Physical design, techno-economic analysis and optimization of distributed compressed air energy storage for renewable energy integration

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Article

Reference

Physical design, techno-economic analysis and optimization of distributed compressed air energy storage for renewable energy

integration

HEIDARI, Mahbod, PARRA MENDOZA, David, PATEL, Martin

Abstract

The increasing penetration of stochastic renewable energy has raised interest in energy storage to supply electricity on demand. Batteries are currently the preferred solution but concerns about their environmental impact remain. An alternative solution can be Compressed Air Energy Storage (CAES), which is intrinsically more ﬂexible since, contrary to batteries, the energy capacity and power rating are decoupled. In this study, we present a detailed thermodynamic model of a multistage quasi-isothermal CAES, which is optimized to increase photovoltaic (PV) self-consumption in a micro-grid located in Switzerland. A Genetic Algorithm (GA) opti-mization is applied to determine the best operation schedule as well as capacity and power sizing and a parametric study is performed for various ratios of PV generation to load. Our results show that for a multi-family house that already invested in a PV system, adding CAES is not economically viable for a power level below 50 kW. However, CAES could become cost-effective for microgrids with a large PV generation share, since the cost of the energy-related part is rather low [...]

HEIDARI, Mahbod, PARRA MENDOZA, David, PATEL, Martin. Physical design,

techno-economic analysis and optimization of distributed compressed air energy storage for renewable energy integration. Journal of Energy Storage , 2021, vol. 35, no. 102268

DOI : 10.1016/j.est.2021.102268

Available at:

http://archive-ouverte.unige.ch/unige:154424

Disclaimer: layout of this document may differ from the published version.

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Journal of Energy Storage 35 (2021) 102268

Physical design, techno-economic analysis and optimization of distributed compressed air energy storage for renewable energy integration

Mahbod Heidari

^*

, David Parra, Martin K. Patel

University of Geneva, Chair for Energy Efficiency

A B S T R A C T

The increasing penetration of stochastic renewable energy has raised interest in energy storage to supply electricity on demand. Batteries are currently the preferred solution but concerns about their environmental impact remain. An alternative solution can be Compressed Air Energy Storage (CAES), which is intrinsically more flexible since, contrary to batteries, the energy capacity and power rating are decoupled. In this study, we present a detailed thermodynamic model of a multistage quasi-isothermal CAES, which is optimized to increase photovoltaic (PV) self-consumption in a micro-grid located in Switzerland. A Genetic Algorithm (GA) optimization is applied to determine the best operation schedule as well as capacity and power sizing and a parametric study is performed for various ratios of PV generation to load.

Our results show that for a multi-family house that already invested in a PV system, adding CAES is not economically viable for a power level below 50 kW.

However, CAES could become cost-effective for microgrids with a large PV generation share, since the cost of the energy-related part is rather low compared to the power-related part, making it more suitable for longer-term storage solutions (in comparison to batteries).

1. Introduction and literature review

To cap the global warming below 2 ^◦C, CO2 emissions must be reduced by 90% [1], and renewable energy capacity should be increased from less than 8% today to 34% by 2050 globally, according to sustainable development scenario projected by IEA [2]. In Europe (EU28), the share of new renewable energy sources, namely solar photovoltaics (PV) and wind, increased by 108% p.a. from 22 GWh to 407 GWh between 2000 and 2016, when a share of 13% of total electricity generation was reached [3]. In Switzerland, PV and wind power combined accounted only for 13% of the electricity generation mix in 2017, this share is expected to reach 46% in 2050 [4]. However, PV and wind cannot supply electricity on demand and their penetration requires extra flexibility for the energy system. Energy storage technologies enable the supply of stochastic renewable supply on demand and they also help to shave and shift peaks in the electricity demand load, thereby contrib- uting to grid stability [5]. There are different energy storage technologies available that make use of different physical principles, covering widely differing power and energy ranges resulting in different time-scales [6]. While electrochemical batteries are gaining momentum for short-term storage, they face environmental issues (e.g. utilization of rare raw material, recycling issues), and aging phenomena [7]. These problems have increased the attention paid to energy storage technologies with lower environmental impact [6] and longer lifetime.

Recently, Compressed Air Energy Storage (CAES) has attracted significant research interest as a promising storage technology for decen- tralized energy storage for medium-term (from a few hours to a few days) applications with high rated power and energy capacity and low levelized cost [8]. CAES also offers significant environmental advan- tages compared to batteries: The material and components used for manufacturing CAES systems are abundant and ubiquitous. There are no chemical or toxic materials used in their manufacturing process. The lifetime is very long (20–40 years) [9], components can be easily replaced and recycled and low amounts of greenhouse gasses are emitted during their life cycle [8].

A recent study comparing different energy storage technologies (flywheels, electrochemical storage, pumped hydro and CAES) for the integration of wind power generation found that CAES was the most cost-efficient [10]. According to another comparative analysis of energy storage technologies [9], Thermal Energy Storage (TES) has very low energy and power cost, while CAES has a low energy cost and a medium power cost. Another study presented an overview of technical parameters (e.g. energy and power density, energy capacity, power rating, discharge and roundtrip efficiency) for different CAES scales and concluded that CAES is expected to be soon commercialized thanks to the development of a new scroll expander [11].

