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Analytical Solution for the Cost Optimal Electric Energy Storage Size Based on the Effective Energy Shift (EfES) Algorithm

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Energy Informatics (EI.A 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15272))

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Abstract

The importance of Electric Energy Storage (EES) for the transformation to an energy grid with a large share of Renewable Energy Source (RES) has been studied and shown for many decades. While larger storage systems might provide more energetic benefits for the overall grid, they also require higher investment and capital costs. Hence the question of the cost-optimal size of EES and RES is commonly stated in public debates and the related literature. This minimization problem is mainly solved by combining simulation and optimization methods. Even though this enables the analysis of highly complex scenarios, the configuration and computation time are high, and many of the found methods are not reproducible. Within our paper, we introduce an analytical solution for calculating the cost-optimal capacity of an EES that is derived from results computed by the Effective Energy Shift (EfES) algorithm.

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References

  1. Ahlert, K.H., van Dinther, C.: Sensitivity analysis of the economic benefits from electricity storage at the end consumer level. In: 2009 IEEE Bucharest PowerTech, pp. 1–8 (2009). https://doi.org/10.1109/PTC.2009.5282245

  2. Anaza, S.O., Haruna, Y.S., Amoo, A., Sadiq, A.A., Yisah, Y.A.: Micro-grids system: a review of control techniques and strategy, distributed energy sources and energy storage system. In: 2023 2nd International Conference on Multidisciplinary Engineering and Applied Science (ICMEAS), vol. 1, pp. 1–6 (2023). https://doi.org/10.1109/ICMEAS58693.2023.10429898

  3. Bahramirad, S., Daneshi, H.: Optimal sizing of smart grid storage management system in a microgrid. In: 2012 IEEE PES Innovative Smart Grid Technologies (ISGT), pp. 1–7 (2012). https://doi.org/10.1109/ISGT.2012.6175774

  4. Bahramirad, S., Reder, W., Khodaei, A.: Reliability-constrained optimal sizing of energy storage system in a microgrid. IEEE Trans. Smart Grid 3(4), 2056–2062 (2012). https://doi.org/10.1109/TSG.2012.2217991

    Article  Google Scholar 

  5. Comello, S., Reichelstein, S.: The emergence of cost effective battery storage. Nat. Commun. 10(1), 2038 (2019). https://doi.org/10.1038/s41467-019-09988-z

    Article  Google Scholar 

  6. Cunha, P.H., Saavedra, O.R., Oliveira, D.Q.: Critical review of multi-microgrids. In: 2023 15th IEEE International Conference on Industry Applications (INDUSCON), pp. 443–450 (2023). https://doi.org/10.1109/INDUSCON58041.2023.10374924

  7. Darling, S.B., You, F., Veselka, T., Velosa, A.: Assumptions and the levelized cost of energy for photovoltaics. Energy Environ. Sci. 4, 3133–3139 (2011). https://doi.org/10.1039/C0EE00698J

    Article  Google Scholar 

  8. Emrani-Rahaghi, P., Hashemi-Dezaki, H., Hosseini, S.A.: Optimal operation and scheduling of residential energy hubs simultaneously considering optimal sizing of heat storage and battery storage systems. J. Energy Storage 44, 103481 (2021). https://doi.org/10.1016/j.est.2021.103481. https://www.sciencedirect.com/science/article/pii/S2352152X21011646

  9. Fellerer, J., Scharrer, D., German, R.: Analytic closed-form expressions for energetic measures as a function of the capacity of electric energy storage - effective energy shift algorithm. SSRN (2024). https://doi.org/10.2139/ssrn.4804780. https://ssrn.com/abstract=4804780. Submitted version (currently in review)

  10. Grisales-Noreña, L.F., Restrepo-Cuestas, B.J., Cortés-Caicedo, B., Montano, J., Rosales-Muñoz, A.A., Rivera, M.: Optimal location and sizing of distributed generators and energy storage systems in microgrids: a review. Energies 16(1) (2023). https://doi.org/10.3390/en16010106. https://www.mdpi.com/1996-1073/16/1/106

  11. Hermelink, A., Jager, D.: Evaluating our future - the crucial role of discount rates in European commission energy system modelling. Technical report (2015). https://doi.org/10.13140/RG.2.2.20152.65285

  12. Hernández, J., Sanchez-Sutil, F., Muñoz-Rodríguez, F.: Design criteria for the optimal sizing of a hybrid energy storage system in PV household-prosumers to maximize self-consumption and self-sufficiency. Energy 186, 115827 (2019). https://doi.org/10.1016/j.energy.2019.07.157. https://www.sciencedirect.com/science/article/pii/S0360544219314999

