Thermodynamic analysis of pumped thermal electricity storage

TL;DR: In this paper, the authors studied the thermodynamic aspects of PTES, including energy and power density, and the various sources of irreversibility and their impact on round-trip efficiency.

About: This article is published in Applied Thermal Engineering.The article was published on 2013-05-02 and is currently open access. It has received 167 citations till now. The article focuses on the topics: Energy storage & Thermal energy storage.

Summary

1.1 Other storage technologies

• The list of possible, alternative storage methods is extensive and includes: flywheels, super capacitors, batteries and flow batteries, Compressed Air Energy Storage (CAES), Superconducting Magnetic Energy Storage (SMES) and Thermal Energy Storage (TES) in its various forms.
• Some (e.g., flywheels and super capacitors) have very high efficiency, fast response and high power density, but are only able to supply power for short durations.
• They are therefore most appropriate for power quality management applications – e.g., bridging short-duration interruptions and providing voltage and frequency support during rapid supply or demand swings.
• For energy management applications – e.g., levelling daily demand fluctuations and smoothing the output from intermittent renewable sources – CAES is probably the leading competitor to Pumped Hydro Storage (PHS), but it too suffers geographic limitations since large, robust caverns are required for the storage of air at pressures up to 100 bar.
• Amongst the other candidate technologies, few are currently able to provide both multi-megawatt scale capacity and long-duration (i.e., hours) discharge; many are expensive (often several times the cost of open-cycle standing reserve gas turbines in terms of £/kW installed capacity), and many make use of hazardous, toxic or scarce materials.

1.2 Description of the PTES system

• The subject of the current paper, PTES, is a recent concept which is currently being developed in the UK (see for example ref. [4]) and is also being considered in France [5].
• During charge, the system operates as a high temperature-ratio heat pump, using electrical energy to extract heat from CS and deliver heat to HS.
• This takes place by the progression of hot and cold fronts in the stores, as indicated in the layout figure.
• (Note that if reciprocating devices are used, the flow directions of C and E can be reversed during discharge such that they become an expander and compressor respectively.).
• It is based on well-established technologies and it is therefore possible to estimate its likely performance (round-trip efficiency, storage density and capital cost) with a reasonable level of confidence.

2 Simplified cycle calculations

• The potential success of PTES hinges upon obtaining a satisfactory round-trip efficiency (i.e., electrical energy output/electrical energy input) whilst simultaneously keeping capital costs as low as possible.
• Ultimately, successful design will require comprehensive system modelling, taking into account a wide variety of economic, thermodynamic, mechanical, electrical and other factors.
• Such modelling is underway, but in anticipation of its completion the authors present here instead a simplified model which, nonetheless, provides a basic understanding of how the main operating conditions and loss parameters influence performance.
• The focus is upon thermodynamic aspects of PTES since electrical and mechanical issues are common to several other storage methods.

2.1 Energy and power density

• For a given technology, the capital cost per unit energy storage capacity (in £/kWh) and per unit power capacity (in £/kW) will depend inversely on the energy storage density, ρE, and power density, ρP, respectively.
• These are thus key performance parameters for any storage method.
• The round-trip efficiency for the reversible cycle is unity by definition, irrespective of the cycle pressures and temperatures, but it is nonetheless useful to consider this case as it provides reasonable estimates for ρE and ρP.
• The following may be deduced from these expressions: i. Both the energy and power density are monotonically increasing functions of the temperature ratio τ, which depends on the pressure ratio and the isentropic index (γ) of the gas.
• Table 1 shows estimates of the energy and power densities for PTES compared with pumped hydro and compressed air storage.

2.2 Approximate susceptibility to irreversibility

• System irreversibilities tend to reduce expansion work outputs and increase compressor work inputs during both charge and discharge.
• An approximate estimate of how operating conditions influence the round-trip efficiency for the real system can thus be obtained by scaling compression work by 1/η and expansion work by η, where η may be interpreted here as an average isentropic efficiency.
• The ratio R may be increased by increasing the pressure ratio, decreasing the hot reservoir discharged temperature, T3, or increasing the cold reservoir discharged temperature, T1, all of which are consistent with improving the energy and power densities.
• (These two values of θ bracket the likely practical range and intermediate values provide curves that are intermediately located − i.e., the dependence on θ is monotonic.).
• Such benefits would not be realised, however, if the maximum and minimum temperatures within the cycle were to be constrained, as discussed below.

