capacitor etc., in
⁎
which only PHES and CAES can be utilized on large scale. But appropriate geographical condition including water resource is the main barrier to implement PHES. CAES converts electrical power into mechanical energy during off-peak periods of electricity demand and transforms energy reversely in the on-peak periods. Two traditional CAES plants have been operating for decades in Germany and the US with generating capacities of 321 MW and 110 MW respectively [6,7]. In recent years, adiabatic CAES has been proposed in which the compression heat can be recycled, and thus its roundtrip efficiency is greater than that of traditional CAES. ALACAES demonstration plant [8] and Adele CAES project [9] recycle high temperature compression heat (round 500–600 °C) with packed bed thermal energy storage technology. However, there are still some difficulties in choosing appropriate thermal storage media for the temperature range
Corresponding author at: Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China. E-mail address: [email protected] (H. Chen).
https://doi.org/10.1016/j.applthermaleng.2018.10.115 Received 15 August 2018; Received in revised form 1 October 2018; Accepted 24 October 2018 Available online 25 October 2018 1359-4311/ © 2018 Elsevier Ltd. All rights reserved.
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π
Nomenclature A cp E e h K M m N n p q t T w
Subscripts
area, m2 specific heat at constant pressure, J/kg/K state exergy, J flow exergy, J/kg specific enthalpy, J/kg heat transfer coefficient, W/m2/K mass, kg mass flow rate, kg/s number rotating speed, rpm pressure, Pa heat, W time, s temperature, °C work, W
c ch cold des dis e en hot HX i in max min out pinch s st TES vol w
Greek symbols β γ Δ ε ŋ
expansion ratio
compression ratio exergy destruction rate difference effectiveness of heat exchanger efficiency
compressor charging cold water destruction discharging expander environment hot water heat exchanger ith stage inlet maximum minimum outlet pinch temperature difference isentropic process storage thermal energy storage volume water
factors may also have negative influences on the system performance. Thus a dynamic exergy assessment of the entire process is necessary for the study of CAES systems. Studies of dynamic process of A-CAES systems have been conducted. Adriano et al. [15] developed a dynamic model of packed bed TES in HTA-CAES showing that the roundtrip efficiency can reach 70% when thermal storage efficiency is 95%. Wei He et al. studied the dynamic performance of packed bed TES in HTA-CAES [16] and mentioned that packed bed filled with phase change material can improve system efficiency. They also proposed a quasi dynamic model for simulating radial turbine [17]. Youssef et al. [18] presented a dynamic model of an innovative isobaric A-CAES system, taking into account the mechanical and thermal inertia of system components. Results showed that the time required by the system to reach steady state during charging period and
(500–600 °C) of high temperature compression heat, e.g. melting salt corrosion. Multi-stage compressor with inter-cooler produces low temperature compression heat (round 100 °C) and is suitable for twotank TES technology using pressurized water as thermal storage fluid. Some CAES systems with low-temperature TES have been built, like 1.5 MW A-CAES demonstration facility in Langfang, China [10] and 10 MW advanced CAES plant in Bijie, China [11]. Some studies have been done on thermodynamic process of CAES systems with low-temperature TES, like corresponding-point methodology [12] and analytical solution [13]. However, unlike steady cycles, the pressure in the air storage tank changes during charging and discharging processes and almost all components operate under off-design working conditions [14]. In addition, thermal inertia of components, volumetric effects of pipes, heat exchange between system and environment and other
Fig. 1. Schematic diagram of an 8-stage CAES system with low-temperature TES. 685
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Environment q
Hot fluid q
Thermal mass 1 q q
Environment
q
Environment
Thermal mass 2 q
Cold fluid q
Environment Fig. 4. Model of heat exchanger. Table 1 Exergy destruction of each component in system. Component
Exergy destruction
Compressor
∑ (wc + ein − eout )i
Heat exchanger
∑ (ein,cold + ein,hot − eout,cold − eout,hot )i
Pipe
∑ (ein − eout )i
Expander
∑ (ein − eout − we )i
Water mixer
∑ (ein,1 + ein,2 − eout )i
Air storage
eair,t ·mair,t − (Est,t+Δt − Est,t ) Δt (charging)
i
i
i
i i
Fig. 2. Compressor characteristics map.
(Est,t − Est,t+Δt ) Δt − eair,t+1·mair,t+1(discharging) Water tank
ewater,t ·mwater,t − (Etank,t+Δt − Etank,t ) Δt (charging) (Etank,t − Etank,t+Δt ) Δt − ewater,t+1·mwater,t+1(discharging)
Table 2 Constant parameters of the cycle.
Fig. 3. Expander characteristics map.
during discharging period are 120 s and 382 s respectively. M. Saadat et al. [19] presented a near constant pressure CAES system for wind turbines and used a cycle-average approach to model dynamic process for each component. Zhao et al. [20] conducted a preliminary dynamic behaviors analysis of a proposed flywheel-A-CAES system integrating with wind energy. The simulation results indicated that the total system power can fit load requirement well, providing an efficient management for wind power penetration. However, there is few studies on the dynamic process of CAES
Parameter
Unit
value
Ambient temperature Ambient pressure Pinch temperature difference in heat exchangers Thermal mass of each heat exchanger Total heat exchange area with environment of each heat exchanger K ·A of each heat exchanger K en,mass Khot,en , K cold,en Thermal mass of total pipes Length of pipes Outer diameter of pipes Wall thickness of pipes Kpipes,fluid
°C MPa °C
25 0.101325 5
J/K m2
10,120,000 66
W/K W/(m2·K) W/(m2·K) J/K m mm mm W/(m2·K)
449,320 50 50 1,707,520 50 300 10 250
Kpipes,en
W/(m2·K)
50
Volume of air storage K en,st Maximum pressure of air storage
m3 W/(m2·K) MPa
Minimum pressure of air storage Rated power of compressor Rated power of expander Rated isentropic efficiency of compressor Rated isentropic efficiency of expander
MPa MW MW % %
37,200 50 7 (or depends on charging time) 4.2 26.05 20.08 88 92
systems with low-temperature TES. In this paper, a comprehensive analysis for the dynamic behaviors has been carried out in Simulink software with Thermolib toolbox, based on which the exergy destruction distribution of each component in the whole process can be achieved.
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Table 3 Exergy destruction distribution. Rate of Exergy destruction to input power (%) Compressors Expanders Heat exchangers of compressors Throttle Heat exchangers of expanders Hot water Air storage (whole process) Pipes Water tank Total Exergy destruction rate (%) System roundtrip efficiency (%)
9.24 6.84 4.17 3.64 2.50 0.88 0.75 0.14 0.05 28.21 71.79
Fig. 6. Dynamic distribution of exergy destruction in charging.