  13. Hirsch, A., Parag, Y., Guerrero, J.: Microgrids: a review of technologies, key drivers, and outstanding issues. Renew. Sustain. Energy Rev. 90, 402–411 (2018). https://doi.org/10.1016/j.rser.2018.03.040. https://www.sciencedirect.com/science/article/pii/S136403211830128X

  14. Jülch, V.: Comparison of electricity storage options using levelized cost of storage (LCOS) method. Appl. Energy 183, 1594–1606 (2016). https://doi.org/10.1016/j.apenergy.2016.08.165. https://www.sciencedirect.com/science/article/pii/S0306261916312740

  15. Lai, C.S., McCulloch, M.D.: Levelized cost of electricity for solar photovoltaic and electrical energy storage. Appl. Energy 190, 191–203 (2017). https://doi.org/10.1016/j.apenergy.2016.12.153. https://www.sciencedirect.com/science/article/pii/S030626191631933X

  16. Monchusi, B.B.: A comprehensive review of microgrid technologies and applications. In: 2023 International Conference on Electrical, Computer and Energy Technologies (ICECET), pp. 1–7 (2023). https://doi.org/10.1109/ICECET58911.2023.10389254

  17. Mulleriyawage, U., Shen, W.: Optimally sizing of battery energy storage capacity by operational optimization of residential PV-battery systems: an Australian household case study. Renew. Energy 160, 852–864 (2020). https://doi.org/10.1016/j.renene.2020.07.022. https://www.sciencedirect.com/science/article/pii/S0960148120310983

  18. Navid, G., Morteza, Z., Fatemeh, J.A., Ali, J.A.: Optimal sizing of energy storage system in a micro grid using the mixed integer linear programming. Int. J. Renew. Energy Res. 7(4), 2004–2016 (2017). https://doi.org/10.20508/ijrer.v7i4.6385.g7248

    Article  Google Scholar 

  19. Ntube, N., Li, H.: Stochastic multi-objective optimal sizing of battery energy storage system for a residential home. J. Energy Storage 59, 106403 (2023). https://doi.org/10.1016/j.est.2022.106403. https://www.sciencedirect.com/science/article/pii/S2352152X22023921

  20. Saeed, M.H., Fangzong, W., Kalwar, B.A., Iqbal, S.: A review on microgrids’ challenges & perspectives. IEEE Access 9, 166502–166517 (2021). https://doi.org/10.1109/ACCESS.2021.3135083

    Article  Google Scholar 

  21. Shahgholian, G.: A brief review on microgrids: operation, applications, modeling, and control. Int. Trans. Electr. Energy Syst. 31(6), e12885 (2021). https://doi.org/10.1002/2050-7038.12885. https://onlinelibrary.wiley.com/doi/abs/10.1002/2050-7038.12885

  22. Trevisan, R., Ghiani, E., Ruggeri, S., Mocci, S., Pisano, G., Pilo, F.: Optimal sizing of PV and storage for a port renewable energy community. In: 2022 2nd International Conference on Energy Transition in the Mediterranean Area (SyNERGY MED), pp. 1–5 (2022). https://doi.org/10.1109/SyNERGYMED55767.2022.9941383

  23. Uddin, M., Mo, H., Dong, D., Elsawah, S., Zhu, J., Guerrero, J.M.: Microgrids: a review, outstanding issues and future trends. Energy Strategy Rev. 49, 101127 (2023). https://doi.org/10.1016/j.esr.2023.101127. https://www.sciencedirect.com/science/article/pii/S2211467X23000779

  24. U.S. Energy Informatics Administration: levelized costs of new generation and resources in the annual energy outlook - methodology. Technical report, U.S. Department of Energy (2023). https://www.eia.gov/outlooks/aeo/electricity_generation/pdf/LCOE_methodology.pdf

  25. Zakeri, B., Syri, S.: Electrical energy storage systems: a comparative life cycle cost analysis. Renew. Sustain. Energy Rev. 42, 569–596 (2015). https://doi.org/10.1016/j.rser.2014.10.011. https://www.sciencedirect.com/science/article/pii/S1364032114008284

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Authors and Affiliations

  1. Friedrich-Alexander-Universität Erlangen-Nürnberg, Martensstr. 3, 91058, Erlangen, Germany

    Jonathan Fellerer & Reinhard German

Authors
  1. Jonathan Fellerer
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  2. Reinhard German
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Corresponding author

Correspondence to Jonathan Fellerer .