2.3 Detailed loss analysis

• The aim of this section is to describe the various sources of loss and provide preliminary estimates of their impact on round-trip efficiency.
• The chief sources of loss are as follows: i. Electrical and mechanical losses.
• Reciprocating devices are thus modelled here by specifying (a) a polytropic efficiency to account for thermal dissipation and mixing, and (b) a heat loss (or gain) factor, α, defined as the ratio between net heat transfer and work transfer.
• Firstly, heat exchange with the exterior means that the available energy stored within each reservoir is depleted with time.
• If the discharge pressure ratio is the same as that for charging (Fig. 3a) then the compressor delivery temperature, T3′, lies above T3 and so heat rejected via HX2 (see Fig. 1) such that HS can be restored to its initial, discharged state.

2.3.1 General expression for round-trip efficiency

• The 1/(1–α) factors reflect the occurrence of both heat and work transfer during each of the compression and expansion processes (see ref. [7]).
• This reflects the fact that heat transfer will be to the surroundings for hot components and from the surroundings for cold ones.
• Note that a 10% heat loss from a compressor combined with a 90% polytropic efficiency gives rise to an isentropic process, but the effect is quite different to that of adiabatic reversible compression.

2.3.3 Impact of reservoir heat leakage on efficiency

• The effect of heat leakage to or from the reservoirs (as opposed to losses due to irreversible heat transfer) can be assessed by considering the total availability stored in the HS and CS.
• (Note that for a reversible PTES system, T4/T1 = T3/T2 so the logarithmic terms cancel and an expression similar to Eq. (1) is recovered.).
• Rates of heat loss will be proportional to the difference between the reservoir and environment temperatures, hence the authors write δT2 = –ε(T2–T0) and δT4 = –ε(T4–T0).
• The factor ε, which, for simplicity, is assumed the same for the HS and CS, will depend on the level of insulation and the storage duration.
• This equals 2 if θ = 1 (i.e., T3 = T1, as in ref. [4]), reflecting the fact that heat losses reduce both the stored thermal energy and the efficiency with which it can be converted back into useful work.

2.3.4 Impact of reservoir thermal irreversibility

• Krane [8] has analysed the destruction of availability within a thermal reservoir and conluded that the majority of the entering available energy would be lost.
• His analysis was for a fluid-based storage system for which much of the loss is due to mixing.
• It is worth pointing out that steady state, periodic operation necessarily incurs an exit loss, as suggested by curve (iii) in Fig. 4b which shows the situation near the end of the charge phase and indicates the temperature at the exit of the reservoir beginning to rise.
• This expression does not include the exit loss and the loss associated with thermal equilibration during storage, but these losses are relatively small provided the reservoirs are operated sensibly [10].

2.4 Graphical representation of sensitivity factors

• For the reservoir losses it has been assumed that T3 = T0, as discussed in section 2.3.3.
• Note also that the reservoir thermodynamic loss factor ξ is not strictly a sensitivity factor (i.e., it is not a partial derivative of χ), but the curves nonetheless show the relative temperature dependence of these losses; an arbitrary value of k = 1/2 has been used for the results shown.

3 Discussion

• The results presented in Fig. 5 demonstrate a number points which are of use in guiding research and design efforts.
• The round-trip efficiency is particularly susceptible to the compression and expansion polytropic efficiency, especially at low temperature (and hence pressure) ratios.
• The situation is improved by reducing the ratio θ, in accord with the approximate analysis based on work ratio given in section 2.2.
• This has been the strategy adopted for the turbomachinery-based design presented in ref. [5].
• Pressure losses seem to have a relatively small impact, provide the pressure ratio is not too low.

4 Conclusions

• A new method of electricity storage (PTES) has been described and aspects of its thermodynamic performance investigated, with particular focus on how various sources of loss affect the round-trip efficiency.
• The analysis presented has been very much simplified in order to show general trends which will help guide design.
• Approximate analysis also indicates that, for given compression and expansion efficiencies, it is really the ratio between the highest and lowest temperatures in each of the reservoirs (R=T2/T3= T1/T4) and not the compression temperature ratio that determines the performance.
• Obtaining a satisfactory round-trip efficiency clearly requires highly efficient compression and expansion processes, and it is anticipated that this may be achieved by the use of reciprocating devices.
• Ultimately, however, selecting the optimal operating conditions will require reliable estimates of the various loss parameters which depend on detailed design and, in some cases, are currently subject to a degree of uncertainty.

Figures

Figure 3: Temperature-entropy diagrams for irreversible PTES cycles

Figure 1: Layout of a PTES system and T-s diagram of the ideal cycle shown during charge

Table 1: Energy and power densities for a few storage technologies

Figure 4: Reservoir temperature profiles for different modes of operation (taken from [10])

Figure 2: Approximate round-trip efficiency and energy density for θ=1 (bold) and θ=0.4 (faint)

Figure 5: Variation of the loss sensitivity factors with isentropic temperature ratio for θ=1 (bold) and θ=0.4 (faint). Note that the ξ curves (right-hand figure) are with k=1/2.

