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Journal ArticleDOI

Parametric studies and optimisation of pumped thermal electricity storage

TL;DR: In this paper, a thermodynamic analysis is presented based on traditional cycle calculations coupled with a Schumann-style model of the packed beds, and results of an optimisation study are then given in the form of trade-off surfaces for roundtrip efficiency, energy density and power density.
About: This article is published in Applied Energy.The article was published on 2015-01-01 and is currently open access. It has received 182 citations till now. The article focuses on the topics: Energy storage & Cryogenic energy storage.

Summary (6 min read)

1. Introduction 1

  • The finite nature of fossil fuel reserves together with a wide range of health and environmental concerns 2 arising from the release of combustion products have been acting as drivers for the increasing uptake of 3 renewable sources of energy, such as solar and wind [1].
  • 30 31 The present paper focuses on a form of TES system referred to here as ‘pumped thermal’ electricity storage 32 (PTES)*, several independent patents for which seem to have emerged almost simultaneously [4]–[7].
  • For the system 10 proposed in Ref. [6] however, compression and expansion are achieved by reciprocating devices since there 11 is evidence that these are capable of higher polytropic efficiencies than turbomachinery.
  • System optimisation remains a complex task due to 29 the large number of operational and design parameters, the multiple and often conflicting objectives (e.g. 30 efficiency and energy/power density) and the uncertainty associated with some aspects of the loss modelling.

2. Baseline Design 36

  • A system of this size has been adopted for the analysis presented here and it is useful to first provide 38 estimates for the main system parameters.
  • The power and storage capacity given below are ‘nominal’ 39 values in the sense that they are the values that would be achieved in the absence of losses and in the 40 case where the reservoirs can be fully charged.

2.1 Operating pressures and temperatures 1

  • Figure 1 shows the basic layout of a PTES system, together with T-s (temperature-entropy) diagrams for 2 typical discharge and charge processes, which follow the standard and reverse Joule cycle respectively.
  • The 3 main system components are two compression-expansion devices (CE and EC) and two thermal reservoirs 4 (one hot, HR, and one cold, CR).
  • Following [6], the discharged state of the reservoirs is set close to 5 ambient temperature: 310 K in the present case.
  • With argon as the working fluid (as proposed in Ref. [5]), 6 and with a pressure ratio of 10:1, the nominal hot and cold storage temperatures (based on isentropic 7 compression and expansion) are then 778 K and 123 K respectively.

2.2 Reservoir sizing 10

  • For a reversible, adiabatic PTES system, the stored energy that can be converted back to useful work (i.e., 11 the ‘available’ energy) is simply the difference between the stored internal energies of the two reservoirs, 12 E = Ms hcs h(T2 −T3)−.
  • The right hand equality in 15 Eq. (1) arises from the requirement that the two reservoirs should charge in the same period and must 16 therefore have the same heat capacity.
  • As discussed in Ref. [13], Fe3O4 provides a suitable storage material 17 due to its high heat capacity per unit volume and its low fractional variation of heat capacity over the 18 temperature ranges of interest.
  • The reservoir volumes are also given in the table, calculated 20 on the basis that the storage material is in the form of a packed bed of spherical pebbles with an average void 21 fraction of 0.35.
  • Note that these volumes would correspond to ‘square’ (i.e., L/D=1) cylinders with internal 22 diameters of 4.5 m and 5.3 m for the hot and cold stores respectively.

2.3 Compression and expansion device sizing 25

  • The resulting swept volumes are shown 35 in Table 3, together with various cylinder dimensions computed on the basis of 6-cylinder devices running 36 at 1200 RPM, with each cylinder having an aspect ratio (stroke/diameter) of 0.25.
  • This low aspect ratio is 37 proposed in the designs described in Ref. [12] on the grounds that the resulting low piston velocity will 38 give low valve pressure losses and low inertial loading.

2.4 Other design considerations 1

  • In addition to the main components described above, the PTES system also requires heat exchangers (HX1 2 and HX3 in Fig. 1), and a buffer vessel .
  • The heat exchangers are needed to counter the 3 effects of irreversibility throughout the system and their size can only be determined, therefore, after 4 consideration of the cycle efficiency.
  • The buffer vessel is required because the total mass of gas within the 5 two reservoirs changes during charge.
  • The total change between fully charged and fully discharged for the 6 nominal design is 142 kg, as indicated from the figures in Table 2.

