Where a licence is displayed above, please note the terms and conditions of the licence govern your use of this document.

Transcription

1 Dynami simulation of Adiabati Compressed Air Energy Storage (A-CAES) plant with integrated thermal storage Link between omponents performane and plant performane Siaovelli, Adriano; Li, Yongliang; Chen, Haisheng; Wu, Yuting; Wang, Jihong; Garvey, Seamus; Ding, Yulong DOI: /j.apenergy Liense: Creative Commons: Attribution-NonCommerial-NoDerivs (CC BY-NC-ND) Doument Version Peer reviewed version Citation for published version (Harvard): Siaovelli, A, Li, Y, Chen, H, Wu, Y, Wang, J, Garvey, S & Ding, Y 017, 'Dynami simulation of Adiabati Compressed Air Energy Storage (A-CAES) plant with integrated thermal storage Link between omponents performane and plant performane' Applied Energy, vol. 185, no. Part 1, pp DOI: /j.apenergy Link to publiation on Researh at Birmingham portal General rights Unless a liene is speified above, all rights (inluding opyright and moral rights) in this doument are retained by the authors and/or the opyright holders. The express permission of the opyright holder must be obtained for any use of this material other than for purposes permitted by law. Users may freely distribute the URL that is used to identify this publiation. Users may download and/or print one opy of the publiation from the University of Birmingham researh portal for the purpose of private study or non-ommerial researh. User may use extrats from the doument in line with the onept of fair dealing under the Copyright, Designs and Patents At 1988 (?) Users may not further distribute the material nor use it for the purposes of ommerial gain. Where a liene is displayed above, please note the terms and onditions of the liene govern your use of this doument. When iting, please referene the published version. Take down poliy While the University of Birmingham exerises are and attention in making items available there are rare oasions when an item has been uploaded in error or has been deemed to be ommerially or otherwise sensitive. If you believe that this is the ase for this doument, please ontat UBIRA@lists.bham.a.uk providing details and we will remove aess to the work immediately and investigate. Download date: 13. De. 018

2 Dynami simulation of Adiabati Compressed Air Energy Storage (A-CAES) plant with integrated thermal storage link between omponents performane and plant performane Adriano Siaovelli *a, Yongliang Li a, Haisheng Chen b, Yuting Wu, Jihong Wang d, Seamus Garvey e, Yulong Ding a a Birmingham Centre for Energy Storage, Shool of Chemial Engineering, University of Birmingham, Birmingham, B15 TT, UK b Institute of Engineering Thermophysis, Chinese Aademy of Sienes, Beijing, , China Key Laboratory of Enhaned Heat Transfer and Energy Conservation, Beijing University of Tehnology, Beijing, China d Shool of Engineering, University of Warwik, UK e Faulty of Mehanial Engineering, University of Nottingham, Nottingham NG7 RD, United Kingdom * Corresponding author. a.siaovelli@bham.a.uk; Tel. +44 (0) ; Abstrat The transition from fossil fuels to green renewable resoures presents a key hallenge: most renewables are intermittent and unpreditable in their nature. Energy storage has the potential to meet this hallenge and enables large sale implementation of renewables. In this paper we investigated the dynami performane of a speifi Adiabati Compressed Air Energy Storage (A-CAES) plant with paked bed thermal energy storage (TES). We developed for the first time a plant model that blends together algebrai and differential sub-models detailing the transient features of the thermal storage, the avern, and the ompression/expansion stages. The model allows us to link the performane of the omponents, in partiular those of the thermal storage system, with the performane of the whole A-CAES plant. Our results indiate that an A-CAES effiieny in the range 60-70% is ahievable when the TES system operates with a storage effiieny above 90%. Moreover, we show how the TES dynami behaviour indues off-design onditions in the other omponents of the A-CAES plant. Suh devie-to-plant link of performane is ruial: only through integration of TES model in the whole A- CAES model is possible to assess the benefits and added value of thermal energy storage. To the authors knowledge the present study is the first of this kind for an A-CAES plant. Nomenlature A Area (m ) C Heat apaity rate (J s -1 K -1 ) D,d Diameter (m) p Speifi heat (J kg -1 K -1 ) Ex in Exergy flux (W K -1 ) Redued flow rate (-) G h Speifi enthalpy (J kg -1 ) h v Volumetri heat transfer oeffiient (W m -3 K -1 ) H Height (m) k Speifi heat ratio (-) k a, k s Thermal ondutivity (W m -1 K -1 ) Mass flow rate (kg s -1 ) m Mass (kg) Redued speed (-) p Pressure (Pa) T Temperature (K) U Overall heat transfer oeffiient (W m - K -1 ) u Veloity (m s -1 ) W Power (W) m n Greek letters α Influene fator (-) β Compression ratio (-) ε Effetiveness, void fration (-) η Isoentropi effiieny (-)