2. System description The CAES system with low-temperature TES applies a similar principle as that of conventional CAES system, but cancels combustion chamber and introduces hot/cold energy storage tanks. As shown in Fig. 1, the present system includes a compression train with heat exchangers, an expansion train with heat exchangers, a compressed air storage, hot and cold thermal energy storage reservoirs, two pumps and a throttle valve. In charging process, air from atmosphere is compressed and delivered to the compressed air storage, with part of compression heat transferred to water and stored in TES. Likewise, in discharging process, air passes through the throttle valve then enters the expansion train with heat exchangers, and finally gets into atmosphere. With relatively more compression stages, the temperature of thermal storage fluid could not reach very high (the greatest temperature is round 100 °C under the condition of 10 MPa storage pressure and 8 compression stages), and pressurized water could be used as TES media. Thus indirect-contact heat exchangers with two water reservoirs are adopted in this system for heat recovery. The heat stored in charging process is more than the heat released in discharging process because of finite temperature difference in heat transfer. In order to cool down the hot water to the atmosphere temperature, heat exchanger 0 is introduced in the system. The throttle valve is used to adjust air pressure before the expansion train to ensure that air enters at a constant pressure. This is beneficial to a steady and high-efficiency operation of the expansion train. Slidingpressure operating condition is not considered in this paper.
Fig. 7. Exergy destruction contribution in charging.
compressor are shown as (1)-(3):
ηc,i = (hout,c,i,s − h in,c,i ) (hout,c,i − h in,c,i )
(1)
wc,i = mc (h out,c,i − h in,c,i)
(2)
Nc
wc =
∑ mc (hout,c,i − hin,c,i) i=1
3. Thermodynamic model and cycling performance
(3)
Off-design performance model of the compressor is considered by using characteristic maps [15,21], which is
3.1. Compressors
βi βi,0 = c1 ṁ c2 + c2 ṁ c + c3
The isentropic efficiency, power of one stage, total power of the
Fig. 5. Energy distribution of the whole process. 687
(4)
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Fig. 11. Total power and mass flow rate in charging.
Fig. 8. Outlet water temperature of exchangers in charging.
Fig. 12. Dynamic distribution of exergy destruction in discharging.
Fig. 9. Power of compressor in charging.
Fig. 13. Exergy destruction contribution in discharging. Fig. 10. Efficiency of compressor in charging. ·
ηc,i ηc,i,0 = [1 − c4 (1 − ṅc )2](ṅc ṁ c )(2 − ṅc ṁ c )
m = (mc Tc,in Pc,in ) (mc Tc,in Pc,in )0 c
(5)
·
n = (nc
where subscript 0 denotes design values, βi represents compression · ratio of the ith compressor and ηc,i represents isoentropic efficiency. m ·
c
Tc,in ) (nc
Tc,in )0
(6) (7)
and c1-c4 are parameters which can be calculated as follows,
c
and n are dimensionless flow rate and dimensionless rotating speed
·
c
·
·
·
c1 = n [p (1 − q n c ) + n c (n c − q)2]
which can be calculated as follows,
c
688
(8)
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[15,21] where a modified Flügel formula is used, and the expander characteristics map is shown in Fig. 3. ·
m= e
·
1.4 − 0.4ne Tt0,in Tt,in
(πt2 − 1) (πt02 − 1)
(15)
2
ηe
· ⎤ · · ⎛ · · ⎞ ⎡ ηe,0 = ⎢1 − 0.3 ⎜⎛1 − n⎟⎞ ⎥ ⎜⎛n m⎟⎞ ⎜2 − ⎜⎛n m⎟⎞ ⎟ e e e e e ⎝ ⎠ ⎦⎝ ⎠⎝ ⎝ ⎠⎠ ⎣
(16)
·
m = (me Te,in Pe,in ) (me0 Te,in Pe,in )0
(17)
e
·
n = (ne
Te,in ) (ne
e
Te,in )0
(18)
Like the compressor, volumetric effects for the expander is considered. It is assumed that the volume locates after its corresponding stage and its output mass flow rate equals the input mass flow rate of next stage. For the volume,
Fig. 14. Power of expander in discharging.
(19)
dMvol dt = m in − mout 3.3. Heat exchangers
Counter flow heat exchangers are modelled by employingε -NTU method. Another constraint condition is the pinch temperature difference, which is set as a constant.
qHX = mair (h c/e,out,i - 1 − h c/e,in,i) = m w (h w,out,i − h w,in,i )
(
ε = qHX
qmax =
1 − exp ⎛⎜ (−NTU )· 1 − ⎝ 1−
NTU = Fig. 15. Total power and mass flow rate in discharging.
(mc )min (mc )max
(
(
(mc )min (mc )max
exp (−NTU )· 1 −
(20)
) ⎞⎠
⎟
(mc )min (mc )max
))
KA (mc )min
Tpinch = min(Tc/e,out,i - 1 − Tw,out,i, Tc/e,in,i − Tw,in,i ) ·⎞
c2 = ⎜⎛p − 2q n2 ⎟ c ⎠ ⎝
·
·
·
c3 = −⎜⎛pqn − q2ṅc3⎟⎞ ⎝ c ⎠
·
·
(9)
·
[p (1 − q nc ) + nc (nc − q)2]
qhot,mass = Khot,en Ahot,en (Ten − Thot )
(24)
qcold,mass = K cold,en Acold,en (Ten − Tcold )
(25)
Thermal inertia of heat exchangers: It is assumed that each of the two flows entering the heat exchanger exchanges heat with its own thermal mass (heat capacity [J/K]), which is half of the total thermal mass. The two thermal masses are not interacting, but they have a term representing the heat exchange with environment [23], shown in Fig. 4. The heat exchange between flow and thermal mass is also calculated based on NTU method,
εHX,mass = qHX,mass qmax = 1 − exp(−KHX,mass AHX,mass m fluid ·cp)
(11)
qen,mass = K en,mass Aen,mass (Ten − Tmass )
(12)
we,i = me (h in,e,i − h out,e,i)
(13)
Ahot,en = Acold,en = 0.5Aen,mass = 0.25Aen,HX
Ne
∑ me (hin,e,i − hout,e,i) i=1
(27)
Total heat exchange area with environment of each heat exchanger is set to 66 m2 according to a CAES project of our group in Bijie, China. Aen,mass is assumed to half of the total heat exchange area with environment, Aen,HX .
The isentropic efficiency, power output of one stage, total power output of the expander can be shown as (12)-(14):
ηe,i = (h in,e,i − h out,e,i ) (h in,e,i,s − h out,e,i )
(26)
Heat exchanged with environment for thermal mass:
3.2. Expanders
we =
(23)
(10)
where p = 1.8, q = 1.8, c4 = 0.3 [21].These formulas (4)–(10) were proposed by Na Zhang and Ruixian Cai [22] according to particularity of radial compressors. The compressor characteristics map is shown in Fig. 2. The compressor has a volume and when the operating condition changes the temperature and pressure could be influenced by volumetric effects. It is assumed that the volume locates after its corresponding stage and its output mass flow rate equals the input mass flow rate of next stage. For the volume,
dMvol dt = m in − mout
(22)
Heat exchanged with environment for hot and cold fluids:
·
[p (1 − q nc ) + nc (nc − q)2]
(21)
(28)
3.4. Pipes (14)
Pipes are assumed to have thermal mass (heat capacity), which is calculated by ε -NTU method,
Off-design performance model of the expander is considered 689
400
12
Air mass in storage
380
11
360
Temperature /K
320
9
Temperature
300
8
280
7
Pressure
260
Pressure /MPa
10
340
6
240
5
220 200 0
10
20
30
40
50
60
70
80
90
4 100
3000 2800 2600 2400 2200 2000 1800 1600 1400 1200 1000 800 600 400 200 0
Air mass in storage /kg
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Time /h
400
12
Air mass in storage
380
11
360
Temperature /K
320
9
Temperature
8
300 280
7
Pressure
260
6
240
5
220 200 0
10
20
30
40
50
60
70
80
90
4 100
Pressure /MPa
10
340
3000 2800 2600 2400 2200 2000 1800 1600 1400 1200 1000 800 600 400 200 0
Air mass in storage /kg
(a) Operating method 1
Time /h
(b) Operating method 2 Fig. 16. Variation of parameters in air storage reservoir for multi-cycle.