3. System and Component Modelling 10

  • In order to determine the influence of the various system parameters on round trip efficiency, power 11 density and storage density, a simple system model has been developed based on quasi-steady analysis of 12 each of the system components.
  • Heat exchangers, compressors and expanders are treated as steady flow 13 devices (in the time-averaged sense), but the equations governing heat transfer within the reservoirs are 14 integrated in time in order to track the hot and cold thermal fronts.
  • This is necessary because the stored 15 available energy and the exergetic losses in the reservoirs are dependent upon the time-history of their 16 operation, as described in Refs. [13,14].
  • For the other components, estimates are first made for various loss 17 parameters, based on the nominal design described above.
  • Several of these parameters are, however, 18 subject to considerable uncertainty, either because they depend on detailed design (e.g., pressure losses 19 within pipework) or because the underlying theory has not yet been sufficiently developed (e.g., for 20 compression and expansion efficiencies).

3.1 Compression and expansion losses 25

  • The simplest approach for modelling ‘steady flow’ compressors and expanders is by either an isentropic or 26 polytropic efficiency.
  • For turbomachines, published data suggest polytropic efficiencies (i.e., infinitesimal 27 stage efficiencies) of about 90% are achievable.
  • Much of the loss in reciprocating devices is associated with valve pressure drop and there 30 may be scope for considerable improvement.
  • Similar expressions to (4) and (5) apply to expansion 1 processes.
  • The fundamental difficulty lies in estimating values for α and η.

3.2 Pressure losses 11

  • Pressure losses in valves, pipework, heat exchangers and the reservoirs all contribute to the expander 12 seeing a lower pressure ratio than the compressor.
  • These losses are represented here by fractional pressure 13 loss factors, fp = Δp/p, since these are most closely tied to exergetic losses.
  • But losses within 16 manifolds, ducts and heat exchangers etc. cannot easily be estimated without knowledge of the detailed 17 geometry, and so a range of fp values has been considered.
  • 20 Pressure losses in the reservoirs are treated separately and calculated explicitly, as discussed below.

3.3 Thermal reservoir losses 23

  • The main sources of loss within the reservoirs are frictional pressure loss and heat transfer 24 irreversibility.
  • Estimates suggest that a 1% heat leakage to or from each reservoir would typically 26 reduce round-trip efficiency by about 2% since leakage reduces both the stored energy and the Carnot 27 efficiency at which that energy can be converted to work [9].
  • The model used to quantify these losses is based on the well-established Schumann model of 31 heat transfer in packed beds [17], which assumes that the flow is one-dimensional and that heat transfer is 32 limited by surface effects (i.e., the internal thermal resistance of particles is negligible).
  • Most of these have only a minor impact, but the variation of cs 5 can significantly affect the thermal losses.
  • Full details of the numerical method are given in Refs. [13] and 6 [14], and typical temperature profiles for a cold reservoir are shown in Fig.

3.4 Heat exchanger and other losses 21

  • Geometric and other design details of the heat exchangers have not been included at this stage.
  • Instead 22 datum temperatures at Points 1 and 3 in the cycle are specified for each calculation and the heat exchange 23 required to maintain these temperatures is then computed.
  • As noted above, heat rejection must occur in 24 order to counter irreversibility throughout the cycle and, because it occurs at above the environment 25 temperature, there is a further exergetic loss associated with the heat exchangers themselves.
  • In addition, 26 there is a small throttling loss associated with returning the buffer volume gas to the low-pressure part of 27 the cycle.
  • Estimates indicate that this is very small and it has been neglected in these calculations.

4. Parametric Studies 30

  • Before presenting an optimisation study, it is useful to examine how the various system parameters impinge 31 upon overall performance.
  • Loss factors, operating conditions and geometric parameters have all been 32 varied over the ranges shown in Table 4.
  • As each quantity is varied, all others listed in the table are held at 33 their nominal values, except when varying pressure ratio, as discussed further below.