Frequently asked questions

Q1. What are the contributions in "Thermodynamic analysis of pumped thermal electricity storage" ?

This paper is concerned with a relatively new concept which will be referred to here as Pumped Thermal Electricity Storage ( PTES ), and which may be able to make a significant contribution towards future storage needs. The paper focuses on thermodynamic aspects of PTES, including energy and power density, and the various sources of irreversibility and their impact on round-trip efficiency. 

Q2. What is the effect of system irreversibilities on the efficiency of a gas turbine?

System irreversibilities tend to reduce expansion work outputs and increase compressor work inputs during both charge and discharge. 

Q3. What is the effect of a sloping front?

The sloping front constitutes a loss of stored available energy and also prevents the reservoir from being fully charged without hot (or cold) gas first issuing from the exit, thereby incurring an exit loss. 

Q4. What is the effect of a compression heat loss during the charging phase?

A compression heat loss during the charging phase, for example, will reduce the storage temperature (and hence reduce the stored energy), but it will also reduce the work input for the compression process. 

Q5. How can one estimate the thermal losses of a reservoir?

Since reservoir thermal losses clearly depend on the charge-discharge history, accurate modelling can only really be undertaken by developing an overall system model that couples unsteady heat transfer calculations with thermodynamic cycle calculations, and includes the time-varying characteristics of the electrical network to which the storage system is connected. 

Q6. What is the impact of the reciprocating device on the round trip efficiency?

In terms of impact on the round-trip efficiency, it is the fractional pressure loss, f = Δp/p, in each device that is most relevant since this is proportional to the entropy increase and hence to the lost work. 

Q7. What is the advantage of reducing the ratio between hot and cold store discharged temperatures?

For a turbomachinery-based PTES system, the effects of compression and expansion irreversibility can be mitigated by reducing the ratio between hot and cold store discharged temperatures, which also has the advantage of increasing the energy and power densities. 

Q8. What is the effect of a in the periodic cyclic mode?

It is most likely that PTES will be used in the periodic cyclic mode and, in any case, the effect of a is relatively small so it is set to zero in what follows. 

Q9. What is the way to reduce the discharge pressure ratio between successive cycles?

Note also that using a lower discharge pressure ratio and then bypassing HX1 enables θ = T3/T1 to be reduced between successive cycles in order to obtain the benefits described in sections 2.1 and 2.2. 

Q10. What is the entropy generation rate for the gas-solid interfacial area?

The net entropy generation rate due to heat transfer between gas and solid is given by:g sg s( )T T S h dA T T − = ∫ [12]where h is a surface heat transfer coefficient, Tg and Ts are the local gas and solid temperatures, and the integration is carried out over the entire solid-gas interfacial area, A. 

Q11. Why is Argon proposed as the working fluid?

It is for this reason that Argon is proposed as the working fluid, rather than air, since the same value of τ can be achieved at a lower pressure ratio due to Argon’s higher isentropic index. 

Q12. What is the effect of the different temperature ratios on the compressor?

The various temperature ratios, τ, are related to the corresponding pressure ratios, β, by expressions of the form τ = βn, where n = (γ–1)(1–αe)ηe/γ for expanders and n = (γ–1)(1–αc)/ηcγ for compressors (see ref. [7] for derivation). 

Q13. What is the round-trip efficiency for the reversible cycle?

The round-trip efficiency for the reversible cycle is unity by definition, irrespective of the cycle pressures and temperatures, but it is nonetheless useful to consider this case as it provides reasonable estimates for ρE and ρP. 

Q14. How is the entropy generation rate calculated?

The loss in availability is given by integrating this entropy generation rate over the charge-discharge periods and multiplying by the environment temperature, T0. 

Q15. What is the coefficient of a for high frequency cycles?

The coefficient a varies from 0 for high frequency cycles (analytical solution) to 1/12 for single charge operation (numerical approximation, but with very small error). 

Q16. What is the way to restore HS to its initial discharged state?

If the discharge pressure ratio is the same as that for charging (Fig. 3a) then the compressor delivery temperature, T3′, lies above T3 and so heat rejected via HX2 (see Fig. 1) such that HS can be restored to its initial, discharged state. 

Q17. What is the way to determine the efficiency of a PTES system?

Comparisons between technologies should be treated with caution, but it is nonetheless reasonable to conclude that PTES has very good energy density and a power density that is not too much below that of a low-spec gas turbine.