Thermodynamic and exergy analysis of a combined pumped hydro and compressed air energy storage system

Sustainable Cities and Society 48 (2019) 101527

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Thermodynamic and exergy analysis of a combined pumped hydro and compressed air energy storage system

T

⁎

Hamidreza Mozayeni, Xiaolin Wang , Michael Negnevitsky School of Engineering, University of Tasmania, Hobart, TAS 7001, Australia

A R T I C LE I N FO

A B S T R A C T

Keywords: Pumped hydro Compressed air Thermodynamic analysis Exergy analysis Energy storage

The Pumped-Hydro and Compressed-Air (PHCA) is a new energy storage system which can be coordinated with renewable energy sources such as wind and solar. In this paper, a comprehensive thermodynamic and exergy model is developed to study the thermal characteristics of a combined Pumped-Hydro and Compressed-Air (PHCA) energy storage system. The effect of key parameters, including storage pressure, pre-set pressure, aircompression mode and pump/hydroturbine efficiency on system performance is investigated. The results showed that an optimum pre-set pressure existed to maximize energy storage level for a specific storage pressure. The storage pressure also showed a large effect on the energy storage level and work output. As the storage pressure increased from 4 to 16 MPa, the energy storage level and work output increased remarkably. Furthermore, the performance of a PHCA system was largely influenced by the air compression/expansion mode in the energy storage vessel. The PHCA system stored 10% more energy through an isothermal compression process than that through an isentropic air compression process. It generated 14% more work output through an isothermal expansion process than that through an isentropic air expansion process. The exergy analyses showed that exergy destruction in pump was about 15% higher than that in hydroturbine.

1. Introduction Limited fossil fuel resources will not cover energy needs of the sustainable city and society as the world population continuously grows. Therefore, there is a world-wide tendency to improve the energy sustainability via decreasing the dependence on fossil fuels and developing power generation from clean and renewable energy sources (AlMarri, Al-Habaibeh, & Watkins, 2018; Robert, Sisodia, & Gopalan, 2018). Renewable energy sources such as wind and solar, have vast potential to offer cost competitive energy solutions, reduce dependence on fossil fuels, and address environmental concerns associated with the electricity sector (Bazmi & Zahedi, 2011; Lund & Salgi, 2009). Many countries have now established ambitious renewable energy targets. In the United States (US), from 2007 to 2017 the investment in renewable generation, smart grid, storage, and electric transport technologies totaled $558 billion. Particularly for wind energy, the cumulative installed capacity of wind turbines in the US had reached 88.973 GW (16.5% of the world installed capacity) by the end of 2017 (Louw, 2019; US Department of Energy Office of Energy Efficiency & Renewable Energy, 2019). Jacobson et al. (2018) developed roadmaps to transition 53 towns and cities in North America to 100% wind, water, and sunlight in all energy sectors by no later than 2050, with at least ⁎

80% by 2030. The European Union (EU) is also on course to achieve its target of producing one-fifth of its energy from renewable sources by 2020 (Cruz & Dias, 2016). In 2013, new renewable energy generation capacity in China exceeded new fossil fuel and nuclear capacity for the first time. Australian Federal government policy also underpinned around 20% of Australia’s electrical energy from renewables (mainly wind and solar) by 2020. However, the volatile and intermittent nature of renewable energy sources has inhibited their wide utilisation. There has been increased demand for the deployment of energy storage (ES) as an essential component of future energy systems that adopt large amounts of variable renewable generation (Clark & Isherwood, 2004; Lokeshgupta & Sivasubramani, 2019; Lund, 2005; Nkwetta & Haghighat, 2014; Parra, Walker, & Gillott, 2014; Seddegh, Joybari, Wang, & Haghighat, 2017). More than 30 electrical energy storage (EES) technologies have been used worldwide, with over 500 pilot projects underway (Cavallo, 2001; Sundarabalan, Tejasree, Shankar, Puttagunta, & Vignesh, 2019). Amongst different types of EES technologies, pumped hydro (PH) energy storage and compressed air energy storage (CAES) systems can offer sufficient energy capacity, high cycle life and fast response time (Beaudin, Zareipour, Schellenberglabe, & Rosehart, 2010). Currently, PH is the most practical and mature energy storage technology and has

Corresponding author. E-mail address: [email protected] (X. Wang).

https://doi.org/10.1016/j.scs.2019.101527 Received 10 December 2018; Received in revised form 29 March 2019; Accepted 31 March 2019 Available online 15 April 2019 2210-6707/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature

C Cp Cv E h I m n P R s S T U v V w W

X

Exergy

Greeks

Specific heat Specific heat at constant pressure Specific heat at constant volume Stored energy Enthalpy Exergy Destruction Mass Polytropic constant Pressure Specific gas constant Entropy per unit mass Entropy Temperature Internal energy Specific volume Volume Work per unit mass Work

η ρ

Efficiency Density

Subscripts

0 c e ex h in out p s w

Atmospheric state Compressor Expander Exergy Hydro-turbine Input Output Pump Isentropic process Water