4.2 Variation of performance with operating conditions 23

  • Figure 4 shows the effect of various cycle operating conditions on efficiency and power density.
  • Pressure losses in the reservoirs are then adjusted in accord with Eq. 26 (11), but the nominal fp values have been retained for valve, pipework and manifold losses.
  • These 30 trends are consistent with the findings reported in Ref. [9] where it was argued that, if compression and 31 expansion losses dominate, then the efficiency is governed mainly by the ratio T2/T3 since this determines the 32 ratio between compression and expansion work.
  • If the maximum and minimum cycle temperatures (T2 and T4) are fixed, 38 instead of fixing T1 and T3, then variation of the pressure ratio gives trends similar to those observed for gas 39 turbine cycles for which there are optimum pressure ratios, as shown in Fig. 4(b).
  • This precludes the possibility of rejecting heat in HX3, 42 making it difficult to manage the thermal fronts as they emerge from the reservoirs.

4.3 Variation of performance with geometric factors 10

  • The geometric parameters varied here are the hot and cold reservoir aspect ratios (L/D) and particle 11 diameters, dp.
  • The resulting maxima in efficiency shown in Fig. 5 reflect the trade-off, inherent in most 12 heat exchange processes, between heat transfer losses and pressure losses.
  • Small particles 13 give large heat exchange area but increase the frictional effects.
  • Likewise, long reservoirs give lower 14 thermal losses [14], but the associated reduction in cross-sectional area implies higher fluid velocities and 15 hence higher pressure drop.
  • It should be recalled that these results have been obtained with all other parameters 18 fixed at their nominal values, and the picture changes when overall system optimisation is considered.

5. Preliminary Optimisation Studies 21

  • The design space for a PTES system is multi-dimensional and is possibly multi-modal and disjoint due to the 22 large number of design variables, objectives and constraints.
  • A stochastic optimisation algorithm has therefore been applied to identify 24 promising designs.
  • This is necessary in order 35 to manage the thermal fronts as they emerge from the reservoirs.
  • Ranges for all the design variables under 36 consideration are given in Table 5.
  • Two design scenarios are considered: an optimistic scenario, for which 37 η=0.99, and a standard scenario with η=0.90 (i.e., achievable in principle with turbomachinery).

5.1 Pareto fronts and parallax plots 41

  • The best designs emerging from the optimisation are shown in Fig. 6 in the form of ‘Pareto fronts’.
  • These 42 are the leading edges of the design space in that all other solutions lie either below or to the left of these 43 fronts.
  • The Pareto fronts thus show the trade-off between the different objective functions and allow the 1 designer to see the entire range of potential solutions.
  • 2 3 As expected, there is a trade-off between efficiency and energy density (Fig. 6(a)), whereas Fig. 6(b) 4 indicates that efficient designs are consistent with high power density.
  • Thus, for example, a thermodynamic efficiency of 85% and energy density of 200 MJ/m3 could 7 be achieved simultaneously in the optimistic case.

5.2 Parallax plots 10

  • To avoid overcrowding, only four designs have been plotted (Points 1 through 4 on Fig. 6), but 12 by examining a parallax plot for the full Pareto front it is possible to draw out information about the best 13 designs.
  • From Fig. 7 it is apparent that: 16 (i) The main factor controlling the trade-off between efficiency and energy density is the utilisation, Π. 17 (ii) High polytropic efficiency, (η=0.99), seems to correlate with low pressure ratio (typically around 7.5:1) 18 and high T1. 23 (iii) Optimum discharge pressure ratios lie slightly below the charge pressure ratio.
  • This should only be done whilst also considering economic and other 27 practical factors.

5.3 Comparison of loss distributions 34

  • The optimal designs in the optimistic scenario have considerably higher efficiency than the nominal design 35 (even when account is taken of the higher assumed value for η) and it is interesting to see how this has been 36 achieved.
  • Figure 8 compares the breakdown of losses for the nominal design (but with η=0.99) and for the 37 design corresponding to Point 3 in Fig.
  • As expected, optimisation 41 of the stores for high efficiency (i.e., Point 3) results in roughly a half-and-half split between thermal and 42 pressure losses.
  • The resulting geometry is perhaps a little unrealistic in that the short, fat reservoirs would be 43 prone to uneven flow distributions through the packing, would require a larger footprint and would lead to 44 manifold and pipework complications.
  • This merely reflects the assumed heat leakage factors of 2% for both CE 5 and EC, and it is possible that lower heat leakage could be achieved in practice.