CAES is based on the natural compressibility of air, making use of the potential energy of compressed air once it has been pressurized. For

* Corresponding author.

E-mail address: [email protected] (M. Heidari).

Contents lists available at ScienceDirect

Journal of Energy Storage

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

https://doi.org/10.1016/j.est.2021.102268

Received 22 August 2020; Received in revised form 13 December 2020; Accepted 4 January 2021

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example, the two CAES systems already installed worldwide (in Ger- many and the U.S.) use off-peak electricity to compress the air and store it in a reservoir, either in an underground cavern or aboveground vessels. This energy can be utilized at peak times using an expander coupled to an electric generator [12].

Three types of CAES systems can be distinguished based on the type of air storage and heat utilization: 1) Diabatic CAES, 2) Adiabatic CAES and 3) Isothermal CAES. Traditional (Diabatic) CAES uses turbo- compressors to pressurize the air to around 70 bar before storage.

Without effective intercooling, the air temperature rises to around 900 K, leading to the loss of compression heat and making the processing and storage of the gas challenging in both technical and economic terms unless air is cooled down. To increase the output power, fuel is injected into the expanding air and ignited in a turbine [13]. In Adiabatic CAES (A-CAES) the heat of compression is stored (instead of released to the atmosphere) and is utilized during the expansion, thereby avoiding the need for reheating with natural gas [14]. This can be done in two ways:

A-CAES without TES and A-CAES with TES. A-CAES without TES stores the heat of air as thermal energy inside the compressed air storage reservoir, which limits the storage pressure and consequently energy density, due to the high temperatures achieved even at rather low-pressure ratios (e.g. 10 bar) [15]. Thus, this concept needs temperature resistant storage material, which increases the capital cost. To solve this problem in A-CAES with TES, the air’s heat is separately stored in a TES, enabling high energy density due to the storage of cooled, high-pressure air (at least 60 bar) ([16, 17]).

Isothermal CAES (I-CAES) is an alternative technology, which at- tempts to overcome some of the limitations of traditional (diabatic or adiabatic) CAES. To eliminate the need for numerous stages to compress, cool, expand and heat the air, isothermal CAES technologies attempt to maintain an isothermal process inside the compression and expansion chamber, yielding high round-trip efficiency (up to 90% according to [18]) and lower capital costs, thanks to minimizing the compression heat [19]. These features make isothermal CAES the most suitable CAES technology for small-scale applications and especially for future distributed generation systems. However, I-CAES is technologically challenging since it requires continuous heat removal from the air during the compression and, on the other hand, continuous heat addition to the air during expansion, to approach an isothermal process. The heat transfer rate is proportional to the product of temperature gradient and the contact area; therefore, to transfer heat at a high rate with a small temperature difference, a very large heat transfer area is required, resulting in costly heat exchangers. Recently, several methods have been attempted to approach the isothermal process such as spraying fine droplets of water into the compression and expansion chambers [20];

using a finned metal piston [21]; a liquid piston [22]; and inserting porous media [23].

There have been multiple studies about CAES, addressing for example thermodynamic design and modeling [23–25], and techno-economic analysis [26-28], as well as a previous review [24].

This review concluded that further efficiency improvement and cost reduction are necessary for the attractive integration of CAES with renewable energy technologies, in particular for the distributed scale.

Other studies focused on the energy conversion in CAES, for example Odukomaiya et al. analyzed multiple paths for the compression and expansion of a CAES system by using spray cooling/heating and waste heat utilization with different configurations, thereby modeling heat transfer in a detailed manner [25]. Among the studies that evaluated the cavern or reservoir of a CAES system, Kushnir et al. derived the evolu- tion of temperature and pressure in the air cavern of CAES systems, based on numerical and approximate analytical solutions of mass and energy conservation [26]. Also, Raju et al. determined the heat transfer coefficient of a CAES cavern and validated the results with the Huntorf CAES plant in Germany [27]

In addition to the literature that investigated different CAES processes and technologies, several techno-economic analyses have been

performed for different types of CAES and scales. Techno-economic modeling of both large-scale adiabatic and classic CAES systems (diabatic) led to the conclusion that the overall efficiency of the adiabatic system can be considerably higher but that the breakeven electricity selling price of the adiabatic system was much higher than that of the classic system due to the higher capital investment of the former [28].

Also, Wang et al. presented an optimization method for determining the rated power and energy capacity of a CAES system to maximize profit.

They tested this method when CAES was coupled to eight wind farms to avoid wind curtailment and concluded that a properly sized CAES system might be economically feasible [29]. For CAES performing electricity arbitrage in wholesale markets, Lund et al. developed two optimal strategies (namely historical and prognostic) and showed that a CAES plant could reach between 80 and 90% of the maximum economic potential [30].

Recently a few studies focused on integrating small-scale CAES with renewable energy sources for residential buildings. Castellani et al.

presented an experimental study to assess the PV-integrated small-scale CAES for a historical building [31]. They concluded that using higher pressure CAES system can increase the share of PV self-consumption. In another experimental study conducted by Maia et al., a turbocharger is utilized to build a micro-CAES system for residential building scale [32].

Similarly, Jannelli et al. proposed a small-scale CAES integrated with a TES that can also be configured as a polygeneration unit delivering heating and cooling service to the building [33].