εpipes,fluid = qpipes,fluid qmax = 1 − exp(−Kpipes,fluid Apipes,fluid m fluid ·cp)
3.6. Mixer for water (29)
m in,i h in,i + m in,j h in,j = (m in,i + m in,j) hout,ij
Heat exchanged with environment for pipes:
qpipes,en = Kpipes,en Apipes,en (Ten − Tpipes)
(30)
(34)
3.7. Throttle valve
hbefore = hafter
(35)
3.5. Compressed air storage 3.8. Cycling performance
Air storage tank is seen as a sphere in this paper.
dmst dt = mst,in − mst,out
(31)
dUst dt = h in − h out + q
(32)
Table 1 shows exergy destruction of each component, in which E = U − U0 − T0 (S − S0) + p0 (V − V0) (state exergy of air storage or water tank, J), and e = h − h 0 − T0 (s − s0) (flow exergy, J/kg). T0 is 25 °C. Exergy destruction rate for each component in charging and discharging process (real time):
(33)
γch = edes wc
Heat exchanged with environment for air storage:
qen,st = K en,st Aen,st (Ten − Tst )
690
(36)
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pressure operation. However, sliding pressure operation would result in a low performance of expanders, which is not considered in this paper. There are 0.88% of the input energy left in hot water after discharging and the loss of air storage contributes to 0.75% of the total energy. They are both low grade thermal energy that could not be recycled easily. Exchanging heat with environment for pipes and the mix of hot water with different temperatures cause losses of energy with 0.14% and 0.05% respectively. The roundtrip efficiency for the system is 71.79%.
Table 4 Simulation results of multi-cycle. (a) Operating method 1
Charging energy (MWhe) Charging time (h) Highest air pressure (MPa) Discharging energy (MWhe) Discharging time (h) Roundtrip efficiency (%) Roundtrip efficiency for per unit mass of air (%)
1st cycle
2nd cycle
3rd cycle
4th cycle
102.77 4 6.65 61.77 3.08 60.1 72.8
104.20 4 7.02 73.90 3.68 70.9 71.8
104.29 4 7.04 74.74 3.72 71.7 71.7
104.29 4 7.04 74.74 3.72 71.7 71.7
1st cycle
2nd cycle
3rd cycle
4th cycle
119.52 4.62 7 72.55 3.61 60.7 72.3
102.40 3.93 7 73.43 3.66 71.7 71.8
102.30 3.93 7 73.43 3.66 71.8 71.8
102.30 3.93 7 73.43 3.66 71.8 71.8
4.1. Exergy analysis for charging process As shown in Fig. 6 and 7, the compressor contributes most to the total exergy destruction in charging process with an average exergy destruction rate of 9.24%. As the compression train operates under the off-design operating condition before the end of charging process and its isentropic efficiency increases during charging process, the exergy destruction decreases with time. During start-up period, the compressor has a relatively higher exergy destruction because of cold start. Heat exchangers contribute the second highest exergy destruction in charging process. The exergy destruction rate is relatively high in first 10 mins because of thermal inertia. After that, the exergy destruction rate remains stable at 4.17%. As for the air storage reservoir, the air in it is gradually compressed and thus its temperature rises. As a result, the heat exchanged with the environment increases and the exergy destruction also goes up. The average exergy destruction rate is 0.75%. The exergy destruction for pipes is caused by the heat exchanged with the environment and its thermal inertia, which accounts for 0.14% of the compression work. The pressure in tank rises during charging process, but the increasing rates for 8 stages are different. This leads to differences of outlet water temperature which can be seen in Fig. 8. The exergy destruction of water tank is caused by mixing water with different temperatures together and the average exergy destruction rate is 0.05%. The average exergy efficiency of charging process is 85.65%. Power and efficiency of compressor in charging process are shown in Fig. 9 and 10. During start-up period according to Eq. (6), air temperature is inversely correlated with air mass flow rate while other parameters remain the same. Thus the air flow rate is relatively high at the beginning (see Fig. 11). The rated power for the first stage is slightly lower than the other 7 stages (see Fig. 9), which is because the inlet air temperature of the first stage is lower than those of the others. During the whole charging period, the pressure ratio, output power and isentropic efficiency of higher compression stages are affected more than the lower stages by the pressure change in air storage reservoir. The evolution of total power can be seen in Fig. 11. At the beginning, it is influenced mainly by the mass flow rate and reaches the lowest point at 4.5 min. After that, the main factor affecting total power is the pressure in air reservoir, and the total power rises with the pressure. The mass flow rate reduces with the pressure ratio, which would lead to the reduction of power. Total power is influenced by above two factors and increases. The difference between the maximum and minimum of total power is 9.91%.