6. Conclusions 11

  • A study of thermodynamic aspects of pumped thermal electricity storage (PTES) has been presented, based 12 on steady flow analysis of the compression and expansion devices coupled with a Schumann-style model of 13 the hot and cold thermal stores.
  • Parametric studies reveal that there are optimum values for some design 14 variables, whilst others either lead to a trade-off between efficiency and energy density or can be varied so 15 as to improve both these quantities together.
  • Predicted efficiencies 26 and storage densities obviously depend on the assumed loss factors; with an ‘optimistic’ set of parameters 27 that might be achievable with reciprocating devices, the thermodynamic round-trip efficiency could exceed 28 85% whilst the system simultaneously achieves an energy density almost an order of magnitude greater 29 than that for CAES.
  • Ms mass of storage material, kg valve-to-piston open area ratio m gas mass flow rate, kg s –1 time scale, s, or temperature ratio p pressure, Pa q heat transfer per unit mass Subscripts and superscripts rv volume ratio.

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Citations
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Cites background from "Parametric studies and optimisation..."

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References
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TL;DR: This paper suggests a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties, and modify the definition of dominance in order to solve constrained multi-objective problems efficiently.
Abstract: Multi-objective evolutionary algorithms (MOEAs) that use non-dominated sorting and sharing have been criticized mainly for: (1) their O(MN/sup 3/) computational complexity (where M is the number of objectives and N is the population size); (2) their non-elitism approach; and (3) the need to specify a sharing parameter. In this paper, we suggest a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN/sup 2/) computational complexity is presented. Also, a selection operator is presented that creates a mating pool by combining the parent and offspring populations and selecting the best N solutions (with respect to fitness and spread). Simulation results on difficult test problems show that NSGA-II is able, for most problems, to find a much better spread of solutions and better convergence near the true Pareto-optimal front compared to the Pareto-archived evolution strategy and the strength-Pareto evolutionary algorithm - two other elitist MOEAs that pay special attention to creating a diverse Pareto-optimal front. Moreover, we modify the definition of dominance in order to solve constrained multi-objective problems efficiently. Simulation results of the constrained NSGA-II on a number of test problems, including a five-objective, seven-constraint nonlinear problem, are compared with another constrained multi-objective optimizer, and the much better performance of NSGA-II is observed.

37,111 citations

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TL;DR: In this article, the published heat transfer data obtained from steady and nonsteady measurements are corrected for the axial fluid thermal dispersion coefficient values proposed by Wakao and Funazkri.

993 citations

Book
02 Dec 2008
TL;DR: The fact of global climate change is, famously, contested but, as the scientific evidence has accumulated, a broad consensus has emerged that warming of the earth is indeed happening and that this is anthropogenic as mentioned in this paper.
Abstract: The fact of global climate change is, famously, contested but, as the scientific evidence has accumulated, a broad consensus has emerged that warming of the earth is indeed happening and that this is anthropogenic. Now the main debate (we will ignore here the minority of naysayers) has moved from ‘whether’ (it is happening) to ‘what’ (to do about it); this debate is not going well, if the measure of success is practical actions, globally agreed (or even agreed on a nation-by-nation basis), to reduce the rate of emissions of greenhouse gases with the aim, ultimately, of reducing the actual amount of such gases in the atmosphere.

904 citations


"Parametric studies and optimisation..." refers background in this paper

  • ...In the UK, for example, it is estimated that over the 11 next few decades the integration of intermittent sources into the power infrastructure will require storage 12 capacities of the order of hundreds of GWh – an order of magnitude greater than current capacity [2]....

    [...]

30 May 2016
TL;DR: In this article, the authors highlight the importance of Germany as a unique market, development platform and export hub for energy storage systems, and open up a vista of opportunities for companies looking to cooperate with German part-of-the-art, become involved in demonstration projects, and expand through direct investment.
Abstract: Energy storage systems are an integral part of Germany’s Energy Transition (Energiewende). While the need for energy storage is growing across Europe, Germany remains the lead target market and the first choice for companies seeking to enter this developing industry. It stands out as a unique market, development platform and export hub. Germany Trade & Invest helps open up a vista of opportunities for companies looking to cooperate with German part­ ners, become involved in demonstration projects, and expand through direct investment. Video: Energy Storage in Germany

215 citations


"Parametric studies and optimisation..." refers background in this paper

  • ...[6], the charging (heat pumping) phase is achieved 35 by an electrically driven reverse Joule-Brayton cycle, which establishes a temperature difference between 36 two packed-bed thermal stores....