3 η yle Round trip effiieny (-) η th Thermal storage effiieny (-) π Expansion ratio (-) ρ Density (kg m -3 ) Φ Heat transfer rate (W) Introdution In 013 the eletriity prodution has reahed TWh/year of whih oil, natural gas, and other fossil fuels aount for 68% while renewable soures ontribute for less than 6% [1]. Overome this energy senario is imperative as CO emissions and global warming are already taking their toll on our soiety and planet Earth []. To ontain global warming below C arbon dioxide emission must derease by 90% by 050 through an intense penetration of renewable resoures whih ould reah a global share of 65% aording to senarios foreasted by IEA [3]. This great potential an be untapped only if the intrinsi variability of renewables, suh wind and solar energy, is mitigated through energy storage (ES). ES tehnology provides several funtions to failitate the use of renewables: it enables to apture wrong time energy and make it available when needed, it helps to shave and shift load peaks, and it improves reliability of energy systems [4,5]. Alongside with pumped hydroeletriity storage, ompressed air energy storage (CAES) is among the few grid-sale energy storage tehnology with power rating of 100s MW [6,7]. CAES operates in suh a way that eletrial energy is stored in the form of ompressed air onfined in a natural or artifiial reservoir. Then, during periods of high energy demand, stored energy is retrieved by withdrawing high pressure air and expand it through a series of turbines to generate eletriity. Traditionally, for example in the Huntorf plant [7,8], before expansion air is heated in a ombustion hamber burning onventional fossil fuels. This leads to two drawbaks: CAES is not CO free and round trip effiieny is limited to 40-50% [6,7]. To overome suh disadvantages adiabati ompressed air energy storage (A-CAES) has been proposed. Instead of burning fuel, in A-CAES the heat generated by ompression is stored in a Thermal Energy Storage (TES) and then used to heat air from the reservoir before it enters the turbines [7,9]. As a result, round trip effiieny inreases to 70-75% aording to [7,10,11] and fuel onsumption is avoided. The vast majority of the studies on A-CAES onsider indiret heat exhangers (HEXs) and a separate thermo-fluid to store the heat of ompression [9,11-18]. The heat of ompression, exhanged via air-to-fluid HEXs, inreases the internal energy of the working fluid whih ats as a sensible heat storage medium. Commonly, HEXs have been onsidered installed between eah ompression stage, to store heat, and between eah expansion stage to retrieve heat during disharge fo ACAES plant [11-18]. Another proposed A-CAES onfiguration uses a solid medium, typially natural roks, to store the heat of ompression [7,19]: during A-CAES harging heat is stored by flowing hot air from ompressors through a paked bed of roks; when disharge ours air from the avern flows through the paked bed retrieving the heat previously stored and then expands through turbines train to generate eletriity. Literature presents multiple studies on paked beds dealing with the design [0-4], the heat transfer performane [5-30], and the effet of operating onditions [31-34]. However, the dynami performane of A-CAES plant with an integrated paked bed thermal storage remain unaddressed. With this study we fill suh a gap in the literature by presenting for the first time a full investigation of an A-CAES plant with paked bed thermal storage. The mathematial model we developed is fully dynami and it inludes off-design performane of eah omponent of the A-CAES plant. The model blends together algebrai and differential sub-models that detail the transient features of the thermal storage, the avern, and the ompression/expansion stages. This allows to link the performane of the omponents, in partiular those of the thermal storage system, with the performane of the

4 whole A-CAES plant. Suh devie-to-plant link is ruial: only through integration of TES in the whole A- CAES system is possible to assess the benefit and added value of thermal energy storage. To the authors knowledge the present study is the first of this kind for an A-CAES plant. System desription Figure 1 presents the speifi adiabati ompressed air energy storage system (A-CAES) studied in this work. Table 1 summarizes the major features of the A-CAES plant. A paked bed thermal energy storage (TES) ensures the adiabati onditions: after the HPC ompression stage, hot air flows through the paked bed and exhanges heat with the gravel ontained in the TES. The gravel ats as sensible storage material and aptures heat for later purposes. Air leaves the TES system nearly at ambient temperature and enters the avern at high pressure. It is worth noting that we foused on a speifi A-CAES onfiguration. A Similar plant onfiguration is also onsidered by RWE Power in the EU projet ADELE [35] and by Airlight Energy [36] although other A-CAES designs are also possible [6,11,14,17,18]. An inter-refrigeration heat exhanger ools the air flow before it enters the high pressure stage. This onfiguration was also onsidered in [7] to prevent exessively high air temperature at the outlet of HPC. The ompressors operate over a range of ompression ratios sine air pressure in the aver spans the range 46 to 7 bar, whih is the typial range adopted for the Huntorf plant and Mahintosh plant [7,8]. The avern s size onsidered is a typial one for natural salt averns [6,7]. During the disharge proess, energy is retrieved by withdrawing air from the avern at high pressure and expand it through the train of turbines. Two disharge modes have been onsidered in the literature: variable inlet pressure and onstant inlet pressure [7,37]. In the former one high pressure air from the avern diretly expands through the turbines whih therefore experiene a variable (in time) expansion ratio. We onsidered onstant inlet pressure mode: as depited in Fig. 1, a throttling system maintains the turbine inlet pressure onstant. Suh an operating mode allows to operate the turbine train at onstant expansion ratio and near to design onditions thus at maximum effiieny for the entire disharge proess. Design expansion ratio (Table 1) for HPT and LPT were hosen as the one for existing CAES plants [8]. Tables and 3 present the thermodynami state points for ompression and expansion under design onditions. The thermodynami properties were evaluated with EES (Engineering equation solver) using the data in Table 1 as input parameter. For the design onditions reported in Tables and 3 we onsidered the same temperature for the air temperature at ompressor outlet (point 1) and the air temperature at the outlet of TES (point 4). Clearly, a temperature drop is expeted under operation (that is T 1 > T 4) beause of finite heat transfer between air and the filling material of the TES. As illustrated in the Results setion T 1 and T 4 differs minimally whih support the assumption, for design alulations, of T 1 = T 4. For the purpose of simulation of A-CAES plant operation we onsidered n equal yles of 10 hours harge, 4 hours disharge and 10 hours idle, as shown in Figure. Suh a figure present the nominal yle with onstant power input during harge and onstant power output during disharge. The atual profile of eah yle was determined through the simulations performed, as detailed in the Results setion. The nominal profile of Fig. was hosen onsidering the A-CAES plant operating for peak shaving, minute reserve, or ompensation of flutuation in wind power. Suh operation modes are typial of existing CAES plants [7,8], and present disharge time of 3-4 hours, as in the ase of Fig.. The total number n of yles onsidered in the study was 30.