(b) Operating method 2
Charging energy (MWhe) Charging time (h) Highest air pressure (MPa) Discharging energy (MWhe) Discharging time (h) Roundtrip efficiency (%) Roundtrip efficiency for per unit mass of air (%)
γdis = edes ((Est,t − Est,t + 1) + (Etank,t − Etank,t + 1))
(37)
Exergy efficiency in charging (entire charging process): ch,end
ηch = ((Est + Etank )ch,end − (Est + Etank )ch,initial)
∫
wc dt
ch,initial
(38)
Exergy efficiency in discharging (entire discharging process): dis,end
∫
ηdis =
we dt
((Est + Etank )dis,initial − (Est + Etank )dis,end) (39)
dis,initial
Roundtrip efficiency: dis,end
ηround =
∫ dis,initial
ch,end
we dt
∫ ch,initial
wc dt (40)
The losses of motor and generator are not considered in this paper. 4. Results and discussion In this paper, the effects of part-load operation regularities of compressors and expanders, thermal inertia of components, volumetric effects of pipes and heat exchanged with environment are taken into consideration. Some constant parameters are shown in Table 2. Total energy distribution including the exergy destruction distribution can be obtained and shown in Table 3 and Fig. 5. As the compressors usually have lower efficiencies than those of the expanders in real projects, the isentropic efficiencies for compressors and expanders are assumed 0.88 and 0.92 respectively in this paper and thus, exergy destruction of compressors is higher than that of expanders (9.24% vs 6.84%). During the charging process, the variation of air pressure in air tank increases, leading to the changes of air temperature at the outlet of every compressor especially higher pressure stages. This causes an uneven temperature difference for every heat exchanger of compressors during charging process. By contrast, the working condition of discharging process is much more stable (the input pressure of the first stage expander is fixed) because of the throttle, so the temperature difference in the heat exchangers of expanders are almost unchanged except the first heat exchanger. Thus the exergy destruction for heat exchangers of expanders is much lower than that of compressors (2.5% vs 4.17%). The energy loss of throttle accounts for 3.64% of the input power and this can be eliminated by adapting sliding
4.2. Exergy analysis for discharging process Exergy destruction rate for different components in discharging process can be seen in Fig. 12 and 13. The expander contributes most to the total exergy destruction in discharging process with an average exergy destruction rate of 7.84%. Because the temperature in air storage reservoir decreases with time, the air outlet temperature of the exchanger for first expander reduces, which leads to the deviation from the design point and the exergy destruction of expander increases slightly. As for the throttle, because its pressure difference drops with time and finally reaches 0 after the discharging process, the exergy 691
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expanders, thermal inertia of components, volumetric effects of pipes and heat exchange between system and environment in whole energy storage process and start-up procedure have been studied and analyzed. From analysis results, the following conclusions can be drawn:
destruction at initial time is the largest and reduces with time. The average exergy destruction rate is 4.12%. Heat exchangers contribute the third to the total exergy destruction. The exergy destruction rate is relatively high in the first 9 min because of its thermal inertia. After that in the discharging process, there is a slight rise in the exergy destruction with time due to larger heat transfer temperature difference. The average exergy destruction rate is 2.87%. The thermal energy recovered from compression process can not all be transferred to the expansion process due to the temperature difference in heat exchangers, so part of the thermal energy would be taken away by the hot water after the heat exchangers of expanders, leading to an exergy destruction. In the start-up period, there is less exergy destruction for hot water because the thermal mass of heat exchangers could utilize the thermal energy. After this period (9 min), its exergy destruction keeps unchanged and the average exergy destruction rate is 1.01%. The temperature in air storage decreases with its pressure and thus more heat exchanged with the environment with time in the discharging process. This leads to the exergy destruction of the air storage reservoir which rises in discharging. The average exergy destruction rate is 0.74%. The average exergy efficiency of the discharging process is 83.41%. Both inlet air temperature and air mass flow rate can affect the power of expanders. In the start-up period, inlet air temperature has a greater influence on the power and the power for every stage grows gradually (see Fig. 14). Air mass flow rate reduces in this period, shown in Fig. 15. After this period, the power of first stage falls because of the decrease of the inlet temperature (the temperature in air tank drops with time and it leads to the decrease of expander inlet temperature) meanwhile the power of other 7 stages keeps unchanged (see Fig. 14). Total power can also be seen in Fig. 15 that before 9 min the total power has a rising trend and after that it almost keeps stable.
(1) The exergy destructions with time for each component during entire energy storage process were revealed and time reaching steady state can be obtained, e.g., the compressor train takes 4.5 min to reach steady state, and lower air temperature would lead to a higher mass flow rate and more power with a lower charging efficiency in this cold start process. (2) In a complete cycle, compressors contribute most to energy loss at 9.24%, which is followed by expanders at 6.84%. Heat exchangers of compressors cause more energy loss (4.17%) than heat exchangers of expanders (2.5%) due to more stable operation during discharging process. Throttle contributes 3.64% of energy loss which cannot be neglected for constant-pressure operation. Exergy loss of every other component is less than 1%. (3) After three full cycles, CAES system can achieve a stable condition. Because of the influence of initial condition, air flows into the system while charging is more than that flows out of the system while discharging in the first cycle. Thus the efficiency of first cycle is round 10 percent points lower than those of other cycles. But if calculating the roundtrip efficiency for per unit mass of air, the efficiencies of different cycles are almost the same. Acknowledgements The authors would like to thank the following organizations for financial support of the work: National Natural Science Foundation of China (NSFC) under Grant No. 51706222, National Basic Research Program of China (973 Program) under Grant No. 2015CB251302, Transformational Technologies for Clean Energy and Demonstration, Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No. XDA21070200, The Frontier Science Research Project of CAS under Grant No. QYZDB-SSW-JSC023 and the program of China Scholarships Council under Grant No. 201802180087.
4.3. Influence of operation cycle number There are two operating methods simulated in this article. Operating method 1 is that the charging time is fixed to 4 h and the discharging process ends when the air pressure in tank is 4.2 MPa. Operating method 2 is that the charging process ends when the pressure in air tank reaches 7 MPa and discharging process ends when this pressure reaches 4.2 MPa. The settling period after charging is 8 h and every cycle has 24 h for the two methods. The operation results can be seen in Fig. 16 and Table 4. Due to the heat exchanged with environment, the system can be stable after several cycles. It can be seen from Fig. 16 that the performance of the fourth cycle is exactly the same as that of the third, which means that three cycles are enough to make the cycle operation stable. We can see from Table 4 that the roundtrip efficiencies of the first cycle are around 10 percent points lower than those of the second and the third cycles for both two operating methods (e.g., 60.1%, 70.9% and 71.7%). This is because for the first cycle, the initial temperature or pressure is different from the cycles after stable operation and the air flows into the system while charging is more than that flows out of the system while discharging. So the calculated system efficiency of the first cycle would be lower. This influence could be eliminated mostly in the second cycle and completed eliminated in the third cycle. However, if calculating the roundtrip efficiency for per unit mass of air, the first cycle has a slightly higher value than the third (e.g., 72.8% vs. 71.7%) as the pressure in air tank of the first cycle before discharging is a bit lower than that of the third and thus the exergy loss of throttle of the first cycle is lower.
Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2018.10.115. References [1] Global Energy Statistical Yearbook 2017. Enerdata; 2017.https://yearbook.enerdata.net/world-electricity-production-map-graph-and-data.html#renewable-inelectricity-production-share-by-region.html. [2] E. Barbour, D. Mignard, Y. Ding, Y. Li, Adiabatic compressed air energy storage with packed bed thermal energy storage, Appl. Energy 155 (2015) 804–815. [3] H. Chen, T.N. Cong, W. Yang, C. Tan, Y. Li, Y. Ding, Progress in electrical energy storage system: a critical review, Prog. Nat. Sci. 19 (2009) 291–312. [4] J.P. Barton, D.G. Infield, Energy storage and its use with intermittent renewable energy, IEEE Trans. Energy Convers. 19 (2004) 441–448. [5] J.M. Carrasco, L.G. Franquelo, J.T. Bialasiewicz, E. Galvan, R.C.P. Guisado, M.A.M. Prats, et al., Power-electronic systems for the grid integration of renewable energy sources: a survey, IEEE Trans. Indust. Electron. 53 (2006) 1002–1016. [6] Crotogino F, Mohmeyer K-U, Scharf R. Huntorf CAES: More than 20 years of successful operation. Orlando, Florida, USA. 2001. [7] M. Nakhamkin, M. Chiruvolu, C. Daniel, Available compressed air energy storage (CAES) plant concepts, Energy 4100 (2010) 81. [8] ALACAES. https://alacaes.com/. [9] S. Zunft, Adiabatic CAES: The ADELE-ING project, SCCER Heat & Electricity Storage Symposium. Villigen, Switzerland, 2015. [10] Advanced compressed air energy storage won the first prize of Beijing science and technology.[accessed 02. 02.18]. [11] Thermodynamic Analytical Solution and Exergy Analysis for Supercritical Compressed Air Energy Storage System. https://reginnovations.org/key-energystorage-system/thermodynamic-analytical-solution-exergy-analysis-supercriticalcompressed-air-energy-storage-system/ [accessed 06.06.18]. [12] H. Guo, Y. Xu, H. Chen, X. Zhang, W. Qin, Corresponding-point methodology for
5. Conclusions In this paper, a dynamic model of CAES system with TES was developed. Effects of part-load operation regularities of compressors and 692
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Comprehensive exergy analysis of the dynamic process of compressed air energy storage system with low-temperature thermal energy storage
T
Cong Guoa, Yujie Xua,b, Huan Guoa, Xinjing Zhanga,b, Xipeng Lina, Liang Wanga,b, Yi Zhanga,b, ⁎ Haisheng Chena,b, a b
Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China University of Chinese Academy of Sciences, Beijing 100049, China
H I GH L IG H T S
process of CAES system with low-temperature TES was modeled. • Dynamic destructions for each component in dynamic process were presented. • Exergy • Influence of ambient factors on multi-cycle performance was revealed.