compression/expansion power ratio of 70/40. Also, Mozayeni, Negnevitsky, Wang, Cao, and Peng (2017) developed a thermodynamic model to evaluate the performance of an A-CAES system. In another research study, a hybrid energy storage system consisting of A-CAES and flywheel energy storage for wind power applications was proposed by Zhao, Dai, and Wang, (2014). One of the essential challenges of ACAES systems is to absorb and store the heat of compression in the TES. A significant amount of thermal energy is often lost from the TES and the storage cavern during the system operation. There are strict stability and maintenance protocols for the underground cavern to prevent its damage or/and collapse depending on its depth and pressure range (Ingersoll, Aborn, Blieske, Marcus, & Brookshire, 2015). Another inherent issue of A-CAES systems is that the outlet air temperature from the cavern continuously decreases during the power generation process. Hence, A-CAES systems are not typically able to generate power reliably (Nielsen & Leithner, 2009). Another concept proposed to improve the CAES system performance is the isothermal compression and expansion cycle. In a quasi-isothermal compression process, heat transfer is employed between the air and a high-density fluid, such as water, in the compressor/expander to allow the air to be compressed/expanded without noticeable temperature change. As a result, the required work for the compression process is minimised. Qin and Loth, (2016) and Qin, Loth, Li, Simon, and Van de Ven (2014) theoretically investigated the direct injection of water in the compressor for compressed air energy storage systems. Results showed that a multi-zone configuration was required to achieve good compression efficiency at both first- and second-stage compression cycles. Lim, Mazzoleni, Park, Ro, and Quinlan, (2013) proposed conceptual design for an isothermal ocean compressed air energy storage system. Such a system was further analysed and optimized by Park et al. (2012). In these systems, a water piston is applied to achieve an isothermal thermodynamic cycle. Although isothermal CAES systems are claimed to have high efficiency, the idea of using such systems was not very practical. It is because those typical compression processes take less than a second; however, isothermal compression takes much longer resulting in reduction in power density, long cycle times and requirement for large compressors/expanders (Lim et al., 2013; Srivatsa & Li, 2019). Also, the design of isothermal compressor and turbine is still a challenge despite many efforts that researchers have put in. In order to make use of the advantages of PH and CAES systems and resolve the inherent issues associated with these systems, Wang, Wang, Wang, and Yao (2013) proposed a hybrid pumped-hydro-compressedair (PHCA) energy storage system. Yao, Wang, Liu, and Xi (2014)

the highest penetration in the global energy storage market (99% of installed electrical energy storage) (Connolly, Lund, Finn, Mathiesen, & Leahy, 2011; Deane, Gallachóir, & McKeogh, 2010; Loose, 2011). Deane et al. (2010) reviewed the existing and future-planned PH plants and discussed the technical and economic drivers for PH storage systems. Capital costs per kW for a PH plant, according to this review, range between €470/kW and €2170/kW highly dependent upon site and project specifics. Nazari et al. (Nazari, Ardehali, & Jafari, 2010) introduced an optimization methodology and investigated the performance of a PH unit in a thermal generating unit. Results showed that the costs for fuel, start-up schedule and emissions of the thermal unit could all be minimized by use of the PH system. However, the dependence of the PH system on specific geological and environmental conditions, the need for water sources with relatively low evaporation, along with large investment prerequisites and long construction periods, makes the development of PH technology very difficult in many countries (Ibrahim, Ilinca, & Perron, 2008; Kapsali & Kaldellis, 2010). CAES is another large-scale energy storage technology (Barnes & Levine, 2011; Crotogino, Mohmeyer, Scharf, & Huntorf, 2001; Luo, Wang, Dooner, & Clarke, 2015; Succar & Williams, 2008). It has not been widely commercialised due to: its low efficiency; stability and sealing problems with the underground air storage cavern; auxiliary heating problems of compressed air; as well as geological constraints; and its complicated structure. To improve the CAES efficiency, the Adiabatic CAES (A-CAES) system was proposed (Liu et al., 2014; Succar & Williams, 2008; Succar, Denkenberger, & Williams, 2012). In an ACAES system, Thermal Energy Storage (TES) is utilized to extract thermal energy from the stage of air compression and reuse it for the air expansion and electricity generation process. With thermal energy recovery in the air compression process, A-CAES has the potential to achieve a higher cycle efficiency than conventional CAES (Grazzini & Milazzo, 2012; Hartmann, Vöhringer, Kruck, & Eltrop, 2012; Luo et al., 2015; Wolf & Budt, 2014; Wolf, 2011). Grazzini and Milazzo (Grazzini & Milazzo, 2012) performed a thermodynamic analysis of an A-CAES system with an artificial reservoir and hence proposed a set of criteria for the A-CAES system with particular attention to heat exchangers. Hartmann et al. (2012) conducted a simulation study of cycle efficiency of A-CAES systems, which showed the efficiency of a polytropic configuration is about 60%, and the efficiency of an ideal isentropic configuration is about 70%. Wolf and Budt (Wolf & Budt, 2014) recently proposed a low-temperature A-CAES design concept with cycle efficiency in the range 52–60%. Wolf (2011) further demonstrated that the most efficient compression configuration is a three-stage layout with a 2

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energy level in storage vessel and work output are improved. When electricity is required, the pressurized water flows out from the storage vessel and passes through the hydro turbine that drives the electric generator and generates electricity. The water from the hydro turbine exit flows back to the water reservoir for further use in the next cycle. During the energy charge process, as water is pumped into the PHCA storage vessel, air is compressed, and its temperature increases. The compressed air exchanges heat with the water via direct contact. The air compression in the storage vessel is a polytropic process. If the energy charging process is very slow allowing enough heat transfer, a great amount of heat is transferred between the air and water. The polytropic process is approaching to a quasi-isothermal compression process that minimizes the pump work required during the charging process. However, if the energy charging process is very fast and the compression air heat cannot be transferred to the water fast enough, the polytropic process is close to the isentropic process. During the energy discharge process, air is expanded, and its temperature drops. Heat transfers back from the water to the air, and the air expansion is also a polytropic process. This polytropic process is approach the quasi-isothermal expansion process if the energy discharge is very slow, whilst it is close to the isentropic process if the energy discharge process is very fast. Therefore, the isentropic and isothermal compression/expansion processes are the two extreme energy charging/discharging processes which are considered in this study to evaluate the performance of the PHCA system under different operating conditions.