5 MW M LPC HPC HPT LPT 0 MW Air flow Air avern Air flow Figure 1: Adiabati ompressed air energy storage (A-CAES) plant with sensible thermal energy storage Figure : Charge and disharge yle. Table 1. Major parameters of A-CAES system Quantity Value Ambient temperature K Ambient pressure bar Expansion train rated power 0 MW HP turbine design inlet temperature K HP turbine design inlet pressure 46 bar HP turbine design expansion ratio 4.18 LP turbine design inlet temperature K LP turbine design inlet pressure 11 bar LP turbine design expansion ratio 11 Turbines design effiieny 88% Compression train rated power 100 MW

6 State HP ompressor design inlet temperature K HP ompressor design ompression ratio 8.4 LP ompressor design ompression ratio 8.4 Cavern volume m 3 Cavern min/max pressure 46/7 bar Cavern wall heat transfer oeffiient [43] m m 0. 8 Temperature [ C] 0 in iout Table. Thermodynami states for the harging proess Pressure Enthalpy [bar] [kj/kg] Entropy [kj/(kg*k)] State Table 3. Thermodynami states for disharging proess Pressure Enthalpy [bar] [kj/kg] Temperature [ C] Entropy [kj/(kg*k)] Mathematial modelling of A-CAES plant and validation Mass flow rate [kg/s] Mass flow rate [kg/s] This setion presents the mathematial models for eah omponent of the A-CAES plant depited in Fig. 1. Eah model is first presented separately along with the underlying assumption adopted in the study. The setion ends with the desription of the solution strategy used to link eah sub-model to simulate the whole A-CAES plant. Where not stated expliitly the modelling was performed in Matlab/Simulink 014 [38]. Compressors Modelling of low pressure ompressor (LPC) and high pressure ompressor (HPC) involves mass and energy balane in order to ompute temperature of air exiting eah stage and the ompression work. Isoentropi air outlet temperature was omputed as: is, out, in k 1 i k T T (1) where β i = β HPC, β LPC is the ompression ratio of eah stage. Atual outlet temperature T,out was obtained using ompressor isoentropi effiieny defined as: is T, out T, in () T T, out, in The power of ompressors onsumed during harge was evaluate by an energy balane at eah ompressor negleting variations in inlet to outlet kineti energy of air:

7 h h W m, out, in (3) In this work we onsidered off-design performane of ompressors during the operation of the A-CAES plant. Off-design are ommonly inluded in models of energy systems, however CAES systems are often studied onsidering only design onditions [9,11,18]. Suh an approah may neglet important dynami effets when ompression train model is inluded in the whole A-CAES plant model, as we will show in the Results setion. We inluded off-design alulations through ompressors harateristi maps [39] that quantify ompression ratios β i and isoentropi effiieny η i as funtion of dimensionless flow rate. The harateristi maps were approximated aording to [40], namely: G G 3 (4) i n n G n G (5) where 4 G and n are the redued flow rate and the redued speed, respetively. Figure 3 presents the harateristi maps for the ompressors. The definitions for redued quantities and oeffiients of Eqs. 4 and 5 are the following ones: G n m T, in P, in m T, in P, in n T, in n T, in 0 0 (6) n 1 3 m p mn p1 n n m m p 1 n n 3 m pmn m n p 1 n n m n n m n Subsript 0 in previous equations denotes design onditions while p = 1.8, m = 1.4 and 4 = 0.3 [40]. (7) Figure 3: Charateristi maps for the ompressors. a) Compression ratio vs. redued flow rate; b) Isoentropi effiieny vs. redued flow rate. Turbines

8 HP and LP turbine were modelled through mass and energy balane following the same approah adopted for the ompressors. Defined the expansion ratio as p p, the temperature of air exiting eah turbine stage was obtained from the isoentropi temperature and the definition of isoentropi effiieny: is, out t, in k 1 i k t in T t T (8) out T t, intt, out t (9) T T t, in is t, out where π i = π HPT, π LPT. Finally, the power output was alulated as W t mt ht, out ht, in (10) An improved Flugel formula [40] was used to desribe the off-design performane of turbines: 159 m m T t t0, in t t0 Tt, in t (11) 160 t t 0 1 t1 n n G n G t t t t t (1) The definition for redued flow and redued speed for turbines are: G t t n m t Tt, in Pt, in m t Tt, in Pt, in n t Tt, in n t Tt, in 0 0 Fig. 4 illustrates the harateristi maps desribed by Eqs. (11) and (1). (13) Figure 4: Charateristi maps for the turbines. a) Expansion ratio vs. redued flow rate; b) Isoentropi effiieny vs. redued flow rate. Heat exhanger The inter-refrigeration heat exhanger between LPC and HPC was modelled using energy balane equation and ε-ntu method [41]; onsidering a ounter flow onfiguration the effetiveness was alulated as:

9 exp NTU 1 exp NTU 1 where (14) NTU UA C min (15) Cmin Cmax During the harging proess effetiveness (14) was evaluated at eah instant of time and the atual heat transfer rate was omputed as: HEX C min Tin, h Tin, (16) From heat transfer rate Φ HEX the air outlet temperature (i.e. the HPC inlet temperature) was obtained through the energy balane equation for the heat exhanger. Compressed air reservoir We employed a dynami model to simulate the transient behaviour of temperature of air within the avern. The model onsists of two ordinary differential equations that stem from energy balane and mass balane equations for the air in the avern [4]: dt dt r dm dt r 1 m r in 1 h waw Tw Tr 1 m intin m outtr (17) k p, a m m (18) out In equation (17) the first term on the right hand side aounts for energy transfer due to injetion/withdraw of air from the avern under the assumption that air leaves the avern at the avern s air temperature. The seond term quantifies the heat transfer between air and avern s walls. Heat transfer oeffiient h w was evaluated as indiated in [43]. Finally, pressure p within the ompressed air reservoir was omputed with ideal gas law p RT. The model of the avern was validated against the data gathered by Crotogino et at [8] from the operation of the Huntorf plant. Figure 5 ompares the experimental data and the numerial preditions for avern s temperature and pressure. The experimental data were reorder during a trial avern disharge of 16 hours. As detailed in [8] the withdrawal rate was 417 kg/s for about 4 hours and then gradually dereased to 150 kg/s at the end of the test. The numerial results math the experimental data for the whole proess and orretly predits the initial derease of temperature due to high withdrawal rate and the final temperature inrease aused by heat transfer with the avern s walls.