A R T I C LE I N FO
A B S T R A C T
Keywords: CAES Dynamic modeling Exergy analysis Electrical energy storage
Compressed air energy storage (CAES) system with low-temperature thermal energy storage (TES) has advantages of profitability and start-up characteristics in the field of electrical energy storage, and many CAES pilot plants have been built in China. However, CAES systems face challenge of different working conditions in operation process due to changing pressure of air storage, influence of components’ thermal mass and other boundary conditions. In this paper, we simulated a dynamic CAES system in which part-load operation regularities of compressors and expanders, thermal inertia of components, volumetric effects of pipes and heat exchange between system and environment were taken into consideration. Based on this, exergy analysis of whole energy storage process and influence of ambient factors on multi-cycle performances have been conducted. The results indicate detailed features of the dynamic charging and discharging processes including system performance at start-up stage and entire process, which are beneficial to a comprehensive understanding of operation process and can be a reference in design and operation of CAES plants.
1. Introduction Global electricity production increased steadily over the past few decades and has reached 25,592 TWh by the end of 2017. With rapid development of hydro power, solar power and wind power etc., the proportion of renewable energy in all energy sources rises year by year, achieving 24.8% in 2017 [1]. However, due to the intrinsic intermittence and fluctuation, renewable energy cannot replace all traditional fossil fuels [2]. Electrical energy storage (EES) can store electricity when it is abundant and release it when necessary, therefore, EES is identified as one of the most prospective technologies for balancing power in time scale [3–5]. EES includes pumped hydro energy storage (PHES), compressed air energy storage (CAES), battery, flywheel and super capacitor etc., in
⁎
which only PHES and CAES can be utilized on large scale. But appropriate geographical condition including water resource is the main barrier to implement PHES. CAES converts electrical power into mechanical energy during off-peak periods of electricity demand and transforms energy reversely in the on-peak periods. Two traditional CAES plants have been operating for decades in Germany and the US with generating capacities of 321 MW and 110 MW respectively [6,7]. In recent years, adiabatic CAES has been proposed in which the compression heat can be recycled, and thus its roundtrip efficiency is greater than that of traditional CAES. ALACAES demonstration plant [8] and Adele CAES project [9] recycle high temperature compression heat (round 500–600 °C) with packed bed thermal energy storage technology. However, there are still some difficulties in choosing appropriate thermal storage media for the temperature range
Corresponding author at: Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China. E-mail address: [email protected] (H. Chen).
https://doi.org/10.1016/j.applthermaleng.2018.10.115 Received 15 August 2018; Received in revised form 1 October 2018; Accepted 24 October 2018 Available online 25 October 2018 1359-4311/ © 2018 Elsevier Ltd. All rights reserved.
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π
Nomenclature A cp E e h K M m N n p q t T w
Subscripts
area, m2 specific heat at constant pressure, J/kg/K state exergy, J flow exergy, J/kg specific enthalpy, J/kg heat transfer coefficient, W/m2/K mass, kg mass flow rate, kg/s number rotating speed, rpm pressure, Pa heat, W time, s temperature, °C work, W
c ch cold des dis e en hot HX i in max min out pinch s st TES vol w
Greek symbols β γ Δ ε ŋ
expansion ratio
compression ratio exergy destruction rate difference effectiveness of heat exchanger efficiency
compressor charging cold water destruction discharging expander environment hot water heat exchanger ith stage inlet maximum minimum outlet pinch temperature difference isentropic process storage thermal energy storage volume water
factors may also have negative influences on the system performance. Thus a dynamic exergy assessment of the entire process is necessary for the study of CAES systems. Studies of dynamic process of A-CAES systems have been conducted. Adriano et al. [15] developed a dynamic model of packed bed TES in HTA-CAES showing that the roundtrip efficiency can reach 70% when thermal storage efficiency is 95%. Wei He et al. studied the dynamic performance of packed bed TES in HTA-CAES [16] and mentioned that packed bed filled with phase change material can improve system efficiency. They also proposed a quasi dynamic model for simulating radial turbine [17]. Youssef et al. [18] presented a dynamic model of an innovative isobaric A-CAES system, taking into account the mechanical and thermal inertia of system components. Results showed that the time required by the system to reach steady state during charging period and
(500–600 °C) of high temperature compression heat, e.g. melting salt corrosion. Multi-stage compressor with inter-cooler produces low temperature compression heat (round 100 °C) and is suitable for twotank TES technology using pressurized water as thermal storage fluid. Some CAES systems with low-temperature TES have been built, like 1.5 MW A-CAES demonstration facility in Langfang, China [10] and 10 MW advanced CAES plant in Bijie, China [11]. Some studies have been done on thermodynamic process of CAES systems with low-temperature TES, like corresponding-point methodology [12] and analytical solution [13]. However, unlike steady cycles, the pressure in the air storage tank changes during charging and discharging processes and almost all components operate under off-design working conditions [14]. In addition, thermal inertia of components, volumetric effects of pipes, heat exchange between system and environment and other
Fig. 1. Schematic diagram of an 8-stage CAES system with low-temperature TES. 685
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Environment q
Hot fluid q
Thermal mass 1 q q
Environment
q
Environment
Thermal mass 2 q
Cold fluid q
Environment Fig. 4. Model of heat exchanger. Table 1 Exergy destruction of each component in system. Component
Exergy destruction
Compressor
∑ (wc + ein − eout )i
Heat exchanger
∑ (ein,cold + ein,hot − eout,cold − eout,hot )i
Pipe
∑ (ein − eout )i
Expander
∑ (ein − eout − we )i
Water mixer
∑ (ein,1 + ein,2 − eout )i
Air storage
eair,t ·mair,t − (Est,t+Δt − Est,t ) Δt (charging)
i
i
i
i i
Fig. 2. Compressor characteristics map.
(Est,t − Est,t+Δt ) Δt − eair,t+1·mair,t+1(discharging) Water tank
ewater,t ·mwater,t − (Etank,t+Δt − Etank,t ) Δt (charging) (Etank,t − Etank,t+Δt ) Δt − ewater,t+1·mwater,t+1(discharging)
Table 2 Constant parameters of the cycle.
