Corrigendum to “Cost-effective electro-thermal energy storage to balance small scale renewable energy systems” [J. Energy Storage 41 (2021) 102829](S2352152X21005557)(10.1016/j.est.2021.102829)

Sampson Tetteh*, Maryam Roza Yazdani, Annukka Santasalo-Aarnio

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


The authors regret < Note The changes altered in the paper are highlighted in yellow. The leading cause for these changes is because misread of data, resulting in inaccurate efficiency. However, this is a minor change, and straightforward equation for the calculations is provided. These changes made are highlighted in yellow as follows. Abstract To decarbonise the energy production system, the share of renewable energy must increase. Particularly for small-scale stand-alone renewable energy systems, energy storage has become essential in providing electricity when the demand is high, for example, during the night. Although there are many different storage technologies, only a few are suitable for small-scale stand-alone renewable systems. Those systems must be modular and scalable to be deployed according to the capacity needed. Currently, batteries are among the leading grid storage technologies, but the demand, particularly for Lithium-ion batteries, is also high because of the electrification needs of the transportation sector. Therefore, the question of material availability might become an issue in the future, as Lithium is a scarce and critical element. As an alternative, we introduce a new modular electro-thermal energy storage (ETES) technology that is suitable for various storage needs. This storage unit can utilise various thermal storage materials (thermal oil, molten salt, and sand) at high capacities and improved efficiencies. Our design consists of the embedment of Stirling engines and an electric heater into a thermally insulated storage tank. The source electricity is first converted to heat stored in the storage tank and then converted back to electricity when needed. Among the thermal energy storage materials studied here, sand enabled the storage system's efficiency to reach 47.4%, thanks to its wide range of operating temperatures. The cost is projected to be up to six times lower than that of current Lithium-ion batteries. This new electro-thermal energy storage provides a promising cost-efficient, high capacity alternative for stand-alone energy systems. Page 4 studies indicated that from 550 °C, temperature decreases at a rate of 4 °C/h and less than 1.5 °C/h when the temperature is below 300 °C [73]. A low-temperature gamma type Stirling engine [74] was selected, and the parameters are shown in Table 1. [Table presented] With these assumptions defined and by setting temperature resolutions, the storage's charging and discharging data can be developed according to the type of thermal storage material used. To determine the charging data set, we can derive the quantity of electricity (P) needed to charge the energy storage from the following equation for calculating heat energy over time: [Formula presented]where m is the mass of the thermal storage material, Cp is the average specific heat capacity of the thermal storage material at the target temperature range, ΔT is the temperature difference during charging, and t is the time taken. He et al. (2011) predicted that the performance of a selected Stirling engine at an output power rate of 2.5 kW is 21% thermal to electric efficiency, representing 63% of the Carnot efficiency at the temperatures stated in Table 1 [74]. Therefore, the discharging data was generated from the corrected factor of Carnot efficiencies to obtain the thermal to electric efficiencies at each temperature difference resolution according to the following relation: [Formula presented]where Ƞth is the varying Carnot efficiency, Tl is the constant cold temperature of the Stirling engine, and Th is the varying temperature of the hot side cylinder of the Stirling engine embedded in the storage tank. [Formula presented]where P out is the discharge power from the thermal energy storage system at its highest temperature level. The type of thermal storage material determines the temperature limits at which the ETES operates. For instance, the minimum operating temperature of the ETES with oil or sand differs from molten salt and can operate at a low temperature of 180 °C. This is because molten salts start to crystallise below 200 °C, which is undesirable for the storage. Likewise, the maximum operating temperature varies on the type of thermal storage material used. Some thermal oils can reach the maximum of 400 °C, while some molten salts at 500 °C and sand at 950 °C. This is because the thermal oil will evaporate, molten salts will degrade, and sand will turn solid and may destroy the ETES at temperatures above the maximum temperature limit. Page 6 Furthermore, the TES materials have a significant impact on the ETES system and its efficiency. Table 2 shows a summary of operational values and efficiencies of the TES materials in the ETES system. [Table presented] Thermal oils have limited working temperatures because, as an organic component, they boil at extreme temperatures. Although it only requires a low amount of energy to charge the storage, the storage time is also low. On the other hand, molten salts require more energy to charge the storage for a limited temperature range operation and therefore supply exceptionally low efficiency for this type of system. The ETES system operates mainly as sensible heat storage based on the specific heat capacity of the thermal material. In the case of molten salt, only the first cycle requires melting the salt, which is enabled by the latent heat of the salt. However, after this cycle, the system is maintained in the molten state so that ETES works solely based on sensible heat. Thermal oils and molten salts may underperform with the ETES system; nevertheless, they are excellent candidates as heat transfer fluids, which is the reason for their wide usage in solar thermal applications [76–78]. Among the studied thermal materials, sand provides