further developed a mathematical model for a constant pressure PHCA system and evaluated the system performance. The performed economic analysis revealed that the constant-pressure PHCA system is more economic than CAES and PH energy storage systems because of its simple structure. Bi and Li (2015) and Bi, Liu, and Li (2016) further investigated the operational characteristics of the proposed system under different operating modes. However, these works are still in the preliminary research stage. Further research is needed to understand the system operating characteristics better. The PHCA is a new energy storage system which can be coupled with power generation from renewable energy sources such as wind and solar. For urban areas and remote communities such as small islands, stand-alone renewable energy power system will help the city and society to achieve sustainable future (Hamilton, Negnevitsky, Wang, & Lyden, 2019). The energy storage system plays a key role in such systems to maintain stable and high-quality electricity supply to end users. When designing a PHCA system, the system capacity, size of storage vessel, storage pressure and initial pressure largely depends on the availability and intermittent nature of wind and solar energy sources. The high fluctuation of wind and solar energy would lead to large capacity or high storage pressure of the PHCA system and low fluctuation might require a small capacity or low storage pressure system. Furthermore, the initial pre-set pressure and thermal compression mode in the storage vessel also have effects on energy storage level and system efficiency. Therefore, it is important to understand the operating behaviour of a PHCA system under different operating conditions. This will allow optimization of a PHCA system to suit for different characteristics of wind and solar energy systems. This paper aims to investigate the characteristics of a PHCA system under different operating conditions. The system performance is characterised by the pump power consumption, energy storage level in the vessel, work output from the turbine, overall system efficiency, and the exergy destruction in the pump and hydro turbine. A comprehensive thermodynamic and exergy model is developed to investigate (i) the system performance under different operating conditions; (ii) effect of the key operating parameters on the system performance of a PHCA system; (iii) the design bottleneck of the PHCA system to achieve an efficient and reliable system performance. The thermodynamic model is first used to identify the governing parameters of the PHCA system and investigate their effects on main characteristics of the system. Then, the exergy model is applied to evaluate exergy destruction of each system component to identify the design bottleneck. The results of this research provide researchers and engineers with useful information for the system design and optimization.

3. Mathematical model In order to conduct a thermodynamic and exergy analysis of the PHCA system, a thermodynamic and exergy model is developed based on mass and energy balance (Cengel & Boles, 2002; Kim, Shin, & Favrat, 2011; Woudstra, 2019) with the following assumptions:

• The air is treated as an ideal gas. • The kinetic and potential energy and pressure loss along the piping are ignored in the system. • There is no phase change of water in the storage vessel of the PHCA. • Initial air temperature during the charging process is assumed to be the ambient temperature.

3.1. Thermodynamic model 3.1.1. Pump Since the pressure inside the storage vessel varies from initial preset pressure to a storage pressure, the pump head varies according to the vessel pressure. The pumping power (wp) per unit mass at a given vessel pressure can be calculated using energy and mass balance and is expressed by Cengel and Boles (2002):

2. Working principles of the PHCA system Fig. 1 shows a schematic drawing of a PHCA system that consists of a compressed air-water storage vessel, a pump, a hydro turbine, a water reservoir, a small compressor, lots of piping and valves. The small compressor is used to pre-pressurize the air-water storage vessel at the initial stage. Once the system reaches real operating conditions, this is no longer required. Wherever there is excess energy from a renewable energy source such as wind and solar, this excess energy drives the water pump to pump water from the water reservoir to the storage vessel. The air volume in the vessel reduces, and the air is compressed as water is pumped into the storage vessel. The compressed air, in turn, pressurizes the water inside the vessel and hence a virtual dam is built between the water reservoir and the storage vessel. For example, a vessel with an interior pressure of 6 MPa represents a dam with a height of 600 m. The pumping process is continued until the pressure in the storage vessel reaches its high threshold called storage pressure. The storage pressure is designed based on the excess energy available from solar or wind energies in the operational area. If there is a large amount of excess energy, a higher value for the storage pressure is designed and/or large volume of the storage vessel is required. In this case, the

Fig. 1. Schematic configuration of a PHCA system. 3

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H. Mozayeni, et al. p

wp =

ηh is the efficiency of the hydro turbine.

P − P0 ρ

∫ vdp = po

(1)

3.1.4. Cycle efficiency Overall cycle efficiency of the PHCA system is defined as the ratio of total work output from the hydro turbine to total work input to the pump as the following:

where P is the outflow pressure, v is the water specific volume, ρ is the water density and P0 is the atmospheric pressure. The mass change of water in the storage vessel is expressed by,

dm = −ρdV

(2)

ηcycle =

where V is the volume of the sealed air in the storage vessel. The air compression process in the storage vessel can be modelled as a polytropic process (PV n=const.) while water is pumped into the vessel. Therefore, the total work per unit air volume required of a real pump to pump the water to increase the vessel pressure from P1 to P2 is calculated using the following equation: 1 1 ⎧ Wp ⎛ 1 ⎛ (P2n − 1 P1) n − P1 P1 ⎞ n ⎞ ⎞ ⎛ ⎪ 1 = − − P 0⎜ ⎟⎟n ≠ 1 V ηp ⎜⎜ n−1 ⎪ ⎝ P2 ⎠ ⎠ ⎟ ⎪ 1 ⎝ ⎝ ⎠ 1 ⎨ n ⎛ ⎞ W ⎛ ⎞ ⎪ p = 1 P ln P2 − P 1 − ⎛ P1 ⎞ 1 0⎜ ⎟⎟n = 1 ⎪ V1 ηp ⎜⎜ P1 ⎝ P2 ⎠ ⎠ ⎟ ⎪ ⎝ ⎝ ⎠ ⎩ ⎜

⎜

3.2.1. Pump The exergy balance for a water pump during the charging process is presented as follows (Kim et al., 2011; Woudstra, 2019), + − I˙p = X˙ p − X˙ p

⎟

(3)

+ X˙ p = W˙ p

⎜

⎟

⎜

⎜

hout , p − h 0 = Cw (Tout , p − T0) +

sout , p − s0 = Cw ln

(10)

P − P0 ρw

(11)

Tout , p (12)

T0

where h, s, C , ρ are specific enthalpy, specific entropy, specific heat and density, respectively, and m˙ w, p is the charging mass flow rate. The subscripts w, 0 represent the water and atmospheric states, respectively, and the subscripts out , p stand for the pump outflow. In Eq. (11), the term on the left-hand side is equivalent to the actual pump work wp and the second term on the right-hand side is the isentropic pump work wp, s . Consequently, the outflow water temperature from the pump is calculated by:

⎟

⎟

(4)

Tout , p = 3.1.3. Hydro-turbine When electricity is required, the high-pressure water stored in the vessel is released through a hydraulic turbine. The energy generated by an ideal hydro turbine (wh, s ) per unit mass at a given time is obtained using the relation below (Cengel & Boles, 2002):

1 (wp − wp, s ) + T0 Cw

(13)

The exergy efficiency of the water pump ηex , p is given by,

ηex , p =

X p− X p+

(14)

In which, the total exergy transfer to the water flow during the charging mode is given by:

V3

wh, s = −

(9)

− X˙ p = m˙ w, p [(hout , p − h 0 ) − T0 (sout , p − s0 )]

1

⎧ ΔEtotal ⎤ ⎛ P1 ⎡ ⎛ P2 ⎞ n P n⎞ ⎪ = − 1⎥ − P0 ⎜1 − ⎛ 1 ⎞ ⎟ n ≠ 1 ⎢ n − 1 ⎢ ⎝ P1 ⎠ ⎪ V1 ⎝ P2 ⎠ ⎠ ⎥ ⎝ ⎣ ⎦ 1 ⎨ n ⎪ ΔEtotal = P ln ⎛ P2 ⎞ − P ⎛1 − ⎛ P1 ⎞ ⎞ n = 1 1 0⎜ ⎟ ⎪ V1 ⎝ P1 ⎠ ⎝ P2 ⎠ ⎠ ⎝ ⎩

− X˙ p

and are where I˙p is the rate of exergy destruction in the pump, the rates of exergy transfer to the system by pumping work and exergy transfer from the pump to water flow, respectively. Assuming that the water flow is transferred to the pump under fixed atmospheric condi+ − tions (T0 = 20 oC , P0 = 1bar) , the two parameters X˙ p , X˙ p are expressed as (Kim et al., 2011; Woudstra, 2019),

3.1.2. Storage vessel During the charging process, water is pumped into the storage vessel. The air pressure increases and its volume decreases. Hence, energy is stored. This stored energy can be released during the expansion process to generate electricity. The total energy stored per unit volume is calculated based on the change in the internal energy of the air and is expressed by: n−1

(8) + X˙ p

⎟

⎟

(7)

3.2. Exergy model

where V1 is the air initial volume in the storage vessel, P1 and P2 are preset vessel pressure and storage pressure, respectively, and ηP is the pump efficiency. Also, n is the polytropic constant which is 1.4 for an isentropic process and 1 for an isothermal process (Cengel & Boles, 2002).

⎜

Wh WP

∫ vdp

(5)

V2

X p− =

During the discharging (expansion) process, the sealed air in the storage vessel is expanded from V2 to V3 and the storage pressure decreases from P2 to P3 . By considering the air expansion as a polytropic process (PV n=const.) , the total work output per unit volume of the storage vessel generated by a real hydro turbine is calculated using the following equation:

∫ X˙ p−dt

(15)

X p+

Also, is the total exergy transfer to the system by pumping work. This quantity is calculated by integrating Eq. (8) and by considering Eq. (1), as follows: 1 1 ⎧ X p+ ⎛ 1 ⎛ (P2n − 1 P1) n − P1 P n ⎞⎞ ⎪ = − P0 ⎜1 − ⎛ 1 ⎞ ⎟ ⎟ n ≠ 1 ⎜ V ηp ⎜ n−1 ⎪ ⎝ P2 ⎠ ⎠ ⎟ ⎪ 1 ⎝ ⎝ ⎠ 1 ⎨ + n ⎛ ⎞ ⎪ X p = 1 P ln P2 − P ⎛1 − ⎛ P1 ⎞ ⎞ n = 1 1 0⎜ ⎟⎟ ⎪ V1 ηp ⎜⎜ P1 ⎝ P2 ⎠ ⎠ ⎟ ⎪ ⎝ ⎝ ⎠ ⎩ ⎜

1 1 ⎧W ⎛ (P n − 1 P1 ) n1 − (P3n − 1 P1 ) n1 ⎛ P n P n ⎞⎞ ⎪ h = ηh ⎜ 2 − P0 ⎜ ⎛ 1 ⎞ − ⎛ 1 ⎞ ⎟ ⎟ n ≠ 1 ⎜ n−1 P3 ⎪ V1 ⎝ P2 ⎠ ⎠ ⎟ ⎪ ⎝⎝ ⎠ ⎝ ⎠ 1 1 ⎨ ⎪ Wh = η ⎛ (P n − 1 P ) n1 ln P2 − P ⎛ ⎛ P1 ⎞ n − ⎛ P1 ⎞ n ⎞ ⎞ n = 1 1 0⎜ h⎜ 3 ⎟⎟ ⎪ V1 ⎜ P3 P3 ⎝ P2 ⎠ ⎠ ⎟ ⎪ ⎝⎝ ⎠ ⎝ ⎠ ⎩ ⎜

⎜

⎟

⎜

⎟

⎜

⎟

⎜

⎟

⎟

(16)

⎟

(6)

3.2.2. Storage vessel During charging and discharging processes, exergy is transferred to

where P3 is the vessel pressure at the end of the expansion process and 4

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in which,

or extracted from the storage vessel. When water is pumped into the storage vessel, the air and water physical properties change from the initial state (State 1) to the final state (State 2). The change in exergy of the air and water in the vessel during this process is obtained using the following equations (Kim et al., 2011; Woudstra, 2019):

ΔXtotal,1 → 2 = [ΔXair + ΔXwater ]1 → 2

(17)

ΔXair = U2 − U1 + P0 (V2 − V1) − T0 (S2 − S1)

(18)

hin, h − hout , h = Cw (Tin, h − Tout , h) +

sin, h − sout , h = Cw ln

∫ X˙ p−dt

(19)

1

where 2

U2 − U1 = mair

Tout , h =

∫ Cv dT

(20)