Fig. 3. Expander characteristics map.
during discharging period are 120 s and 382 s respectively. M. Saadat et al. [19] presented a near constant pressure CAES system for wind turbines and used a cycle-average approach to model dynamic process for each component. Zhao et al. [20] conducted a preliminary dynamic behaviors analysis of a proposed flywheel-A-CAES system integrating with wind energy. The simulation results indicated that the total system power can fit load requirement well, providing an efficient management for wind power penetration. However, there is few studies on the dynamic process of CAES
Parameter
Unit
value
Ambient temperature Ambient pressure Pinch temperature difference in heat exchangers Thermal mass of each heat exchanger Total heat exchange area with environment of each heat exchanger K ·A of each heat exchanger K en,mass Khot,en , K cold,en Thermal mass of total pipes Length of pipes Outer diameter of pipes Wall thickness of pipes Kpipes,fluid
°C MPa °C
25 0.101325 5
J/K m2
10,120,000 66
W/K W/(m2·K) W/(m2·K) J/K m mm mm W/(m2·K)
449,320 50 50 1,707,520 50 300 10 250
Kpipes,en
W/(m2·K)
50
Volume of air storage K en,st Maximum pressure of air storage
m3 W/(m2·K) MPa
Minimum pressure of air storage Rated power of compressor Rated power of expander Rated isentropic efficiency of compressor Rated isentropic efficiency of expander
MPa MW MW % %
37,200 50 7 (or depends on charging time) 4.2 26.05 20.08 88 92
systems with low-temperature TES. In this paper, a comprehensive analysis for the dynamic behaviors has been carried out in Simulink software with Thermolib toolbox, based on which the exergy destruction distribution of each component in the whole process can be achieved.
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Table 3 Exergy destruction distribution. Rate of Exergy destruction to input power (%) Compressors Expanders Heat exchangers of compressors Throttle Heat exchangers of expanders Hot water Air storage (whole process) Pipes Water tank Total Exergy destruction rate (%) System roundtrip efficiency (%)
9.24 6.84 4.17 3.64 2.50 0.88 0.75 0.14 0.05 28.21 71.79
Fig. 6. Dynamic distribution of exergy destruction in charging.
2. System description The CAES system with low-temperature TES applies a similar principle as that of conventional CAES system, but cancels combustion chamber and introduces hot/cold energy storage tanks. As shown in Fig. 1, the present system includes a compression train with heat exchangers, an expansion train with heat exchangers, a compressed air storage, hot and cold thermal energy storage reservoirs, two pumps and a throttle valve. In charging process, air from atmosphere is compressed and delivered to the compressed air storage, with part of compression heat transferred to water and stored in TES. Likewise, in discharging process, air passes through the throttle valve then enters the expansion train with heat exchangers, and finally gets into atmosphere. With relatively more compression stages, the temperature of thermal storage fluid could not reach very high (the greatest temperature is round 100 °C under the condition of 10 MPa storage pressure and 8 compression stages), and pressurized water could be used as TES media. Thus indirect-contact heat exchangers with two water reservoirs are adopted in this system for heat recovery. The heat stored in charging process is more than the heat released in discharging process because of finite temperature difference in heat transfer. In order to cool down the hot water to the atmosphere temperature, heat exchanger 0 is introduced in the system. The throttle valve is used to adjust air pressure before the expansion train to ensure that air enters at a constant pressure. This is beneficial to a steady and high-efficiency operation of the expansion train. Slidingpressure operating condition is not considered in this paper.
Fig. 7. Exergy destruction contribution in charging.
compressor are shown as (1)-(3):
ηc,i = (hout,c,i,s − h in,c,i ) (hout,c,i − h in,c,i )
(1)
wc,i = mc (h out,c,i − h in,c,i)
(2)
Nc
wc =
∑ mc (hout,c,i − hin,c,i) i=1
3. Thermodynamic model and cycling performance
(3)
Off-design performance model of the compressor is considered by using characteristic maps [15,21], which is
3.1. Compressors
βi βi,0 = c1 ṁ c2 + c2 ṁ c + c3
The isentropic efficiency, power of one stage, total power of the
Fig. 5. Energy distribution of the whole process. 687
(4)
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Fig. 11. Total power and mass flow rate in charging.
Fig. 8. Outlet water temperature of exchangers in charging.
Fig. 12. Dynamic distribution of exergy destruction in discharging.
Fig. 9. Power of compressor in charging.
Fig. 13. Exergy destruction contribution in discharging. Fig. 10. Efficiency of compressor in charging. ·
ηc,i ηc,i,0 = [1 − c4 (1 − ṅc )2](ṅc ṁ c )(2 − ṅc ṁ c )
m = (mc Tc,in Pc,in ) (mc Tc,in Pc,in )0 c
(5)
·
n = (nc
where subscript 0 denotes design values, βi represents compression · ratio of the ith compressor and ηc,i represents isoentropic efficiency. m ·
c
Tc,in ) (nc
Tc,in )0
(6) (7)
and c1-c4 are parameters which can be calculated as follows,
c
and n are dimensionless flow rate and dimensionless rotating speed
·
c
·
·
·
c1 = n [p (1 − q n c ) + n c (n c − q)2]
which can be calculated as follows,
c
688
(8)
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[15,21] where a modified Flügel formula is used, and the expander characteristics map is shown in Fig. 3. ·
m= e
·
1.4 − 0.4ne Tt0,in Tt,in
(πt2 − 1) (πt02 − 1)
(15)
2
ηe
· ⎤ · · ⎛ · · ⎞ ⎡ ηe,0 = ⎢1 − 0.3 ⎜⎛1 − n⎟⎞ ⎥ ⎜⎛n m⎟⎞ ⎜2 − ⎜⎛n m⎟⎞ ⎟ e e e e e ⎝ ⎠ ⎦⎝ ⎠⎝ ⎝ ⎠⎠ ⎣
(16)
·
m = (me Te,in Pe,in ) (me0 Te,in Pe,in )0
(17)
e
·
n = (ne
Te,in ) (ne
e
Te,in )0
(18)
Like the compressor, volumetric effects for the expander is considered. It is assumed that the volume locates after its corresponding stage and its output mass flow rate equals the input mass flow rate of next stage. For the volume,
Fig. 14. Power of expander in discharging.
(19)
dMvol dt = m in − mout 3.3. Heat exchangers
Counter flow heat exchangers are modelled by employingε -NTU method. Another constraint condition is the pinch temperature difference, which is set as a constant.
qHX = mair (h c/e,out,i - 1 − h c/e,in,i) = m w (h w,out,i − h w,in,i )
(
ε = qHX
qmax =
1 − exp ⎛⎜ (−NTU )· 1 − ⎝ 1−
NTU = Fig. 15. Total power and mass flow rate in discharging.
(mc )min (mc )max
(
(
(mc )min (mc )max
exp (−NTU )· 1 −
(20)
) ⎞⎠
⎟
(mc )min (mc )max
))
KA (mc )min
Tpinch = min(Tc/e,out,i - 1 − Tw,out,i, Tc/e,in,i − Tw,in,i ) ·⎞
c2 = ⎜⎛p − 2q n2 ⎟ c ⎠ ⎝
·
·
·
c3 = −⎜⎛pqn − q2ṅc3⎟⎞ ⎝ c ⎠
·
·
(9)
·
[p (1 − q nc ) + nc (nc − q)2]
qhot,mass = Khot,en Ahot,en (Ten − Thot )
(24)
qcold,mass = K cold,en Acold,en (Ten − Tcold )
(25)
Thermal inertia of heat exchangers: It is assumed that each of the two flows entering the heat exchanger exchanges heat with its own thermal mass (heat capacity [J/K]), which is half of the total thermal mass. The two thermal masses are not interacting, but they have a term representing the heat exchange with environment [23], shown in Fig. 4. The heat exchange between flow and thermal mass is also calculated based on NTU method,
εHX,mass = qHX,mass qmax = 1 − exp(−KHX,mass AHX,mass m fluid ·cp)
(11)
qen,mass = K en,mass Aen,mass (Ten − Tmass )
(12)
we,i = me (h in,e,i − h out,e,i)
(13)
Ahot,en = Acold,en = 0.5Aen,mass = 0.25Aen,HX
Ne
∑ me (hin,e,i − hout,e,i) i=1
(27)
Total heat exchange area with environment of each heat exchanger is set to 66 m2 according to a CAES project of our group in Bijie, China. Aen,mass is assumed to half of the total heat exchange area with environment, Aen,HX .