10 Figure 5: Validation of avern model; numerial preditions against experimental data from Crotogino F. et al. [8]. Paked bed thermal energy storage We adopted a non-equilibrium model to study heat transfer within the paked bed thermal energy storage (TES). Suh an approah has been suessfully employed in the literature by various authors [,3,8,34] and it onsists in a set of two energy balane equations, the first one for the air (subsript a) in the TES while the seond one for the solid filler material (subsript s): Ta Ta Ta p, a ap, aua ka h T v a s w a 0 T T U T a (19) t x x T T s p, s s v s a (0) t x s s 1 k h T T In Eqs. 19 and 0 we assumed as ommonly done in the literature [,3,8,34] one dimensional heat transfer along the paked bed length x. Void fration ε of the bed was evaluated as funtion of the ratio partile diameter d p to paked bed diameter D [34]: d p d p D (1) D Air veloity u a was evaluated at eah instant of time starting from ompressor mass flow rate, during harge, and turbine mass flow rate during disharge. Uniform veloity throughout the TES transversal ross setion was onsidered. The thermal ondutivity k s of the bed was evaluated by means of the Zehner-Bauer Shlunder model [44]. The seond term on the right hand side of Eq. (0) aounts for the heat transfer between the air and the solid partiles in the thermal storage system. The volumetri heat transfer oeffiient h v was omputed using the Coutier s orrelation [5,34]: G hv () d p

11 where G is the mass flux (kg s -1 m - ) flowing through the paked bed thermal storage system. The last term on the right hand side of Eq. (0) quantifies the heat loss toward the ambient at temperature T 0. We attributed the heat loss entirely to the fluid phase (Eq. 0) sine separate orrelations are not available in the literature and experiment annot distinguish properly between phases [34]. Heat transfer oeffiient U w was determined onsidering heat transfer through a multi-layer ylindrial wall [41]. Table 4 summarizes the major parameters of the TES system. The diameter D and height H of the TES system were obtained through a preliminary design on the basis of data in Tables 1 and together with harge/disharge yle of Fig.. Suh data allows to estimate heat to be stored and thus the geometrial dimensions of the TES system. Suh dimensions are in line with those reported in [19, 45], although other arrangements, suh as multiple TES in parallel/series ould be also onsidered. Table 4. Input parameters for TES model Property Formulation ρ s (kg/m 3 ) 911 [] p,s (J/kg K) AB CT B T [47] k s (W/m K) Zehner-Bauer Shlunder model [44] d p (m) 0.0 [34] H (m) D (m) 0 To validate the model the numerial preditions were ompared with experimental results obtained by Meier et al. [6]. The researhers studied a lab sale paked bed thermal energy storage and reorded temperature along the paked bed during harge. The major parameters of the experimental set up onsidered by Meier et al. are available in [6,34]. Our paked bed model, omprising Eqs. 19-, was run in standalone mode using mass flow rate and thermos-physial properties available in [6,34] as input parameters. Clearly, in our validation study we adopted the same paked bed diameter D and length L onsidered by Meier et al [6]. Figure 6 ompares the temperature profile along the TES predited by our model and the experimental data from [6] at different instants of time. The omparison demonstrates that the model is apable of prediting both temperature and position of the thermal front with good auray. Disrepany between experiments and simulation an be attributed to the small ratio D 7. 5 onsidered in [6]: when partile diameter d p is d p relatively large ompared to paked bed diameter D a non-negligible fration of the air mass flow rate passes near the walls of the paked bed, thus it does not ontribute to heat transfer with the filling material. Therefore, the auray of the model, whih is already satisfatory for a small lab sale devie, will further improve when a full sale system is onsidered.

12 solid lines: numerial markers: experimental Temperature [ C] Figure 6: Validation of paked bed model; Numerial preditions against experimental data from Meier et al. [6]. Performane indiators The round trip effiieny and the thermal storage effiieny were used to assess the performane of the whole A-CAES plant and the thermal energy storage system. The round trip effiieny for eah harge/disharge yle was alulated as: t d E Wtdt out 0 yle (3) E t in W dt 0 The time integration is performed over eah harging period ( t ) and disharging period ( t d). The performane of the TES system was assessed through the thermal storage effiieny defined as follows: t 0 d m t h4 h0 dt th (4) t m h h dt Where h 4 is the speifi enthalpy of air at the outlet of the TES system during disharging while h 1 is the speifi enthalpy of air the inlet of TES system during harging. A-CAES plant simulations height [m] The previous equations were implemented in Matlab/Simulink to simulate the entire A-CAES plant. The blok diagram of Fig. 7 shows how the sub-systems interat during alulation for harging and disharging proesses. The equations were solved using 4 th order Runge Kutta method with variable time step. Two distint sub-sets of equations were solved depending if the plant operates in harge or disharge mode. The interations between the omponents of the plant lead to two sub-sets of oupled equations, as larified by the proess flow indiated by the arrows in Fig. 7. The arrows in the figure indiates whih omponents (bloks), and therefore the orresponding equations, involved during simulation of harge and disharge proesses. Separate bloks exhanging information (mass flow rate, pressure and temperature) at eah instant of time were implemented in Simulink.