    [...]

  • ...Following [6], the discharged state of the reservoirs is set close to 5 ambient temperature: 310 K in the present case....

    [...]

  • ...[6] however, compression and expansion are achieved by reciprocating devices since there 11 is evidence that these are capable of higher polytropic efficiencies than turbomachinery....

    [...]

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TL;DR: In this paper, a new type of thermal energy storage process for large scale electric applications was presented, based on a high temperature heat pump cycle which transformed electrical energy into thermal energy and stored it inside two large regenerators, followed by a thermal engine cycle which transforms the stored thermal energy back into electrical energy.

212 citations


"Parametric studies and optimisation..." refers background in this paper

  • ...7 8 Previous theoretical work relating to PTES includes ‘endoreversible’ analysis of a generic system [10] and 9 more practical studies of open [8] and closed-cycle devices [11] based on turbomachinery....

    [...]

Frequently Asked Questions (16)
Q1. What are the contributions in this paper?

In this paper, the authors focus on a form of TES system referred to here as `` pumped thermal '' electricity storage. 

Due to the lower average gas density, pressure losses are more significant in 16 the cold reservoir and hence the optimum aspect ratio is lower and optimum particle size larger than for the 17 hot reservoir. 

In the optimised designs, 24 losses associated with pressure drop and irreversible heat transfer in the stores are only a few percent, so 25 the success of PTES is likely to hinge upon compressor and expander performance. 

The model used to quantify these losses is based on the well-established Schumann model of 31 heat transfer in packed beds [17], which assumes that the flow is one-dimensional and that heat transfer is 32 limited by surface effects (i.e., the internal thermal resistance of particles is negligible). 

The finite nature of fossil fuel reserves together with a wide range of health and environmental concerns 2 arising from the release of combustion products have been acting as drivers for the increasing uptake of 3 renewable sources of energy, such as solar and wind [1]. 

Increasing Π 2 (i.e., longer charge and discharge period) obviously increases the energy stored per cycle, but this is at the 3 expense of lower efficiency. 

Parametric studies reveal that there are optimum values for some design 14 variables, whilst others either lead to a trade-off between efficiency and energy density or can be varied so 15 as to improve both these quantities together. 

Heat exchangers, compressors and expanders are treated as steady flow 13 devices (in the time-averaged sense), but the equations governing heat transfer within the reservoirs are 14 integrated in time in order to track the hot and cold thermal fronts. 

The associated reduction in heat exchanger loss is really due to 39 the avoidance of exit losses that occur when the thermal fronts emerge from the stores (these losses are passed 40 on to the heat exchangers, rather than being associated with the stores themselves). 

In the UK, for example, it is estimated that over the 11 next few decades the integration of intermittent sources into the power infrastructure will require storage 12 capacities of the order of hundreds of GWh – an order of magnitude greater than current capacity [2]. 

39 40 The important factors in determining the merit of any electrical energy storage technology are its round-trip 41 efficiency (i.e., the fraction of electrical energy input retrieved upon discharge) and its capital costs per MW 42 installed capacity and per MWh of storage. 

Based on estimates from 6 early prototypes and approximate (not fully non-dimensionalised) scaling, Howes [12] argues that heat 7 leakage for a 2 MW machine should be negligible, which according to Fig. 8 would reduce thermodynamic 8 losses by another 3.5%. 

Predicted efficiencies 26 and storage densities obviously depend on the assumed loss factors; with an ‘optimistic’ set of parameters 27 that might be achievable with reciprocating devices, the thermodynamic round-trip efficiency could exceed 28 85% whilst the system simultaneously achieves an energy density almost an order of magnitude greater 29 than that for CAES. 

9 10A study of thermodynamic aspects of pumped thermal electricity storage (PTES) has been presented, based 12 on steady flow analysis of the compression and expansion devices coupled with a Schumann-style model of 13 the hot and cold thermal stores. 

The power and storage capacity given below are ‘nominal’ 39 values in the sense that they are the values that would be achieved in the absence of losses and in the 40 (hypothetical) case where the reservoirs can be fully charged. 

For a 2 MW machine using an 5 induction motor-generator, electrical efficiencies of 97% (in each direction) are commonplace, but 6 mechanical losses for a custom-built reciprocating compressor-expander are less easy to estimate.