1 2

⎡ S2 − S1 = mair ⎢ ⎣

∫ 1

(30)

Tin, h Tout , h

(31)

where m˙ w, h is the discharging mass flow rate. Subscripts in, handout , h represent the state at the inlet and outlet of the hydro turbine. In Eq. (30), by considering the left-hand side term as the actual work wh of the hydro turbine and the second term in the right-hand side as the isentropic work wh, s of the hydro turbine, the outflow temperature from the machine can be found using the following relation:

2

ΔXwater =

P − P0 ρw

1 [wh, s − wh] + Tin, h Cw

(32)

The exergy efficiency of the hydro turbine ηex , h is defined as below:

Cp (T ) T

P⎤ dT − R ln 2 ⎥ P1 ⎦

ηex , h =

(21)

(22)

ΔXair = U3 − U2 + P0 (V3 − V2) − T0 (S3 − S2)

(23)

(33)

where, Xh− is the total exergy transfer from the hydro turbine to the generator. By taking into account Eqs. (5) and (28), this term is defined as follows:

In these equations, U andS are the total internal energy and entropy, respectively. Also, R is the gas constant and Cp, Cv are the specific heat at constant pressure and volume, respectively. If the exergy loss is assumed to be negligible in the transmission pipelines between the pump and storage vessel, the rate of exergy transfer to the storage vessel with a reference state (T0, P0) is equal to that transferred to the water flow by the pump. When water flows out of the vessel, the exergy of the vessel gradually decreases. During the discharging process, the physical properties of air and water change from the initial state (State 2) to the final state (State 3). The exergy changes in the storage vessel due to the water discharging process is obtained using the equations below (Kim et al., 2011; Woudstra, 2019).

ΔXtotal,2 → 3 = [ΔXair + ΔXwater ]2 → 3

Xh− Xh+

1 1 ⎧ X− ⎛ (P n − 1 P1 ) n1 − (P3n − 1 P1 ) n1 ⎛ P n P n ⎞⎞ ⎪ h = ηh ⎜ 2 − P0 ⎜ ⎛ 1 ⎞ − ⎛ 1 ⎞ ⎟ ⎟ n ≠ 1 ⎜ n−1 P3 ⎪ V1 ⎝ P2 ⎠ ⎠ ⎟ ⎪ ⎝⎝ ⎠ ⎠ ⎝ 1 1 ⎨ − n n ⎛ ⎞ ⎪ Xh = η (P n − 1 P ) n1 ln P2 − P ⎛ ⎛ P1 ⎞ − ⎛ P1 ⎞ ⎞ n = 1 1 0⎜ h⎜ 3 ⎟⎟ ⎪ V1 ⎜ P3 P3 ⎝ P2 ⎠ ⎠ ⎟ ⎪ ⎝⎝ ⎠ ⎝ ⎠ ⎩ ⎜

⎜

⎟

⎜

⎟

⎜

⎟

⎟

(34) The term Xh+ is the total exergy transfer from the water flow to the hydro turbine and is calculated by:

X p+ =

∫ X˙ p+dt

(35)

3

ΔXwater =

∫ X˙ h+dt

4. Results and discussion (24)

2

The thermodynamic analysis is first verified using data available in the literature (Bi & Li, 2015) and then performed to investigate the effect of each key parameters on the pump power consumption, energy storage level in the vessel and work output from the turbine. Afterwards, the overall system performance and comparison between the proposed system and other large-scale energy storage systems such as PH and CAES are analyzed. The exergy analysis is further conducted to investigate exergy destruction of each major component in the system to identify the design bottleneck for a PHCA system. The key operating parameters of the PHCA system including pre-set pressure and storage pressure are selected based on the study in the literature (Bi & Li, 2015; Wang et al., 2013) and industrial energy storage systems (Venkataramani, Parankusam, Ramalingam, & Wang, 2016). The studied pre-set pressure ranges from 1 to 4 MPa and the storage pressure ranges from 4 to 16 MPa.

where 3

U3 − U2 = mair

∫ Cv dT

(25)

2

⎡ S3 − S2 = mair ⎢ ⎣

3

∫ 2

Cp (T ) T

dT − R ln

P3 ⎤ P2 ⎥ ⎦

(26)

As the exergy loss in transmission lines between the vessel and hydro turbine is negligible, the rate of exergy transfer from the storage vessel is equal to that transferred to the hydro turbine by the water flow + X˙ h . 3.2.3. Hydro turbine The exergy balance for a hydro turbine during the discharging process is obtained as (Kim et al., 2011; Woudstra, 2019): + − I˙h = X˙ h − X˙ h

4.1. Thermodynamic analysis

(27) The thermodynamic performance of the PHCA system is evaluated using the thermodynamic model under different working conditions. The effects of the governing parameters, such as the pre-set pressure, storage pressure, pump and hydro turbine efficiencies on the performance of the PHCA system are also presented. Results are presented for two extreme air compression/expansion processes in the vessel, namely, isentropic and isothermal. Generally, isentropic air compression or expansion may arise if the input/output flow rate is quite large and the period of charging/discharging process is short as discussed in

+ where, I˙h is the rate of exergy destruction, X˙ h is the rate of exergy − transfer from the water flow to the turbine and X˙ h is the rate of exergy transfer from the turbine to the generator. If the hydro turbine outflow + − pressure is assumed to reach atmospheric pressure, X˙ h and X˙ h are expressed as, − X˙ h = W˙ h

(28)

+ X˙ h = m˙ w, h [(hin, h − hout , h ) − T0 (sin, h − sout , h )]