There are only two CAES plants that have been in operation for de- cades: the 290 MW Huntorf CAES plant in Germany and the 110 MW McIntosh plant in the USA, which both use underground caverns ([5], [13]). As discussed in the literature review, most of the works related [31] to thermodynamic modeling and analysis have studied these two plants ([26], [27] and [28]) and other large-scale adiabatic CAES schemes ([14], [17] and [34]). In these studies, monotonic pressure and power variation were assumed, resulting in steady-state operation of compression and expansion as a result. These assumptions have also been used for the previous techno-economic analysis ([28], [30]) and another study relied on an approximated roundtrip efficiency [8].

However, the coupling of CAES systems with renewable energy from distributed generation systems poses new challenges. Since the generation profile of solar and wind is stochastic, a steady-state thermodynamic model for the CAES system is not appropriate, especially during start-up [35]. Instead, a dynamic model should be developed to account for the time-dependent and cycle-to-cycle variation of thermodynamic parameters (e.g., pressure and temperature in reservoir and exhaust of compressor). Furthermore, the techno-economic analysis should be based on the results of such a thermodynamic model to pro- vide accurate results.

Traditionally, the preferred energy storage solution in the Swiss context has been pumped-hydro. However gradual phase-out of current nuclear power plants and their eventual replacement with distributed intermittent renewable energy sources have changed the prospects of the energy storage. In addition, electrification of heating and mobility will call for a new additional economical and efficient distributed energy storage technology. Most of the previous literature addressing CAES has focused on bulk scale applications that are placed close to electricity generation. However, considering the transition towards distributed energy systems, the development of small scale (micro-CAES) close to energy demand is also of great interest.

Based on the literature review presented, a comprehensive thermodynamic and techno-economic understanding of small-scale CAES systems in the context of distributed generation is still lacking. The objective of this work is to address this research gap by performing a thorough thermodynamic investigation of a distributed CAES system, followed by a detailed techno-economic assessment. The CAES system should allow to perform both PV self-consumption (to substitute expensive grid power by using more locally harvested PV electricity) and also demand load shifting (charging the CAES from and exporting

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electricity to the grid) if it can increase the profit.

Thus, the research questions we are aiming to address in the proposed work are:

•Does CAES have the potential to become an economically viable option to increase the value of distributed PV and if so, under which conditions?

•What are the optimal operation conditions, capacity and power for CAES design to be coupled with distributed PV?

•What is the ratio between the power and energy capacities which maximises the value of CAES for a distributed application?

•How CAES profitability vary with increasing local PV generation?

The designed CAES system is analyzed using a time-dependent model that includes the reservoir, conversion (electric motor/compressor and expander/generator), and the electrical grid component. This enables us to characterize the dynamics of thermodynamic parameters of the system such as pressure, temperature, mass flow and volume in conversion and storage units. The CAES system is coupled with PV technologies to increase local PV self-consumption and/or to perform demand load shifting under actual electricity tariff schemes. An optimization is performed with the objective of maximizing the profit of the CAES plant subject to different design variables (e.g., power rating and energy capacity) and operation schedule.

This article is structured in six sections following the introduction: In the first section the proposed CAES system is described and some design aspects such as multistage compression and expansion, as well as part- load efficiency are explained. In Section 2, technical and economic input data are presented. The input data is given in Section 3 and thermodynamic model and techno-economic analysis is developed in Section 4, while the optimization and parametric study are explained in Section 5. The results are presented in Section 5 followed by discussion and conclusion in the last section.

2. CAES system description

The mechanical part of a CAES system comprises the compressor, expander, reservoirs and valves, while TES in combination with heat exchangers are optional components. For such a system and depending on the required power and energy capacity, a range of compression and expansion technologies (volumetric or turbomachinery), processes (isothermal, adiabatic) and a varied number of stages are possible. For instance, the type of compressor (reciprocating, radial, axial…) depends on the required CAES pressure ratio and flow rate [36]. On this basis, additional features such as TES or heat exchangers might be advisable and should then be included in the design. The selection of the best compression and expansion system configuration requires an integrated approach which should comprise technical but also operational and economic aspects.

The pressure used for a large scale CAES system is about 80 bar, for which multi-stage compressors are used, and normally, a combination of axial flow compressors and centrifugal compressors is utilized. Howev- er, for distributed CAES with a limited reservoir volume, a high-pressure storage (e.g., 200 bar or even 400 bar [37]) is required for the CAES reservoir, typically making the use of multi-stage reciprocating compressors necessary. The CAES system proposed in this study is a three-stage quasi-isothermal reciprocating compressor-expander that is coupled to a 3-phase motor-generator (M/G) set (see Fig. 1). The pressurized air generated by the compression unit is stored in a pressure vessel and is discharged in the expansion unit when required. The PV system is connected to the electricity demand load and CAES storage system through an inverter, while a 3-phase AC converter is also needed for the CAES system downstream.

Reciprocating compressors have pressure ratios between 4 and 7. In order to reach higher storage pressure and energy density, multistage compression is employed. The overall efficiency increases with the

number of stages but costs and practicalities need to be considered. For a given number of stages, the total compression work is minimum and the total expansion work is maximum when pressure ratios between the stages are equal, which results in equal work and power delivered in each stage [38]. This fact is shown for a three-stage (n =3) system in Fig. 2. In addition, however distributed CAES systems can be operated over the entire pressure range, the maximum power cannot be guaran- teed at low pressures (See Fig. 2).