The isentropic efficiency, power output of one stage, total power output of the expander can be shown as (12)-(14):
ηe,i = (h in,e,i − h out,e,i ) (h in,e,i,s − h out,e,i )
(26)
Heat exchanged with environment for thermal mass:
3.2. Expanders
we =
(23)
(10)
where p = 1.8, q = 1.8, c4 = 0.3 [21].These formulas (4)–(10) were proposed by Na Zhang and Ruixian Cai [22] according to particularity of radial compressors. The compressor characteristics map is shown in Fig. 2. The compressor has a volume and when the operating condition changes the temperature and pressure could be influenced by volumetric effects. It is assumed that the volume locates after its corresponding stage and its output mass flow rate equals the input mass flow rate of next stage. For the volume,
dMvol dt = m in − mout
(22)
Heat exchanged with environment for hot and cold fluids:
·
[p (1 − q nc ) + nc (nc − q)2]
(21)
(28)
3.4. Pipes (14)
Pipes are assumed to have thermal mass (heat capacity), which is calculated by ε -NTU method,
Off-design performance model of the expander is considered 689
400
12
Air mass in storage
380
11
360
Temperature /K
320
9
Temperature
300
8
280
7
Pressure
260
Pressure /MPa
10
340
6
240
5
220 200 0
10
20
30
40
50
60
70
80
90
4 100
3000 2800 2600 2400 2200 2000 1800 1600 1400 1200 1000 800 600 400 200 0
Air mass in storage /kg
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Time /h
400
12
Air mass in storage
380
11
360
Temperature /K
320
9
Temperature
8
300 280
7
Pressure
260
6
240
5
220 200 0
10
20
30
40
50
60
70
80
90
4 100
Pressure /MPa
10
340
3000 2800 2600 2400 2200 2000 1800 1600 1400 1200 1000 800 600 400 200 0
Air mass in storage /kg
(a) Operating method 1
Time /h
(b) Operating method 2 Fig. 16. Variation of parameters in air storage reservoir for multi-cycle.
εpipes,fluid = qpipes,fluid qmax = 1 − exp(−Kpipes,fluid Apipes,fluid m fluid ·cp)
3.6. Mixer for water (29)
m in,i h in,i + m in,j h in,j = (m in,i + m in,j) hout,ij
Heat exchanged with environment for pipes:
qpipes,en = Kpipes,en Apipes,en (Ten − Tpipes)
(30)
(34)
3.7. Throttle valve
hbefore = hafter
(35)
3.5. Compressed air storage 3.8. Cycling performance
Air storage tank is seen as a sphere in this paper.
dmst dt = mst,in − mst,out
(31)
dUst dt = h in − h out + q
(32)
Table 1 shows exergy destruction of each component, in which E = U − U0 − T0 (S − S0) + p0 (V − V0) (state exergy of air storage or water tank, J), and e = h − h 0 − T0 (s − s0) (flow exergy, J/kg). T0 is 25 °C. Exergy destruction rate for each component in charging and discharging process (real time):
(33)
γch = edes wc
Heat exchanged with environment for air storage:
qen,st = K en,st Aen,st (Ten − Tst )
690
(36)
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pressure operation. However, sliding pressure operation would result in a low performance of expanders, which is not considered in this paper. There are 0.88% of the input energy left in hot water after discharging and the loss of air storage contributes to 0.75% of the total energy. They are both low grade thermal energy that could not be recycled easily. Exchanging heat with environment for pipes and the mix of hot water with different temperatures cause losses of energy with 0.14% and 0.05% respectively. The roundtrip efficiency for the system is 71.79%.
Table 4 Simulation results of multi-cycle. (a) Operating method 1
Charging energy (MWhe) Charging time (h) Highest air pressure (MPa) Discharging energy (MWhe) Discharging time (h) Roundtrip efficiency (%) Roundtrip efficiency for per unit mass of air (%)
1st cycle
2nd cycle
3rd cycle
4th cycle
102.77 4 6.65 61.77 3.08 60.1 72.8
104.20 4 7.02 73.90 3.68 70.9 71.8
104.29 4 7.04 74.74 3.72 71.7 71.7
104.29 4 7.04 74.74 3.72 71.7 71.7
1st cycle
2nd cycle
3rd cycle
4th cycle
119.52 4.62 7 72.55 3.61 60.7 72.3
102.40 3.93 7 73.43 3.66 71.7 71.8
102.30 3.93 7 73.43 3.66 71.8 71.8
102.30 3.93 7 73.43 3.66 71.8 71.8
4.1. Exergy analysis for charging process As shown in Fig. 6 and 7, the compressor contributes most to the total exergy destruction in charging process with an average exergy destruction rate of 9.24%. As the compression train operates under the off-design operating condition before the end of charging process and its isentropic efficiency increases during charging process, the exergy destruction decreases with time. During start-up period, the compressor has a relatively higher exergy destruction because of cold start. Heat exchangers contribute the second highest exergy destruction in charging process. The exergy destruction rate is relatively high in first 10 mins because of thermal inertia. After that, the exergy destruction rate remains stable at 4.17%. As for the air storage reservoir, the air in it is gradually compressed and thus its temperature rises. As a result, the heat exchanged with the environment increases and the exergy destruction also goes up. The average exergy destruction rate is 0.75%. The exergy destruction for pipes is caused by the heat exchanged with the environment and its thermal inertia, which accounts for 0.14% of the compression work. The pressure in tank rises during charging process, but the increasing rates for 8 stages are different. This leads to differences of outlet water temperature which can be seen in Fig. 8. The exergy destruction of water tank is caused by mixing water with different temperatures together and the average exergy destruction rate is 0.05%. The average exergy efficiency of charging process is 85.65%. Power and efficiency of compressor in charging process are shown in Fig. 9 and 10. During start-up period according to Eq. (6), air temperature is inversely correlated with air mass flow rate while other parameters remain the same. Thus the air flow rate is relatively high at the beginning (see Fig. 11). The rated power for the first stage is slightly lower than the other 7 stages (see Fig. 9), which is because the inlet air temperature of the first stage is lower than those of the others. During the whole charging period, the pressure ratio, output power and isentropic efficiency of higher compression stages are affected more than the lower stages by the pressure change in air storage reservoir. The evolution of total power can be seen in Fig. 11. At the beginning, it is influenced mainly by the mass flow rate and reaches the lowest point at 4.5 min. After that, the main factor affecting total power is the pressure in air reservoir, and the total power rises with the pressure. The mass flow rate reduces with the pressure ratio, which would lead to the reduction of power. Total power is influenced by above two factors and increases. The difference between the maximum and minimum of total power is 9.91%.