(29) 5

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water in the storage vessel. According to Fig. 4, as the pre-set pressure rises from 0.6 MPa to 4 MPa at any specific storage pressure, the increase in air mass and final air volume will both cause an increase in the energy storage level. This increase is continued up to the optimum point. However, as the pre-set pressure goes beyond the optimum point, the reduction in the water pumped into the vessel leads to a decrease in the stored energy. Fig. 4 also shows that if the system is designed for a higher storage pressure, the optimum pre-set pressure is increased. For example, during an isentropic compression, the optimum pre-set pressure is 2.5 MPa at a storage pressure of 8 MPa while it is 3.2 MPa at a storage pressure of 10 MPa. This is because the high storage pressure reduces the effect of the final water volume at the end of the charging process. Once again, the result shows that more energy is stored during the isothermal compression process than that during the isentropic compression process. This figure shows that selection of a proper preset pressure is important to maximize the energy storage at a specific storage pressure. This in turn reduces the system size in the design. As discussed before, the actual air compression process in the storage vessel is polytropic due to heat transfer between air and water, and between the air and vessel surrounding. This polytropic process is bounded between the isentropic and isothermal processes. Fig. 5 shows the effect of the polytropic constant on the stored energy level. As the polytropic constant decreases from 1.4 (isentropic) to 1 (isothermal), the stored energy level increases. This is mainly due to heat transfer. As heat transfer between air and water increases, the compression process shifts from the isentropic process to the isothermal process. The compressed air volume decreases and more water is pumped into the vessel. Hence the stored energy increases. The figure also shows that the polytropic constant has a large effect on the optimal pre-set pressure. As the polytropic constant decreases from 1.4 (isentropic) to 1 (isothermal), the optimum pre-set pressure increases from 3.5 to 4.5 MPa at the given storage pressure of 12 MPa. This increase in the optimum preset pressure is mainly because of the improvement in the energy storage level as the polytropic index is lowered. This finding demonstrate the importance of the heat transfer in the storage vessel, which provides a guideline for engineers in the system design and optimization. Fig. 6 shows the work output per unit volume generated by the hydro turbine during the entire expansion process under isothermal and isentropic air expansion processes in the vessel for two pre-set pressures of 2 MPa and 4 MPa. According to the literature (Adhikari & Wood, 2018), hydro turbine efficiency typically ranges from 70% to 90%. Therefore, a hydro turbine efficiency of 80% is selected in the analysis. As the storage pressure increases from 4 to 16 MPa, the generated work per unit volume increases sharply. The increasing rate is more significant at the high pre-set vessel pressure than low pre-set pressure. For instance, under the isothermal air expansion process, as the storage pressure increases from 4 to 16 MPa, the output work of the hydro turbine increases from 1.069 MJ/m3 to 3.257 MJ/m3 at the pre-set pressure of 2 MPa and from zero to 4.376 MJ/m3 at the pre-set pressure of 4 MPa. This is mainly because the average water head inside the vessel is improved by increasing the pre-set pressure and hence more work is generated by the PHCA system. This figure also compares the work output between the isentropic and isothermal air expansion processes in the air storage vessel. The results show that more work is

the above section. On the other hand, isothermal air compression/expansion inside the vessel can be approximately achieved when a high heat transfer occurs between the air and water while water is pumped into or extracted from the vessel very slowly. To verify the thermodynamic model, Table 1 compared the simulated energy storage density with data available in the literature (Bi & Li, 2015) for a similar PHCA system under the same operating conditions. The comparison results showed that the simulated results in this study agreed well with the data presented in the literature. This indicates that the proposed thermodynamic model can be used to investigate the performance of the PHCA system. Fig. 2 shows the effect of storage pressure on the pump energy consumption under isentropic and isothermal air compression processes in the vessel. As the storage pressure increases from 4 to 16 MPa, the pump work input increases for both isentropic and isothermal compression processes. However, the increasing work input rate varies with the pre-set pressure. The increase in the pump work rises as the pre-set pressure increases. This is mainly because, by increasing the pre-set pressure, the average water pressure inside the vessel is raised. Thus, more pump work is required to increase the vessel pressure from one value to another. Another interesting point revealed in this figure is that, in general, the work input during the isothermal process in the vessel is higher than that during the isentropic process. For instance, by considering a pre-set pressure of 2 MPa, as the storage pressure is raised from 4 MPa to 16 MPa, the required pump work for the isothermal air compression increases from 1.782 MJ/m3 to 5.429 MJ/m3 while it increases from 1.408 MJ/m3 to 5.307 MJ/m3 for the isentropic air compression. This is mainly because the air can be compressed further in the isothermal process and the final compressed air volume is smaller in comparison to that in the isentropic process. Hence more water is pumped into the vessel. Fig. 3 shows the energy storage level in the storage vessel under isothermal and isentropic air compression processes. Generally, as the storage pressure in the storage vessel increases, the energy storage density in the system increases at a given pre-set pressure. However, the increasing rate of the energy storage density with respect to the storage pressure is not the same at different pre-set pressures. The lower the pre-set pressure, the lower the increasing rate in energy storage density as the storage pressure increases. The phenomenon of changing energy storage levels versus storage pressure can be explained using pumped hydro concepts. By pumping water into a storage vessel, it is pressurised within the vessel, and a virtual dam is built between the reservoir and the interior of the storage vessel. The greater the storage pressure, the higher the height of the virtual dam and, therefore, the greater the amount of stored energy in the PHCA system. For example, at a pre-set pressure of 2 MPa, as the storage pressure increases from 4 MPa to 16 MPa, the energy storage density increases from 1.336 MJ/m3 to 4.071 MJ/m3 for the isothermal air compression and from 1.056 MJ/m3 to 3.98 MJ/m3 for the isentropic air compression process. Fig. 3 also shows that more energy is stored in the PHCA system under the isothermal compression process than that under the isentropic compression process. This is because more water is pumped into the vessel with the isothermal compression process and hence more energy is stored. Fig. 4 presents the effect of pre-set pressure on the energy storage level in the proposed PHCA system under storage pressures from 8 to 16 MPa. It is noticed that the energy storage level is maximised at an optimum pre-set pressure for a given storage pressure. This optimum value varies with the storage pressure. As the pre-set pressure increases at any specific storage pressure, the air mass in the vessel and the air volume at the end of charging increase. It is inferred from Eq. (4) that the higher the air volume at the end of charging at the same storage pressure, the higher the energy storage level. On the other hand, if preset pressure increases, less water is pumped into the vessel to fill the gap between the pre-set and storage pressures. Hence, the level of stored energy decreases. Therefore, the optimal pre-set pressure is a trade-off between the air mass and final air volume with the amount of pumped

Table 1 Comparison of the energy storage density between present study and Ref. Bi and Li (2015).