Because turbo-machines used in large-scale plants are usually designed to operate above a minimum operating pressure, a certain amount of mass of air is kept inside the storage at all times to maintain the minimum level of pressure required. Similarly, in small-medium scale CAES systems, compressors and expanders and electric motors and generators coupled to them, are designed for a specific power load, below which their efficiency usually decreases. The efficiency penalty as a consequence of pressure levels below the design value is shown in Fig. 3 [39].

In our case, for a 3-stage quasi-isothermal CAES system with constant volume storage, a maximum pressure of 86 bar (which corresponds to a pressure ratio of 4.45) is determined by the optimization (see Section 6.3) to minimize the cost. The limitations related to power and efficiency in part-load need to be considered to optimize the operation of CAES Fig. 1. Schematic representation of a distributed reciprocating multistage CAES system and its components when connected to a PV system.

Fig. 2. Operating power limitation of multistage CAES system.

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system.

3. Input data

The technological and economic parameters used in the model are presented in this section, including the PV generation, demand load and electricity price as well as equipment cost.

3.1. PV generation, demand load and technical CAES characteristic data CAES systems are not available for powers below 5 kW, so they are not suitable for single-family house applications. Hence, for this study, we consider a multi-family house in Switzerland inhabited by 18 families for which electricity demand and PV generation were monitored in 2015 (see Fig. 4). The data related to PV generation and demand load are based on average daily values throughout the year.

The daily average electricity consumption is 163.7 kWh, and there is an on-site PV installation of 23 kWp with a 30^◦ south orientation, generating 90.7 kWh per day on average. This electricity demand load and PV generation correspond to a PV generation to load ratio (g/L)of 0.55 (where g is the total PV generation and L is the daily load, both in kWh, see Section 5). Without the CAES system, the average total daily PV power fed into the grid and total daily import from the grid are 22.2 kWh and 95.3 kWh respectively. We simulate PV generation using a

standard one-diode model [40], assuming a PV panel with a nominal efficiency of 18.6%, representative of the current state of the art [41].

The model also includes a maximum power point tracker system, as is the case of most PV systems, to maximize the output regardless of the environmental conditions. We aggregated the original 15 min resolution data used for microgrid results in Section 6.2 to 1 h resolution for parametric study in Section 6.3 to accelerate running the model. The various CAES system parameters utilized in the model are presented in Table 1. It should be noted that for a given capacity, it is possible to design the CAES system with a range of maximum pressures and volumes. The maximum pressure presented in Table 1 minimizes the cost of the reservoir (see Section 6.3).

3.2. Economic parameters

The total capital cost of a CAES system can be divided into two components related to the energy capacity and power rating. According to the analysis by Liu et al. [42], the cost of an above-ground gas storage reservoir (steel vessel) can be expressed as a function of maximum pressure and volume of the reservoir as:

CostReservoir($) = (0.042∗p_max(Bar) +1.4) ∗ (

710∗V( m³)_0.54)

(1) In Eq. (1), we do not consider the length to diameter ratio of the vessel as a separate design variable, but we assume that it is set to minimize the cost of the vessel. This ratio is found to be around 3 for minimizing the cost of the vessel [43].

For the distributed CAES system (less than 1 MWh) the investment cost for an above-ground gas storage reservoir is around 150–200

$/kWh [37] (200 $/kWh for smallest systems and decreasing linearly to 150 $/kWh for 1 MWh). Eq. (1) can hence be approximated as follows:

CostReservoir($/kWh) = − 0.1∗Capacity(kWh) +205 (2)

Fig. 3. Electric motor and generator efficiency as function of power load [39].

Fig. 4. Average daily PV generation and electricity demand load profiles throughout the year in the 18-home community selected to simulate distributed CAES.

Table 1

Input parameters of CAES system model.

Parameter (unit) Value Parameter Value

PAtm(Bar) 1 No.of Stages (-) 3

Export price($/kWh) 0.056 O&M Cost 5.1% of power cost [8]

Tamb(K) 293 n (-) 1.04

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Both Eq. (1) and Eq. (2) are plotted in Fig. 5. The cost of equivalent capacity for Eq. (1) (as given in Eq. (16)) is shown in blue dots which is comparable to the result of Eq. (2) (red line).

For a conventional compression system, the cost of the power-related part (including the compressor/expander with electric motor/generator) can be estimated with Eq. (3) [44]:

CostPower($) =(

9800∗Powermax(kW)^0.58)

(3) According to the literature [37], the investment cost for the power-related component of small scale (less than 100 kW) isothermal CAES is estimated to be between 1500 and 6000 $/kW (6000 $/kW corresponds to the smallest scale (i.e. 5 kW) and decreases to 1500 $/kW for 100 kW). The cost of the power-related component for isothermal CAES systems which are less than 100 kW is almost 50% higher than a conventional compression system as shown in Fig. 6. As given in Eq. (4) and Eq. (5), the power rating is mainly a function of mass flow and pressure ratio.