the best thermal storage performance for the ETES. This is because sand has a wide operating temperature range, and it takes low energy to charge the storage, which results in a high-efficiency output. Furthermore, the extremely high-temperature capacity of sand increases the Carnot efficiency of the Stirling engines, which results in an efficiency of 47%. Finally, sand is a readily and locally available thermal storage material that can prevent the transportation and importation stages, which consequently reduces both the cost and carbon footprint of the technology. Page 8 Another aspect to consider during cost analysis projections of energy storage systems is the maturity level of the technology. For instance, it is unlikely to see a significant reduction in the cost of matured technologies such as PHS and CAES by 2030 (Table 3). However, the electrochemical storages, especially LIB that is still developing, and HESS show a huge reduction in cost by 2030. These emerging technologies have the possibility of significant price reduction due to increasing development in manufacturing techniques, customisation of components, as well as their increasing production volume. Thus, considering the economy of scale with the predicted decrease in the price of LIB, it is highly probable that there will be a depletion of these critical materials in the future, which further can cause a rebound in the cost of such systems. [Table presented] For the cost analysis, we selected the ETES system that supplies 88 kWh power capacity from 1.5 m3 of the sand in the thermal storage tank, which is 35 h of discharge from a 2.5 kW rated Stirling engine. The cost analysis results of the ETES system are compiled in Table 4. This system includes a steel tank, insulators and Stirling engine generator set with an estimated cost of $ 24,142[84]. The selected thermal storage material, sand, has a market value of 0.25 $/kg [83], providing a lower cost compared to that of other high-temperature sensible heat storage materials that cost from 4.28 to 334 $/kg [76]. This leads to a full cost of 69 $/kWh for the ETES system with sand material with an estimated round-trip efficiency of 47.4%. When comparing to other storage technologies, we can estimate that the ETES system is six times cheaper than, for example, LIB systems in 2020 (Table 3) and seven times cheaper than VRFB (Table 3). Even with the decreasing trend in the cost of batteries for the following years, the estimated cost of ETES would be still four times cheaper than the expected cost of LIB in 2030 (Table 3). Although, this estimate is just a comparison of the manufacturing cost of the proposed ETES concept to the Levelized Cost of Storage of existing storage technologies. It can be noted that the cost can further be reduced when the full cost assessment is performed, which can only be determined from an existing prototype or a deployed ETES system. Experimental analysis of a built-up prototype ETES will be reported in our future work. Moreover, the cost of the ETES can further be reduced if the Stirling engine is customised for the system instead of relying on other manufactures, which takes up 80% of the total system cost. We can also estimate the life cycle of the ETES to that of power plants ranging from 25 to 50 years since it mainly contains mechanical parts where the FPSE is the critical component of the system, whereas batteries are estimated to have 10 to 20 years of lifetime. The direct thermal energy storage (TES) systems were not taken into account during this cost analysis since their input/output is thermal energy, which makes them less costly than EES storage systems presented in Table 3. Conventional sensible TES systems have a cost of around 22 $/kWh [76], which is lower than that of our proposed technology. In summary, the ETES solution provides the advantage of low cost, similar to a conventional TES, but will deliver electricity as an output with a flexible, modular design. This analysis shows that there is a great potential for the proposed ETES concept as the system eliminates the need for critical materials, the frequent maintenance, the low lifespan, the high cost of energy storage and the risk of fire associated with many current technologies. Conclusion Decarbonisation of electricity production is possible by developing appropriate and suitable energy storage systems for the power grid and for off-grid electrification demands. In this paper, a new electrical grid energy storage system known as ETES was developed. The main constituent of the ETES system is a thermally insulated storage tank with the hot side cylinders of Stirling engines embedded in it. The system is charged with renewable electricity, heating the thermal storage material in the tank, and electricity is discharged from the Stirling engines. Although the storage operates at high temperatures, the risk of fire or explosions is minimum since there are no highly reactive elements involved. We examined thermal oil, molten salts, and sand as potential storage media for the ETES. The choice of best-performing TES material settled on sand, which significantly outperformed the other two studied materials in its storage capacity, stability, availability, and cost. Sand provided higher efficiency (47.4%) because of its wider range of operating temperatures and extremely high-temperature tolerance, increasing the Carnot efficiency of Stirling engines. Since sand is an abundant material, it drives down the cost of energy storage six times compared to LIB and seven times compared to VRFBs. This work points towards promising alternative energy storage solutions for the modern grid infrastructure, facilitating a low environmental footprint and sustainable energy production, especially in remote stand-alone energy systems in rural areas. >. The authors would like to apologise for any inconvenience caused.

Original languageEnglish
Article number104785
Number of pages3
JournalJournal of Energy Storage
Publication statusPublished - Jun 2022
MoE publication typeNot Eligible


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