13 Figure 7: Blok diagram for the whole A-CAES plant model. 4 Results and Disussion The simulations provide results for eah omponent depited in Fig. 1 for 30 onseutive harge/disharge yles. A subset of these results are shown in Fig. 8 to larify the plant operation; detailed results for eah omponent of the plant are presented in the following subsetions. Fig. 8a plots the power input/output for the A-CAES plant. Both ompression train and expansion train operate around the orresponding rated power (100 MW/0MW); the variations in ompression power and expansion power during harge stage and disharge stage are due to off-design operating onditions whih will be detailed in setions 4. and 4.3. Fig. 8b shows the state of harge for the thermal store and the ompressed air reservoir. The stored thermal energy and the air pressure show a similar time pattern, sine both follow harge/disharge yles; 940 MWh th are stored in the TES on average (see Table 5) while TES effiieny, as defined by Eq. (4), is 93%. Cavern pressure spans the range bar. Pressure variation ours also during idle stage: after eah disharge proess avern pressure inreases from ~ 48 bar to about 50 bar due to heat transfer from avern walls to ompressed air, the latter being relatively old beause of the withdraw proess during disharge. A similar effet was also pointed out in [46]. During idle after eah harge, the pressure in the avern slightly drops before the next disharge. In this ase heat flows from the ompressed air to the avern wall ooling the mass of air in the avern and thus leading to a redution of pressure. Figure 9 displays the round trip effiieny and thermal storage effiieny over 30 yles. Both effiienies reah a stable value after an initial inrease during the first operating yles. The key quantity here is the effiieny of the thermal storage system: as soon as TES starts to operate in an effetive way the overall performane signifiantly improves, whih shows how relevant is to integrate arefully the thermal storage with the remaining part of the system. Maximum TES effiieny ours when stati yling operating onditions are established in the thermal storage as explained in the next setion. Clearly, the predited value for of roundtrip effiieny are affeted by the value of parameters used in the model. We adopted, whenever possible, values ommonly used in the CAES literature and that led to aurate results when ompared with experimental data. We estimated, by varying turbine isoentropi effiieny between 0.8 and 0.88, that hanges in roundtrip effiieny stays within ±10%.

14 Figure 8: A-CAES plant performane between 5 th and 10 th operation yle. a) Compression train power during reservoir harge and turbine power output during disharge. b) Thermal energy stored in the sensible TES (left axis) and reservoir pressure variation (right axis) due to injetion/withdraw of ompressed air Figure 9: Effiieny of A-CAES plant. a) Round trip effiieny aording to Eq. (3); b) Effiieny of the thermal energy storage system (Eq. 4). 4.1 Thermal energy storage (TES) system Table 5. A-CAES performane for full load harging/disharging Quantity Value Number of yles (-) 30 Round trip effiieny η yle (-) 74%* Total output energy (MWh e) 100 Charge time (h) 9.1* Disharge time (h) 3.3* Thermal energy stored (MWh th) 940* Thermal energy storage effiieny η th (-) 93%* * Averaged value over 30 yles Figure 10 presents the temperature profile within the TES system and shows how the temperature profile varies from yle to yle. Figure 10a shows temperature after harge (t = 16h within eah yle). Two key features

15 should be notied: the position of the thermal front and how the temperature evolves, after a suffiient number of yles, toward a yling stationary profile. After yle 1 the temperature shows a thermal front around x = 11 m that extends for about 10% of the TES length. The ideal operation of the TES system, as illustrated in [8,31], would preserve the thermal front as sharp as possible from yle to yle, while eah harge/disharge would onsist in suh sharp front travelling bak and forth from x = 0 to x = H. Thermal degradation of the front [8] prevents a pratial implementation of the ideal TES operation, in fat after 5 yles thermal front broadens up to 50% of TES length. Therefore, the thermal store atually operates very similarly to a regenerator: air is gradually ooled during harge, while it is gradually heated from TES inlet to TES outlet during disharge. Suh an operation mode leads to stationary yling operating onditions, where two stationary temperature profiles our after harge and disharge (see yle 30 in Fig. 10). Stationary profile slightly dereases from x = 0 m to x = 10 m due to inrease in air outlet temperature from HP ompressor during harge. During disharge, air withdrawn from the avern is slightly above ambient temperature; this auses the hump at x = 15 m illustrated in Fig. 10b Figure 10: Temperature profile along the length of the thermal energy storage (TES) system. a) Temperature profiles after harging; b) Temperature profiles after disharge. Cyling operating onditions establish after 0 yles of harging/disharging. The time evolution of air at the outlet of TES system orresponding T 4 in Fig. 1 is presented in Fig 11. The outlet temperature stays within a range of 0 C for about 67% of the disharge time; suh an operating ondition orresponds to the time neessary for the flat portion of the TES temperature profile (x < 10 m in Fig. 10a) to leave the thermal store during disharge. During the last stage of disharge the outlet temperature drops of about 15%, as the degraded thermal front exits the thermal store. A more marked drop ours during the first yles beause stationary temperature profile is not established yet in the TES system. Air outlet temperature from the paked bed storage oinides with the HP turbine inlet temperature; thus, any variation of T 4 from design point detriments the performane and effiieny of the expansion train, as explained in Set These results presented here an help CAES operators to oneive optimal operating strategy to redue suh undesired off-design onditions.