The electricity price corresponds to the tariff implemented by the utility company ‘Services Industriels de Gen`eve’ (SIG) in Geneva (Switzerland). This tariff is divided into peak and off-peak hours, with prices being 0.27 and 0.17 USD¹/kWh respectively as seen in Fig. 7. The off-peak hours occur from 10 pm to 7 am throughout the year while the peak periods take the other hours of a day. Similar 2-period Time-of-Use tariffs are available in other countries such as the UK and France. The optimization results reveal that since the electricity import price is al- ways much higher than the export price (by a factor two to four depending on the time of the day), the priority of CAES is to substitute expensive grid power by using more locally harvested PV electricity (PV self-consumption), as such CAES system does not charge from or export electricity to grid (i.e., it does not perform demand load shifting).

In addition, a lifetime of 40 years [9] and a social discount rate of 4%

are assumed in agreement with previous publications focusing on distributed energy technologies in Switzerland [45].

4. Model development 4.1. Thermodynamic modeling

The application of time-dependent mass and energy balances under temperature-dependent values for the specific heat and quasi-isothermal reservoir boundary conditions results in a thermodynamic model for the compressor, expander and reservoir. The model presented in this study

takes into account the time-dependent behavior of pressure levels in air compression and expansion and it has also been used in the previous literature [21, 46] . The simulation of the CAES system yields time-dependent pressure, temperature and mass in the compressed air reservoir for both the charge and the discharge mode.

The electric power required by the compressor is a function of time- dependent pressure delivered to the reservoir:

W˙c=m˙cRTi

n n− 1

[(p_res(t) p₀

)_(n−_1)/n

− 1 ]

η_m (4)

Similarly, the electric power delivered by the expander is a function of time-dependent pressure of the reservoir:

W˙e=m˙eRTe

n n− 1

[ 1−

( p₀ p_res(t)

)_(n−_1)/n]

η_g (5)

The polytropic factor (n) approaches 1 in an ideal isothermal case, and therefore, the work cannot be determined just using Eq. (4) and Eq.

(5). In this case, Eq. (6) and Eq. (7) should be formulated:

W˙c=m˙cRTi

[ ln

(p_res(t) p₀

)]

ηm (6)

W˙e=m˙eRTe

[ ln

( p₀ p_res(t)

)]

ηg (7)

Where:

W˙c,W˙e are the power required by the compressor and power made available by the expander(kW)

m˙c,m˙e are the mass flows of compressor and expander(kg/s) Ti,Te are the inlet temperatures to compressor and expander(K) Fig. 5.Energy-related cost as a function of the energy capacity for an above-

ground gas storage reservoir (steel vessel).

Fig. 6.Power-related cost for conventional and isothermal compression as a function of the power rating for distributed storage systems.

Fig. 7.Electricity prices according to the double tariff for a representative day.

1 Throughout this text it is assumed that 1 CHF is equal to 1 USD so these units can be used interchangeably.

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n is the polytropic exponent for compression and expansion η_m,η_gare the efficiencies of electric motor and generator p0 is the atmospheric pressure (kPa)

pres(t)is the time-dependent reservoir pressure (kPa) Tres(t)is the time-dependent reservoir temperature (K) Ures is the internal energy of the reservoir (kJ) R is the gas constant kJ/(kg.K)

As mentioned, the efficiency of a electric motor and generator is a function of the load factor [38]. This means that the conversion efficiency drops when the power demanded by the compressor is lower than the nominal power. Therefore, our model includes this relationship between the efficiency and power demanded by the compressor (see Fig. 3).

The energy balance in the reservoir can be written as:

dUres

dt =m˙chi− m˙ehe− Q˙_res (8) Where:

Ures=mrescpTres(t) (9)

hi=cpTi (10)

he=cpTe (11)

In Eq. (8) Q˙res is the heat transfer from the reservoir:

Q˙_res=αresAres(Tres(t) − Tw) (12) The mass balance of the reservoir implies that:

mres(t) =

∫^t

0

(m˙c− m˙e)dt (13)

In addition, based on the ideal gas equation we can write:

p_res(t) =mres(t)RTres(t)/Vres (14)

The pressure once the gas cools down in the reservoir can be calculated as:

p_res,_ACD(t) =p₀∗T0

/Tres(t) (15)

hi,he are the inlet enthalpy to the compressor and to the expander (kJ/kg)respectively.

αres is the heat transfer coefficient(W/m²K)and Ares represents the surface area (m²)of the reservoir.

The work potential (Exergy) of the reservoir which is equivalent to storage capacity can be calculated from [38] using Eq. (16):

X2=mresRT0

[p₀ p_res+ln

(p_res p₀ )

− 1 ]

=p_resVres

[p₀ p_res+ln

(p_res p₀ )

− 1 ]

(16) Where

X is the exergy content of the reservoir (kJ) mresis the mass of air in the reservoir(kg) Vres is the volume of the reservoir(m³) 4.2. Techno-economic analysis

For the techno-economic analysis, we evaluate the profitability of a CAES system by using the Net Present Value (NPV):

NPV =∑^LT

i=1

CFi

(1+r)ⁱ− CAPEX (17)

As addressed in Section 3.2, the cost of the power conversion and air

storage (i.e. energy storage) can be decoupled, in contrast to electrochemical batteries. Since the power conversion part (comprising the compressor and expander) has a significantly higher cost than the air storage part (vessels), we optimize the CAES design by adequately sizing these two components. In particular, we determine the NPV per unit of CAPEX which varies between − 1 and +1, and allows for easy comparison of the various configurations. The NPV per unit of CAPEX is defined as the sum of the cash flows over the lifetime of the CAES system and determines whether the investment in the storage system is profitable (>0) or not (<0). It is assumed that the Operation and Maintenance

(O&M) cost or OPEX is included in the CAPEX and that it is paid at the

beginning of the project.