6

Pre-set Pressure (MPa)

Temperature (oC)

5 5

25 25

Air Compression mode

Storage Pressure (MPa)

Energy Density This study

Literature (Bi & Li, 2015)

Isothermal Isothermal

10 15

3.42 5.43

3.78 6.04

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Fig. 2. The pump work versus storage pressure under isentropic and isothermal air compression processes in the vessel.

Fig. 3. The energy storage level versus storage pressure under isentropic and isothermal air compression processes.

Fig. 4. Energy storage level versus pre-set pressure. (a) Isentropic air compression; (b) Isothermal air compression.

extracted from the storage vessel if the sealed air in the vessel is expanded isothermally during the discharging mode. As an example, at a storage pressure of 16 MPa and pre-set pressure of 4 MPa, the PHCA system generates 3.838 MJ/m3 for an isentropic air expansion process and 4.376 MJ/m3 for an isothermal air expansion process, thus an increase of 14% in the work output. In other words, if the work output of the PHCA system is totally converted to the electrical power, the system can provide a power of 1.06 kW h/m3 for an isentropic air expansion and 1.21 kW h/m3 for an isothermal air expansion, which is 14% higher. These findings demonstrate that increasing heat transfer between the air and water during the discharging stage can increase work output because the air expansion process more closely approaches the isothermal process. The air compression and expansion processes are affected by the heat transfer between the air and water inside the vessel, and between the air and surroundings. The isothermal and isentropic processes are the two extreme heat transfer conditions. In practice, the air expansion and compression processes are generally polytropic. Fig. 7 shows the PHCA system efficiency for three distinctive cases of the sealed air in the storage vessel: a) polytropic index of air expansion process is higher than that of the air compression process; b) polytropic indexes of air compression and expansion are the same; and c) polytropic index of the

Fig. 5. Energy storage level versus pre-set pressure under different polytropic compression processes. 7

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performances of the D-CAES, PH and PHCA energy storage technologies are compared and presented in Table 2. The performance of the PHCA is calculated using the thermodynamic model and the data for PH and CAES are obtained from the literature (Rogers et al., 2014). The working principle of the proposed PHCA system is very similar to the PH system. In both systems, energy is consumed by the water pump to transfer the water from low pressure to high pressure level, and work is generated by the hydro turbine when the high pressure water flows through the hydro turbine. Hence, the efficiency of the PHCA and PH systems largely depends on the efficiency of the water pump and hydroturbine. Therefore, the proposed PHCA system showed a similar efficiency to the PH system. Since the efficiencies of the water pump and hydro turbine in the PHCA and PH systems are normally higher than the efficiencies of the air compressor and air turbine in the D-CAES system, respectively, the PHCA and PH systems showed much higher efficiency than the D-CAES system in the table. The operating hours depend on the size of the storage volume. Since the way of storing water in the PHCA and PH systems is similar, the operating hours are also similar depending on the size of the storage cavern. Furthermore, compared to the PH system, the PHCA system uses the compressed air to build the virtue dam in the storage vessel, which eliminates the geological requirements by the PH system. Compared to the CAES system, the water is the energy transformation medium and has much lower leaking rate than air in the CAES system.

Fig. 6. Hydro turbine work versus storage pressure under isentropic and isothermal air compression processes.

4.2. Exergy analysis Due to the irreversibility existing in real processes, entropy is generated, and exergy is destroyed. In general, exergy destruction can provide useful information to find out the bottleneck system component in the design of a whole system. Therefore, it is important to investigate the exergy destruction of the major components in a PHCA system. Figs. 8 and 9 show variations of exergy destruction per unit volume of the vessel for the pump and hydro turbine, respectively. The storage pressure varies from 4 to 16 MPa and selected efficiencies for the pump and hydro turbine are 0.65 and 0.85. In each figure, both isentropic and isothermal air compression/expansion processes are studied, and the pre-set pressure is 2 MPa. In general, the trends of exergy destruction for the pump and hydro turbine are similar. The amount of destroyed exergy in both pump and hydro turbine increases as the storage pressure increases. This increase strongly depends on the efficiency of the component. Utilizing a high-efficient pump/hydro turbine can dramatically reduce the exergy destruction for the pump and hydro turbine. In other words, it can improve the PHCA system efficiency and make the system more cost-effective. Furthermore, the results reveal that, at a given storage pressure, more exergy is destroyed in the pump/hydro turbine if the air compression/expansion is isothermal. Figs. 10 and 11 present the effect of vessel pre-set pressure on the magnitude of exergy destruction during charging and discharging processes for the isentropic and isothermal air compression/expansion processes. The storage pressure remains at 10 MPa. As the pre-set pressure increases from 0.6 to 4 MPa, the exergy destruction firstly increases in both pump and hydro turbine until it reaches a peak value and then the change in exergy destruction becomes negligible as the pre-set pressure continues increasing after the peak value. This

Fig. 7. Overall system efficiency for different polytropic compression and expansion cases at ηh = 85%. (n: polytropic constant. (a) nexp > ncomp, (b) nexp=ncomp, (c) nexp < ncomp).

air compression is higher than that of the air expansion. These results were obtained for the pre-set and storage pressures of 4 MPa and 16 MPa, respectively. The hydro turbine efficiency is assumed to be 85%. For a given component efficiency, the system has a higher efficiency if the polytropic index for the air expansion is smaller than that for the air compression. By improving the heat transfer in the storage vessel during the discharging (expansion) mode, the polytropic index is lowered, and the system produces more work output leading to an improvement of the PHCA system efficiency. Since both Diabatic CAES (D-CAES) and PH have been commercialized (Rogers, Henderson, Wang, & Negnevitsky, 2014), the Table 2 Comparison of three EES technologies. EES Characteristic

PH [Ref. 53]

D-CAES [Ref. 53]

PHCA

System efficiency

70-85% 0.5 – 1.5

42-54% 3-8

60-80% 0.4 – 1.5

1-24 hrs Evaporation Geological requirements

20 hrs Air leak Thermal energy loss and air leak

1-24 hrs Negligible air leak No Geological requirement, less thermal energy loss and air leak

Energy density, kWh/ m3 Energy output period Self-discharge rate Constraints

8

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Fig. 8. Pump exergy destruction versus storage pressure under isentropic and isothermal air compression processes in the vessel.