16 yle 5 yle 15 yle 30 T outlet TES [ C] Figure 11: Temperature profile along the length of the thermal energy storage (TES) system. a) profiles after harging; b) profiles after disharge. Cyling operating onditions establish after 0 yles of harging/disharging. 4. Compression train Disharge time [h] The performane of low pressure ompressor (LPC) and high pressure ompressor (HPC) signifiantly depart from nominal ondition, as both ompressors operate off-design during harging. In fat, the pressure of air in the avern onstantly inreases during harge, ausing an inrease also in the total pressure ratio experiened by the ompressor train. As a onsequene, ompressors operating point moves along harateristi urve (Fig. 3) from low to high pressure ratio. Figure 1 luidly summarizes how the ompression train operates during harge. At the beginning of harging the LPC performs the majority of the ompression work as LP ompression ratio is ~ 16% larger than the HP one. As pressure in the avern rises, both β LPC and β HPC inrement up to the orresponding design values, whih is ahieved only at the end of harge. As harging starts β LPC = 7.6 and β LPC = 6.5, thus LPC ompression ratio and HPC ompression ratio are respetively 10% and % lower that the design value. As a result, the minimum isoentropi effiieny of ompressors ours at the begin of eah harge as shown in Fig. 1a. Figure 1b shows that at the end of harging the HP ompressor outlet temperature is 660 C while from Fig 11 we found at the beginning of disharge air leaves the TES systems at 656 C. Suh a differene between the two temperatures is due to finite heat transfer between the air stream and the roks within the TES. However, the differene is very limited due to the good thermal ontat (large heat transfer area) between air and TES filling material. The ompression power shows a maximum around t = h whih an be explained from the behaviour of mass flow rate (Fig. 13) and ompression ratios (Fig. 1b). The ombination of dereasing trend for m with an inreasing trend for β LPC, β HPC brings a maximum in ompression power W (Eq. 3). The mass flow rate monotonially dereases during harge beause the operating point of ompressors (Fig. 3) shifts from low ompression ratios, so high mass flow rate G, to high ompression ratio and lower mass flow rate. On the other hand, the ompression ratio monotonially inreases during harge as avern pressure rises. 359

17 Figure 1: Compression train performane during harge. a) Compression power and isoentropi effiieny of high pressure and low pressure ompressors. b) Compression ratio and air outlet temperature for high and low pressure ompressors. Compressor train operates under off-design onditions exept at the end of the harging proess. 150 Compressor air mass flow rate [kg/s] Figure 13: Compressor air mass flow rate during harge. During harge ompression ration inreases (Fig. 1b) onsequently mass flow rate diminishes as ompressor operation point moves along the harateristi urve (Fig. 3). 4.3 Expansion train Charge time [h] The expansion train operates under onstant expansion ratio due to the throttling valve (Fig. 1) but with variable inlet temperature of air oming from the thermal energy storage system (Fig. 11). As a results departure from design ondition are limited in omparison with the ompression train, as illustrated in Fig. 14. Both high pressure turbine (HPT) and low pressure turbine (LPT) perform at design isoentropi effiieny for the entire disharge proess. The power output drops of about 5% during disharge due to a ombined effets of derease in inlet temperature (Fig. 11) and variation of the turbine mass flow rate (Fig. 15). Although the turbine mass flow rate inreases, as depited in Fig. 15a, the drop in inlet temperature (Fig 11) dominates the behaviour of turbine power, resulting in a redution of power output from the A-CAES plant. This shows how important is to oneive and operate the thermal storage system in an optimal way, sine TES performane reverberate onto the global performane of the plant. Variations of the turbine mass flow rate are also aused

18 by redution of air inlet temperature: aording to the Flügel formula (Eq. 11) at onstant expansion ratio we have m 1 t T inlet. Finally, the derease of the air outlet temperature from HPT and LPT shown in Fig. 15b stems diretly from the redution in the inlet temperature Figure 14: Expansion train performane during disharge. a) Turbine power and isoentropi effiieny of high pressure and low pressure turbine. b) Expansion ratio and air outlet temperature for high and low pressure turbine. Expansion train operates near design onditions for most of disharge proess beause of onstant inlet pressure Figure 15: Variation of turbine operation over harge/disharge yles. a) Turbine mass flow rate b) Air outlet temperature from low pressure and high pressure turbine. Variation of turbine inlet temperature (Fig. 11) leads to inrease of flow rate due off-design onditions. 4.4 Partial load operation The operation of CAES systems for peak shaving, minute reserve, or ompensation of flutuation in wind power likely involves partial load operation during disharging [37]. The model we developed allows us to study A-CAES performane for partial load operating yle. We onsidered the yle of Fig. 16 to show how partial load onditions may detriment A-CAES performane. In the view of peak shaving operation we onsidered a disharge yle that last four hours (as in ase of Fig. ) but at three different loads. This mimis operating ondition that may realistially ours, as presented in [8,43]. The power output is ontrolled by

19 adjusting the inlet pressure for HP turbine by throttling air flow from the avern. Table 6 summarizes the results for this operation mode. Figure 17 shows the performane indiators for A-CAES plant and TES system. Round trip effiieny detriments due to smaller power output while TES is marginally affeted by partial-load operation whih auses variation of air flow through the TES as detailed below. As the inlet pressure varies with the load, HP and LP expansion ratios adjust aordingly (Fig 18). Maximum relative variation of π HPT is nearly 40% whih auses non-negligible hanges in the orresponding isoentropi effiieny. The outlet temperature from the turbine stages (Fig. 18a) varies following the hanges in the expansion ratios. The outlet temperature drops toward the end of disharging yle sine the temperature of air from TES redues, as previously illustrated for Fig. 11. Cyle-to-yle variations an be seen in Fig. 19, as stationary temperature profile establishes within the thermal energy storage system Charging Disharging Idle Power [MW] time [h] Figure 16: Charge and disharge yle partial load ase Figure 17: Effiieny of A-CAES plant under partial load operation. a) Round trip effiieny aording to Eq. (3); b) Effiieny of the thermal energy storage system (Eq. 4).