NPV per Unit of CAPEX= NPV

CAPEX (18)

CF (Cash Flow) is the avoided electricity costs due to the use of the CAES storage system (see below).

CAPEX is the capital cost of the CAES storage system including the power and energy-related components and also O&M cost (see Table 1).

r is the social discount rate.

LT is the lifetime of the storage system.

Cash flow or avoided electricity costs due to the use of the CAES storage system equals the electricity bill without CAES system minus the electricity bill using CAES system:

CF=Elec billw/o CAES− Elec billWith CAES (19) The electricity bill without CAES system is given by:

Elec billw/o CAES=∑^T

i=1

(GIi∗Pimport i− GEi∗Pexport i

) (20)

Where the electricity balance of the system without CAES is:

GIi=Li− g_i+GEi (21)

And the electricity bill with CAES system is:

Elec billwith CAES=∑^T

i=1

(GIi∗Pimport i− GEi∗Pexport i

) (22)

The electricity balance of the system with CAES is:

GIi=Wcomp i− Wexp i+Li− g_i+GEi (23)

Where:

i is the hour of the day.

GIi is the electricity drawn from the grid(kWh). GEi is the electricity exported to the grid(kWh). Wcomp i is the work consumed by the compressor (kWh). Wexp i is the work delivered by the expander (kWh). Li is the electricity demand load (kWh).

gi is the PV generation (kWh).

Pimport is the electricity import price at which the CAES system is charged (USD/kWh).

Pexport is the electricity export price at which the CAES system is discharged (USD/kWh).

5. Optimization and parametric study

GA have been used in several residential battery scheduling optimization studies. For example, Yoon et al. used GA to optimize battery schedule to reduce the electricity bill, however without considering battery efficiency and capital cost [47]. Pena-Bello et al. optimized the battery schedule and capacity using a GA to improve the profitability of the residential batteries for PV self-consumption and demand load shifting [48]. However, to the best of our knowledge, no similar studies

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have been performed for small scale CAES systems. In this study, the GA algorithm is implemented in MATLAB^Ⓡusing Optimization Tool. The reason for selecting GA is that the thermodynamic model developed above and subjected to the optimization algorithm is highly nonlinear.

The initial population is 1000 with a uniform creation function. Fitness scaling function is proportional and the algorithm uses a uniform selection function. Reproduction uses the default crossover function of 0.8, and the crossover function is scattered. The main reason that the optimization is carried out for average PV generation and average loads for one day is to limit the computation time (The simulation of one day takes around 198 s.). Otherwise, the optimization of a whole year and repeating it for different cases in the parametric study would have taken weeks, which is not practical.

Since the data related to PV generation and demand load are based on average daily values over the year and they represent the average of a rather large number of households, we consider the optimization over a timespan of 24 h to be representative for the whole year and for the upscaled community, as discussed at the end of Section 6. We also assume that electricity prices are known on a day-ahead basis. The objective function is to maximize the NPV as defined in Section 4.2. This objective function is subject to Eq. (21) and Eq. (23) which state the electricity balance of the system.

6. Results

6.1. Results for constant power operation

To demonstrate the thermodynamic and energy characteristics of a CAES system, we first present the results for a simplified system where the reservoir is charged with a multistage compressor with constant power (in each stage) for one hour. Then, the reservoir stores the air for one hour. Finally, the compressed air is expanded and the reservoir is discharged completely. When charging a reservoir with compressed air, the fast filling and large pressure ratios lead to a large temperature increase [49]. The exact variation of temperature in the reservoir is very sensitive to the heat transfer coefficient of the reservoir. It is important to note that large temperature variations reduce the efficiency of the system, as any temperature gradient with respect to ambient will be lost to the environment as wasted heating or cooling energy.

Fig. 8 shows the variation of main parameters during the above- mentioned three-hour period for a three-stage compression expansion system with a pressure ratio equal to 4.45. As mentioned, the power is constant in each stage (a) which leads to a linear work in each stage delivered to the compressor and recovered from the expander (b). The quasi-isothermal compression and expansion with a polytropic factor of n =1.04 lead to a round trip efficiency of 78%. The pressure rises from 1 bar to 86 bar but then quickly drops to 80 bar (c) as a result of the heat transfer from the reservoir to the surroundings which reduces the temperature; (d) and as the consequence the pressure (c) and exergy (f) in the reservoir. The pressure (from Eq. (14)) and the exergy content of the reservoir can be calculated after being cooled down (blue curve) which corresponds to the real work potential of the compressed air in the reservoir.