(b) Operating method 2
Charging energy (MWhe) Charging time (h) Highest air pressure (MPa) Discharging energy (MWhe) Discharging time (h) Roundtrip efficiency (%) Roundtrip efficiency for per unit mass of air (%)
γdis = edes ((Est,t − Est,t + 1) + (Etank,t − Etank,t + 1))
(37)
Exergy efficiency in charging (entire charging process): ch,end
ηch = ((Est + Etank )ch,end − (Est + Etank )ch,initial)
∫
wc dt
ch,initial
(38)
Exergy efficiency in discharging (entire discharging process): dis,end
∫
ηdis =
we dt
((Est + Etank )dis,initial − (Est + Etank )dis,end) (39)
dis,initial
Roundtrip efficiency: dis,end
ηround =
∫ dis,initial
ch,end
we dt
∫ ch,initial
wc dt (40)
The losses of motor and generator are not considered in this paper. 4. Results and discussion In this paper, the effects of part-load operation regularities of compressors and expanders, thermal inertia of components, volumetric effects of pipes and heat exchanged with environment are taken into consideration. Some constant parameters are shown in Table 2. Total energy distribution including the exergy destruction distribution can be obtained and shown in Table 3 and Fig. 5. As the compressors usually have lower efficiencies than those of the expanders in real projects, the isentropic efficiencies for compressors and expanders are assumed 0.88 and 0.92 respectively in this paper and thus, exergy destruction of compressors is higher than that of expanders (9.24% vs 6.84%). During the charging process, the variation of air pressure in air tank increases, leading to the changes of air temperature at the outlet of every compressor especially higher pressure stages. This causes an uneven temperature difference for every heat exchanger of compressors during charging process. By contrast, the working condition of discharging process is much more stable (the input pressure of the first stage expander is fixed) because of the throttle, so the temperature difference in the heat exchangers of expanders are almost unchanged except the first heat exchanger. Thus the exergy destruction for heat exchangers of expanders is much lower than that of compressors (2.5% vs 4.17%). The energy loss of throttle accounts for 3.64% of the input power and this can be eliminated by adapting sliding
4.2. Exergy analysis for discharging process Exergy destruction rate for different components in discharging process can be seen in Fig. 12 and 13. The expander contributes most to the total exergy destruction in discharging process with an average exergy destruction rate of 7.84%. Because the temperature in air storage reservoir decreases with time, the air outlet temperature of the exchanger for first expander reduces, which leads to the deviation from the design point and the exergy destruction of expander increases slightly. As for the throttle, because its pressure difference drops with time and finally reaches 0 after the discharging process, the exergy 691
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expanders, thermal inertia of components, volumetric effects of pipes and heat exchange between system and environment in whole energy storage process and start-up procedure have been studied and analyzed. From analysis results, the following conclusions can be drawn:
destruction at initial time is the largest and reduces with time. The average exergy destruction rate is 4.12%. Heat exchangers contribute the third to the total exergy destruction. The exergy destruction rate is relatively high in the first 9 min because of its thermal inertia. After that in the discharging process, there is a slight rise in the exergy destruction with time due to larger heat transfer temperature difference. The average exergy destruction rate is 2.87%. The thermal energy recovered from compression process can not all be transferred to the expansion process due to the temperature difference in heat exchangers, so part of the thermal energy would be taken away by the hot water after the heat exchangers of expanders, leading to an exergy destruction. In the start-up period, there is less exergy destruction for hot water because the thermal mass of heat exchangers could utilize the thermal energy. After this period (9 min), its exergy destruction keeps unchanged and the average exergy destruction rate is 1.01%. The temperature in air storage decreases with its pressure and thus more heat exchanged with the environment with time in the discharging process. This leads to the exergy destruction of the air storage reservoir which rises in discharging. The average exergy destruction rate is 0.74%. The average exergy efficiency of the discharging process is 83.41%. Both inlet air temperature and air mass flow rate can affect the power of expanders. In the start-up period, inlet air temperature has a greater influence on the power and the power for every stage grows gradually (see Fig. 14). Air mass flow rate reduces in this period, shown in Fig. 15. After this period, the power of first stage falls because of the decrease of the inlet temperature (the temperature in air tank drops with time and it leads to the decrease of expander inlet temperature) meanwhile the power of other 7 stages keeps unchanged (see Fig. 14). Total power can also be seen in Fig. 15 that before 9 min the total power has a rising trend and after that it almost keeps stable.
(1) The exergy destructions with time for each component during entire energy storage process were revealed and time reaching steady state can be obtained, e.g., the compressor train takes 4.5 min to reach steady state, and lower air temperature would lead to a higher mass flow rate and more power with a lower charging efficiency in this cold start process. (2) In a complete cycle, compressors contribute most to energy loss at 9.24%, which is followed by expanders at 6.84%. Heat exchangers of compressors cause more energy loss (4.17%) than heat exchangers of expanders (2.5%) due to more stable operation during discharging process. Throttle contributes 3.64% of energy loss which cannot be neglected for constant-pressure operation. Exergy loss of every other component is less than 1%. (3) After three full cycles, CAES system can achieve a stable condition. Because of the influence of initial condition, air flows into the system while charging is more than that flows out of the system while discharging in the first cycle. Thus the efficiency of first cycle is round 10 percent points lower than those of other cycles. But if calculating the roundtrip efficiency for per unit mass of air, the efficiencies of different cycles are almost the same. Acknowledgements The authors would like to thank the following organizations for financial support of the work: National Natural Science Foundation of China (NSFC) under Grant No. 51706222, National Basic Research Program of China (973 Program) under Grant No. 2015CB251302, Transformational Technologies for Clean Energy and Demonstration, Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No. XDA21070200, The Frontier Science Research Project of CAS under Grant No. QYZDB-SSW-JSC023 and the program of China Scholarships Council under Grant No. 201802180087.
4.3. Influence of operation cycle number There are two operating methods simulated in this article. Operating method 1 is that the charging time is fixed to 4 h and the discharging process ends when the air pressure in tank is 4.2 MPa. Operating method 2 is that the charging process ends when the pressure in air tank reaches 7 MPa and discharging process ends when this pressure reaches 4.2 MPa. The settling period after charging is 8 h and every cycle has 24 h for the two methods. The operation results can be seen in Fig. 16 and Table 4. Due to the heat exchanged with environment, the system can be stable after several cycles. It can be seen from Fig. 16 that the performance of the fourth cycle is exactly the same as that of the third, which means that three cycles are enough to make the cycle operation stable. We can see from Table 4 that the roundtrip efficiencies of the first cycle are around 10 percent points lower than those of the second and the third cycles for both two operating methods (e.g., 60.1%, 70.9% and 71.7%). This is because for the first cycle, the initial temperature or pressure is different from the cycles after stable operation and the air flows into the system while charging is more than that flows out of the system while discharging. So the calculated system efficiency of the first cycle would be lower. This influence could be eliminated mostly in the second cycle and completed eliminated in the third cycle. However, if calculating the roundtrip efficiency for per unit mass of air, the first cycle has a slightly higher value than the third (e.g., 72.8% vs. 71.7%) as the pressure in air tank of the first cycle before discharging is a bit lower than that of the third and thus the exergy loss of throttle of the first cycle is lower.
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