20 Figure 18: Expansion train performane during partial load disharge. a) Turbine power and isoentropi effiieny of high pressure and low pressure turbine. b) Expansion ratio and air outlet temperature for high and low pressure turbine Figure 19: Variation of turbine operation over harge/disharge yles at partial load. a) Turbine mass flow rate b) Air outlet temperature from low pressure and high pressure turbine. 5 Conlusions Table 6. A-CAES performane for partial load operation Quantity Value Number of yles (-) 30 Round trip effiieny η yle (-) 64%* Total output energy (MWh e) Charge time (h) 8.5* Disharge time (h) 3.8* Thermal energy stored (MWh th) 860* Thermal energy storage effiieny η th (-) 96%* * Averaged value over 30 yles In this paper we developed for the first time a fully dynami and off-design performane model of an A-CAES plant with a paked bed thermal energy storage (TES) system. This was possible by integrating together

21 algebrai and differential sub-models that detail the transient features of the thermal storage, the avern, and the ompression/expansion stages, whih is a novelty proposed in this work. Both design and off-design harging/disharging yles were studied for the speifi A-CAES plant onsidered. The results indiate that under nominal harging/disharging a round trip effiieny exeeding 70% an be ahieved when TES effiieny rises above 90%. The link between devie performane with plant performane was eluidated. In fat we an onlude that: i) maximum round trip effiieny ours when yling stationary temperature profiles establishes in the paked bed TES; ii) A-CAES performane detriments toward the end of eah disharging yle due to degradation of the thermal front within the thermal store; iii) redution of air outlet temperature from TES system auses the turbine to operate in off-design onditions leading to an inrease of flow rate; iv) the ompressors operate under strong off-design onditions whih also affet temperature profile in thermal storage system. In summary, we showed that the linking devie dynami performane with system performane is a neessity, sine modern energy storage systems present a strong tendeny toward transient operation. We ahieved suh a goal, for the first time for A-CAES, with the work presented in this paper. Aknowledgments The authors would like to thank the researh grant support from Engineering and Physial Sienes Researh Counil, UK - Next Generation Grid Sale Thermal Energy Storage Tehnologies (NexGen-TEST) (EP/L01411/1) Referenes [1] 015 key world energy statistis. IEA - International Energy Ageny. [aessed ] [] IPCC, 014: Climate Change 014: Synthesis Report. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Core Writing Team, R.K. Pahauri and L.A. Meyer (eds.)]. IPCC, Geneva, Switzerland, 151 pp. [3] Energy Tehnology Perspetive 014 Harnessing Eletriity s Potential. IEA - International Energy Ageny. [aessed ]. [4] Xing Luo, Jihong Wang, Mark Dooner, Jonathan Clarke. Overview of urrent development in eletrial energy storage tehnologies and the appliation potential in power system operation. Applied Energy 015; 137: [5] Haisheng Chen, Thang Ngo Cong, Wei Yang, Chunqing Tan, Yongliang Li, Yulong Ding. Progress in eletrial energy storage system: A ritial review. Progress in Natural Siene 009; 19:91 31 [6] Budt M, Wolf D, Span R, Yan J. A review on ompressed air energy storage: Basi priniples, past milestones and reent developments. Applied Energy 016; 170: [7] Barnes F.S., Levine J.G. Large energy storage system handbook. (011) CRC Press Tylor & Franis Group. Boa Raton FL. [8] Crotogino F, Mohmeyer K-U, Sharf R. Huntorf CAES: more than 0 Years of Suessful Operation. In: Proeedings of SMRI Spring Meeting, Orlando, Florida, USA; April 001. [9] Niklas Hartmann, O. Vöhringer, C. Kruk, L. Eltrop. Simulation and analysis of different adiabati Compressed Air Energy Storage plant onfigurations. Applied Energy 01; 93: [10] Ibrahim H, Ilina A, Perron J. Energy storage systems harateristis and omparisons. Renew Sust Energ Rev 008; 1: [11] Grazzini G., Milazzo A. A Thermodynami Analysis of Multistage Adiabati CAES. Vol. 100, No., February 01 Proeedings of the IEEE. [1] Grazzini G., Milazzo A. Thermodynami analysis of CAES/TES systems for renewable energy plants. Renewable Energy 008; 33:

22 [13] William F. Pikard, Niholas J. Hansing, and Amy Q. Shen. Can large-sale advaned-adiabati ompressed air energy storage be justified eonomially in an age of sustainable energy? Journal of Renewable and Sustainable Energy 009; 1:03310 doi: / [14] Luo X, Wang J, Krupke C, Wang Y, Sheng Y, Li J, Xu Y, Wang D, Miao S, Chen H. Modelling study, effiieny analysis and optimisation of large-sale Adiabati Compressed Air Energy Storage systems with low-temperature thermal storage. Applied Energy 016; 16: [15] Yuan Zhang, Ke Yang, Xuemei Li, Jianzhong Xu. The thermodynami effet of thermal energy storage on ompressed air energy storage system. Renewable Energy 013; 50:7-35. [16] Ke Yang, Yuan Zhang, Xuemei Li, Jianzhong Xu. Theoretial evaluation on the impat of heat exhanger in Advaned Adiabati Compressed Air Energy Storage system. Energy Conversion and Management 014; 86: [17] Pan Zhao, Mingkun Wang, Jiangfeng Wang, Yiping Dai. A preliminary dynami behaviors analysis of a hybrid energy storage system based on adiabati ompressed air energy storage and flywheel energy storage system for wind power appliation. Energy 015; 84: [18] Zuogang Guo, Guangyi Deng, Yonghun Fan, Guangming Chen. Performane optimization of adiabati ompressed air energy storage with ejetor tehnology. Applied Thermal Engineering 016; 94: [19] A. Kéré, V. Goetz, X. Py, R. Olives, N. Sadiki. Modeling and integration of a heat storage tank in a ompressed air eletriity storage proess. Energy Conversion and Management 015; 103: [0] Peiwen Li, Jon Van Lew, Wafaa Karaki, Cholik Chan, Jake Stephens, Qiuwang Wang. Generalized harts of energy storage effetiveness for thermoline heat storage tank design and alibration. Solar Energy 011; 85: [1] Peiwen Li, Jon Van Lew, Cholik Chan, Wafaa Karaki, Jake Stephens, J.E. O Brien. Similarity and generalized analysis of effiienies of thermal energy storage systems. Renewable Energy 01; 39: [] G. Zanganeh, A. Pedretti, S. Zavattoni, M. Barbato, A. Steinfeld. Paked-bed thermal storage for onentrated solar power Pilot-sale demonstration and industrial-sale design. Solar Energy 01; 86: [3] G. Zanganeh, A. Pedretti, A. Haselbaher, A. Steinfeld. Design of paked bed thermal energy storage systems for high-temperature industrial proess heat. Applied Energy 015; 137:81 8. [4] P. Klein, T.H. Roos, T.J. Sheer. Parametri analysis of a high temperature paked bed thermal storage design for a solar gas turbine. Solar Energy 015; 118: [5] Coutier, J.P., Farber, E.A. Two appliations of a numerial approah of heat transfer proess within rok beds. Sol. Energy 198; 9: [6] Meier A., Winkler C., Wuillemin D. Experiment for modelling high temperature rok bed storage. Sol. Energy Mater. 1991; 4: [7] Markus Hänhen, Sarah Brükner, Aldo Steinfeld. High-temperature thermal storage using a paked bed of roks e Heat transfer analysis and experimental validation. Applied Thermal Engineering 011; 31: [8] Hitesh Bindra, Pablo Bueno, Jeffrey F. Morris, Reuel Shinnar. Thermal analysis and exergy evaluation of paked bed thermal storage systems. Applied Thermal Engineering 013; 5: [9] Hao Peng, Rui Li, Xiang Ling, Huihua Dong. Modeling on heat storage performane of ompressed air in a paked bed system. Applied Energy 015; 160:1 9 [30] Ryan Anderson, Liana Bates, Erik Johnson, Jeffrey F. Morris. Paked bed thermal energy storage: A simplified experimentally validated model. Journal of Energy Storage 015; 4:14 3 [31] White A. Loss analysis of thermal reservoirs for eletrial energy storage shemes. Applied Energy 011; 88: [3] Lukas Heller, Paul Gauhe. Modeling of the rok bed thermal energy storage system of a ombined yle solar thermal power plant in South Afria. Solar Energy 013; 93: [33] González I, Pérez-Segarra C.D, Lehmkuhl O, Torras S, Oliva A. Thermo-mehanial parametri analysis of paked-bed thermoline energy storage tanks. Applied Energy 016; 179:

23 [34] Niolas Mertens, Falah Alobaid, Lorenz Frigge, Bernd Epple. Dynami simulation of integrated rok-bed thermoline storage for onentrated solar power. Solar Energy 014; 110: [35] RWE power. ADELE Adiabati ompressed air energy storage for eletriity supply. [36] [aessed ] [37] Pan Zhao, Lin Gao, Jiangfeng Wang, Yiping Dai. Energy effiieny analysis and off-design analysis of two different disharge modes for ompressed air energy storage system using axial turbines. Renewable Energy 016; 85: [38] MATLAB (014). The Language of Tehnial Computing, Matlab 014a, The MatWorks, In., Natik, MA. [39] S. L. Dixon C. A. Hall. Fuid Mehanis and Thermodynamis of Turbomahinery. (014) Seventh Edition Butterworth-Heinemann, Elsevier. Oxford, UK. [40] N. Zhang, R.X. Cai, Analytial solutions and typial harateristis of part-load performane of single shaft gas turbine and its ogeneration, Energy Convers. Manag. 00; 43: [41] Bergman T.L., Lavine A.S., Inropeara F.P., Dewitt D.P. Fundamentals of Heat and Mass Transfer. Seventh Edition. John Wiley & Sons, In 011. [4] L. Nielsen and R. Leithner, "Modelling and Dynami Simulation of an Underground Cavern for Operation in an Innovative Compressed Air Energy Storage Plant," Energy, Environment, Eosystem, Development and Landsape Arhiteture, pp , 009. [43] Mandhapati Raju, Siddhartha Kumar Khaitan. Modeling and simulation of ompressed air storage in averns: A ase study of the Huntorf plant. Applied Energy 01; 89: [44] VDI-Gesellshaft Verfahrenstehnik und Chemieingenieurwesen. VDI Heat Atlas, Springer-Verlag Berlin Heidelberg 010. [45] Nithyanandam, R. Pithumani. Cost and performane analysis of onentrating solar power systems with integrated latent thermal energy storage. Energy 014; 64: [46] R. Kushnir, A. Dayan, A. Ullmann. Temperature and pressure variations within ompressed air energy storage averns. International Journal of Heat and Mass Transfer 01; 55: [47] Kelley, K., Contribution to the data on theoretial metallurgy: XIII high-temperature heat-ontent, heat-apaity, and entropy data for the elements and inorgani ompounds, U.S. Bur. Mines Bull. No. 584, U.S. Government Printing Offie.