6.2. Micro-grid results

Fig. 9 illustrates the average daily PV generation, demand-load, grid import and CAES operation scheduling with the double tariff. In the early morning until 7:30 a.m., the electricity demand load is satisfied by off-peak electricity from the grid. When electricity price increases and PV generation starts at 7:30 a.m., the CAES covers the rest of the demand load; later, PV generation is large enough to simultaneously cover the load and charge the CAES from 9:30 a.m. until 4 p.m. From 4 p.m. until 9 p.m., the CAES is discharged to compensate the shortcoming of PV generation to meet the electricity demand load. However, from 6 p.m.

onwards, to avoid extra cost, CAES power is limited to 5 kW (resulting

from the sizing optimization) which is supplied until 9 p.m. From then onwards, the demand load is entirely covered by the grid taking advantage of the off-peak prices.

As mentioned above, the CAES system is free to perform both PV self- Fig. 8.Variation of reservoir parameters during 1-hour charge, followed by 1- hour storage and finally 1-hour discharge for a simplified CAES system in which Vres=0.11m³and n=1.04.

Fig. 9.Import and export price and average daily power balance of the apartment, including PV generation, demand electric load, grid input and CAES system.

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consumption and demand load shifting if it can increase the profit of the system. However, the system only performs PV self-consumption as the optimization algorithm found demand load shifting not to be profitable.

Fig. 10 shows the variation of pressure and temperature in the reservoir for a one-day operation. We find the optimum reservoir volume and maximum pressure to correspond to Vres=4m³andPres,max = 85bar respectively for a 30kW storage (see Section 6.3). While initial pressure is set to 5000 kPa (50 bar), it reaches the maximum at around 8500 kPa (85 bar) and decreases to nearly the initial pressure at the end of the day. This range of operational pressures ensures full power utilization and avoids part-load inefficiencies as observed for lower pressures in Fig. 2 and Fig. 3. As displayed in Fig. 10, the variation of the temperature in the reservoir leads the pressure variation but it ranges only between 282 K and 310 K (resulting in higher efficiency compared to the temperature variation between 240 and 320 K in Fig. 8).

Another application of CAES in the residential or commercial sectors can be utilizing the waste heat generated by the compressor during the charging phase and cooling provided by the expander during the discharging phase. A part of this heating and cooling capacity is available in the reservoir and can be exploited using a dedicated heat exchanger.

One limitation of this system is that the heating and cooling are available at low grade (e.g. cooling at 9 ^◦C and heating at 37 ^◦C). Another limitation is that heating and cooling capacities may be available in periods when they are not needed. In other words, waste heat is generated during the compressor operation (charging phase) around noon time when heating is not much needed, while cooling capacity is available during the discharging phase in early morning and in the evening when it might not be necessary to cool the building. The second limitation can be addressed using a thermal energy storage system to utilize cooling and heating opportunities on demand. However, the analysis, charac- terization and cost-effectiveness evaluation of such systems is outside the scope of this study and can be explored in future works.

Fig. 11 presents the exergy content of the reservoir and State Of Charge (SOC) of the CAES over one day of operation. The initial and final SOC is around 50% which gives some operational flexibility to the storage system and ensures a cyclical, repeatable process. In addition, this selection of the values for SOC reduces the final to initial pressure ratio both in compression and expansion and as a result the temperature change in the reservoir which minimizes the thermal losses (see Section 6.1). As mentioned, CAES is initially charged at 50% of SOC which corresponds to an exergy content of the storage of 15.8 kWh. The above- mentioned operation of CAES increases its efficiency to 81% (in comparison with 78% found in Section 6.1). The CAES system reaches its minimum SOC of 32% which is equivalent to 11 kWh at around 9:30 a.

m. and its maximum SOC of 94% (equivalent to 31 kWh exergy content) and then is discharged until it achieves nearly the initial SOC.

6.3. Parametric study

In this section, to gain a better understanding of the effect of variation of power and capacity on the profitability of the CAES system, we

show the optimization results for different levels of power and capacity.

As displayed in Fig. 12, the best NPV per unit of CAPEX for the load curve and PV generation shown in Fig. 4 is achieved with a power rating of 5 kW and an energy capacity of 30 kWh; if the reservoir is undersized or oversized, the profitability decreases. For a given capacity, there is an optimum power level. If the power is lower than the optimum value, the CAES system cannot capture all the storage possibilities. On the other hand, if the power is higher than the optimum, the maximum power remains unused most of the time and only increases the capital cost of the system.

Based on the aforementioned analysis, the optimal discharge duration, i.e. energy capacity to power ratio, is found to be around 6 h. This is a result of the low-cost energy-related component of CAES, relative to the power-related cost, opposite to lithium-ion batteries. This is in contrast to the typical daily discharge duration of around 2 h for Li-ion batteries performing PV self-consumption [48], but it could be shorter even if the demand requirements are higher.

It is important to note that for the same capacity of energy storage, the reservoir can be designed with different maximum pressure and volumes (Fig. 13). Fig. 14 shows that there is a minimum cost for a specific maximum pressure (pmax) at which the reservoir should be designed. It shows that this pressure is about 85 bar for an energy capacity of 30kWh. Furthermore, there is a little increase in cost when pressure is varied around the minimum cost pressure (in both directions) but the cost consequences of designing at too low pressure are more severe than at too high pressure.

It should also be mentioned that the optimum maximum pressure is found when the objective function is to maximize the NPV. If storage volume is a limitation and consequently the energy density should be increased, this maximum pressure will increase as mentioned in the literature to 200 bar [50]. However, this will increase not only the cost of the energy related part (reservoir) but also the power-related cost, since additional compression/expansion stages will be required.