Fig. 9. Hydro turbine exergy destruction versus storage pressure under isentropic and isothermal air compression processes in the vessel.

Fig. 10. Pump exergy destruction versus pre-set pressure at the storage pressure of 10 MPa under two air compression processes, (a) Isentropic compression process, (b) Isothermal compression process.

tendency is more pronounced at the low isentropic efficiency. At a high efficiency, the change in exergy destruction versus pre-set pressure is generally negligible. The results also show that more exergy is destroyed in the pump or hydro turbine when the air compression/expansion process in the storage vessel is isothermal. This is mainly because more water is pumped into the vessel and hence more energy is stored for the isothermal air compression process in the vessel. Furthermore, for both pump and hydro turbine, the exergy destruction decreases as the efficiency of the pump and hydro turbine increases. This is consistent with the common practice that high efficiency of the pump and hydro turbine will always be desired to improve the overall system efficiency of the PHCA system. Fig. 12 shows the exergy destruction in the storage vessel. As the storage pressure increases, the exergy destruction increases. However, the results show that the exergy destruction in the storage vessel is insignificant. This is mainly because most of the stored energy can be effectively converted into mechanical work. Both isentropic and isothermal processes have no irreversible losses. However, in the storage vessel, the heat transfer inside the vessel is very complicated, which substantially affects the air compression process and hence the PHCA system performance as shown in Fig. 5. This requires a comprehensive three-dimensional computational simulation that will be conducted in a

separate article. It is important to realise which component has high exergy destruction and so is a design bottleneck for a PHCA system. Fig. 13 shows the distribution of exergy destruction in the pump, hydro turbine and storage vessel. The efficiency of the pump and hydro turbine is set to the same value of 0.75. Also, the pre-set pressure is 2 MPa, and the air compression/expansion process in the vessel is assumed to be isentropic. As discussed in the above section, if the storage pressure increases, exergy destruction increases in all system components and hence the total exergy destruction increases. It shows that the exergy destruction in the pump is much higher than that in the hydro turbine. For instance, at a storage pressure of 10 MPa, exergy destruction in the pump is 0.97 MJ/m3 (about 57% of the total exergy destruction) while it is only 0.73 MJ/m3 (42% of the total exergy destruction) for the hydro turbine. This indicates that a higher portion of energy is wasted in the pump than in the hydro turbine. In practice, the efficiency of the pump is normally lower than that of the hydro turbine due to the nature of the losses in the two components. This means that the pump exergy destruction can be even higher than that of the hydro turbine. Therefore, the pump is the most important component that affects the overall 9

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Fig. 12. The vessel exergy destruction versus storage pressure under isentropic and isothermal air compression processes.

Fig. 13. Distribution of exergy destruction in different components vs the storage pressure.

Fig. 11. Hydro turbine exergy destruction versus pre-set pressure at the storage pressure of 10 MPa under two air expansion processes, (a) Isentropic compression process, (b) Isothermal compression process.

both isentropic and isothermal air compression/expansion processes within the storage vessel. The thermodynamic analysis showed that the pump energy consumption increases with the storage pressure. Also, by increasing the storage pressure, the energy storage level in the storage vessel increases since the air can be further compressed in higher storage pressures and hence the work output from the hydro turbine is improved. Results also showed that an optimal pre-set pressure exists to maximize the energy storage at each specific storage pressure. Furthermore, the PHCA system has better system efficiency if the polytropic expansion constant is smaller than the polytropic compression constant in air storage vessel during the energy charging and discharging processes. It was shown that about 10% more energy stored in the storage vessel under an isothermal air compression process and 14% more work output is from the hydro turbine under an isothermal air expansion process in the storage vessel. In the exergy analysis, results showed that storage pressure had a large influence on exergy destruction. As the storage pressure increases from 4 to 16 MPa, the exergy destruction in the pump and hydro turbine increases under the different pump and hydro turbine efficiencies. This increase is more substantial if the efficiency of the pump and the hydro turbine is low. The pre-set pressure also showed a significant effect on the distribution of exergy destruction in both pump and hydro

efficiency of a PHCA system. When designing and optimizing the PHCA system, a highly-efficient pump is firstly desired to improve the system performance. Meanwhile, the hydro turbine also shows substantial exergy destruction. Increasing the efficiency of the hydro turbine will also reduce exergy construction as discussed in Fig. 9 in the above section. Study to improve the efficiency of the hydro turbine is another important research topic. This figure also reveals that the difference in exergy destruction between the pump and the hydro turbine gets larger as the storage pressure increases. As for the exergy destruction in the vessel, the value is small due to the reasons mentioned above. However, as shown in Fig. 5, heat transfer between air and water, and between air and surrounding environment substantially affects the air compression process and hence affects the amount of energy stored. Therefore, it is also important to investigate further the thermal characteristics inside the storage vessel.

5. Conclusion In this paper, a comprehensive thermodynamic and exergy analysis was conducted to investigate the performance of a PHCA system under 10

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turbine at low component efficiencies. However, this effect was not significant at high component efficiencies. Analysis of the exergy destruction distribution showed that the pump accounted for the largest exergy destruction (57% of the total exergy destruction). This indicated that the pump is the most important component in the design of a PHCA system. Furthermore, the hydro turbine also presented high exergy destruction, which indicated a highly-efficient hydro turbine is desired to improve the PHCA system performance.

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