We have so far assumed (see Fig. 4) that the PV generation and demand load are fixed. However, since (both power and energy related) cost per unit decreases with increasing size, it is of interest to assess the

Fig. 10.Pressure and temperature variation in the CAES reservoir during one day. (Vres =4m³,n=1.04).

Fig. 11.Exergetic content of the reservoir and SOC of CAES for one day.

Fig. 12.Variation of NPV as a function of power for different capacities.

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profitability of upscaled storage systems for a larger number of households. In addition, it can be important for practitioners to study the ratio of PV generation to demand load (g/L)(daily ratio). As mentioned in

the introduction, the capital expenditure of PV panels is not considered in our analysis which deals with the optimal CAES configuration for a given PV and demand balance.

Fig. 15 shows the effect of increasing the power (and capacity) for larger-scale applications. It is observed that a CAES system reaches cost- effectiveness at the power of 50 kW and capacity of 300 kWh which corresponds to a system that is 10 times larger than the considered in the baseline scenario in Section 6.2 (this CAES system would be suitable for a community of 180 households). Moreover, it is observed that an increased ratio of generation to demand load (g/L), which was equal to 0.55 in our baseline scenario, improves the cost-effectiveness of the system. For example, when generation reaches parity with load (g/L= 1), even a 25 kW system can become cost-effective. This is in particular important in the context of the energy transition in Switzerland, as the combined share of PV and wind power is expected to more than triple from 2017 to 2050 [4].

Although our study presents a robust optimization method for different types of applications, power levels and capacities, we acknowledge some limitations. We considered the electricity demand and PV generation for a multi-family house inhabited by 18 families. In the study of the upscaled community at the end of Section 6, we assumed the initial electricity demand profile to be representative and upscaled it for the size of the community. In this case, using the electricity demand profile of a higher number of users can give a more realistic result.

Hence, the rather limited number of electricity demand profiles can be one of the limitations of the upscaled study. Besides, the model assumes a three-stage (n =3) compression/expansion system, which is common practice for the optimum storage pressure found in this study. This assumption might become somehow inaccurate for much higher storage pressures, as the number of stages should be increased for higher storage pressure. This, of course, requires that the cost of the power-related part is considered to be a function of the number of stages as well (in addition to power), which makes the optimization problem too complicated and is outside the scope of this work.

7. Conclusion and future work

In this study, a thermodynamic model was developed to characterize the parameters of a distributed CAES system. On this basis, a techno- economic analysis is performed to assess its cost-effectiveness when Fig. 13. Trade-off between the maximum pressure and volumes for a

given capacity.

Fig. 14.Cost of the reservoir as a function of maximum pressure for a given capacity.

Fig. 15.Variation of NPV as a function of capacity and power for different PV generation to load ratios.

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performing PV self-consumption with an average local PV generation of 90 kWh per day for a multi-family house with 18 apartments consuming 164 kWh of electricity per day. As demonstrated, the CAES system should have an intermediate SOC at the beginning and end of the day to offer flexibility to the storage system and increase efficiency. In addition, to avoid working at part load and also to guarantee the maximum power utilization, the CAES storage system should work above a given pressure (equivalent to 30% of SOC in this study). Since the energy-related system components are low cost, this operation condition only increases the capital cost of the system slightly.

Using CAES for residential applications is also most profitable for increasing self-consumption, i.e. to charge when PV generation exceeds the demand and to discharge when demand load exceeds the produc- tion; nevertheless, some import of electricity from the grid is inevitable in the final peak hours due to power limitations of CAES. Demand load shifting (charging the CAES from the grid or exporting to the grid) was not found to be profitable in our case for the selected community.

We found the optimal energy to power ratio to be equal to 6, with an energy capacity of 30 kWh and a power capacity of 5 kW. However, this case is still not cost-effective. This suggests the optimal discharge duration of around 6 h. Compared to lithium-ion batteries with a typical discharge duration of 2 h, CAES enable longer discharges periods, with 6 h being the optimal discharge of our study, which can be attractive for communities with high PV capacity. From a design perspective, and if the volumetric density is not a constraint, the most economical vessel results in a maximum pressure of around 85 bar and with a volume of 4m³where underdimensioning of the vessel should be avoided. Thanks to economies of scale CAES can reach cost-effectiveness if upscaled by a factor of 10 (50 kW). Also if PV generation is increased to parity with demand load energy (g/L=1), even a fivefold scaled-up system (25 kW) can be cost-effective.

CAES may be more cost-effective using waste heat and cooling capacity when delivering multiple services like Combined Cooling, Heat- ing and Electricity (CCHP). Further research is required to characterize such systems and to evaluate their cost-effectiveness.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research project was financially supported by the Swiss Inno- vation Agency Innosuisse (former name: Swiss Commission for Tech- nology and Innovation, CTI) and is part of the Swiss Competence Center for Research in Energy, Society and Transition (CREST) with grant number 1155002547. It was additionally supported by the Swiss Inno- vation Agency Innosuisse in the context of the Swiss Competence Center for Heat and Electricity Storage (SCCER-HaE), with grant number 11 55002545.

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