Editor information

Editors and Affiliations

  1. University of Southern Denmark, Odense, Denmark

    Bo Nørregaard Jørgensen

  2. University of Southern Denmark, Odense, Denmark

    Zheng Grace Ma

  3. Universitas Gadjah Mada, Yogyakarta, Indonesia

    Fransisco Danang Wijaya

  4. Universitas Gadjah Mada, Yogyakarta, Indonesia

    Roni Irnawan

  5. Universitas Gadjah Mada, Yogyakarta, Indonesia

    Sarjiya Sarjiya

A Appendix

A Appendix

1.1 A.1 Reformulations from Eq. (9) to Eq. (19a)

Reformulations of Eq. (9) with Eqs. (7), (8) and (10) to (16) to get to Eq. (19a):

figure q
figure r

With Eqs. (17) and (18):

figure s

1.2 A.2 Formulation of LCOE and LACE

It is possible to derive the equations for the LCOE of the overall system, as well as for each component. Equivalently to [5, 7, 12, 15] we define the LCOE relative to the provided energy amounts. To distinguish the LACE provided by the RES from the capital costs, we introduce the Levelized Costs of Generation (LCOG) as an equivalent to the LCOS. Hence we get the LCOE \( p _{\text {LCOE,}\textrm{RES}}\) for the generation by the RES as:

$$\begin{aligned} p _{\text {LCOE,}\textrm{RES}}&= \frac{- c _{0}}{ E _{\textrm{cdem}}}= p _{\text {LCOG}}- p _{\text {LACE,}\textrm{RES}}\text { with}\end{aligned}$$
(28a)
$$\begin{aligned} p _{\text {LCOG}}&= \frac{ p _{\textrm{inv},\textrm{RES}}}{{\eta }_{\textrm{du}}}\text {, and}\end{aligned}$$
(28b)
$$\begin{aligned} p _{\text {LACE,}\textrm{RES}}&= p _{\textrm{exp}}{{\,\mathrm{\cdot }\,}}\frac{{\eta }_{\textrm{exp}}}{{\psi }_{\textrm{sc},0}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{du}}}+ p _{\textrm{imp}}{{\,\mathrm{\cdot }\,}} r _{ p }\left( {\eta }_{\textrm{du}}\right) . \end{aligned}$$
(28c)

The LCOE \( p _{\text {LCOE,}\textrm{EES}}\) for adding a EES to the whole system are described by the LCOS \( p _{\text {LCOS}}\) and the avoided costs \( p _{\text {LACE,}\textrm{EES}}\):

$$\begin{aligned} p _{\text {LCOE,}\textrm{EES}}\left( C \right) &= \frac{ p _{\textrm{inv},\textrm{EES}}\left( C \right) {{\,\mathrm{\cdot }\,}} C - p ^{+}{{\,\mathrm{\cdot }\,}} E ^{+}\left( C \right) }{ E ^{+}\left( C \right) }= p _{\text {LCOS}}\left( C \right) - p _{\text {LACE,}\textrm{EES}},\end{aligned}$$
(29a)
$$\begin{aligned} p _{\text {LCOS}}\left( C \right) &= \frac{ p _{\textrm{inv},\textrm{EES}}\left( C \right) }{{\eta }_{\textrm{dch}}{{\,\mathrm{\cdot }\,}}{\mu }\left( C \right) },\end{aligned}$$
(29b)
$$\begin{aligned} p _{\text {LACE,}\textrm{EES}}&= p ^{+}. \end{aligned}$$
(29c)

Finally the LCOE \( p _{\text {LCOE,sys}}\) for the whole system can be calculated as:

(30)

1.3 A.3 Solving the Inequalities for Eq. (22)

$$\begin{aligned} p _{\textrm{inv},\textrm{EES}}- p ^{+}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}{{\,\mathrm{\cdot }\,}}\textsf{m}_{i}&<0\le p _{\textrm{inv},\textrm{EES}}- p ^{+}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}{{\,\mathrm{\cdot }\,}}\textsf{m}_{i+1}\\ - p ^{+}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}{{\,\mathrm{\cdot }\,}}\textsf{m}_{i}&<- p _{\textrm{inv},\textrm{EES}}\le - p ^{+}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}{{\,\mathrm{\cdot }\,}}\textsf{m}_{i+1}\\ p ^{+}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}{{\,\mathrm{\cdot }\,}}\textsf{m}_{i}&\ge p _{\textrm{inv},\textrm{EES}}> p ^{+}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}{{\,\mathrm{\cdot }\,}}\textsf{m}_{i+1}\\ \textsf{m}_{i}&\ge \frac{ p _{\textrm{inv},\textrm{EES}}}{ p ^{+}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}}>\textsf{m}_{i+1} \end{aligned}$$

With Eqs. (15) and (19d):

$$\begin{aligned} m ^{*}=\frac{ p _{\textrm{imp}}{{\,\mathrm{\cdot }\,}} r _{\textrm{inv},\textrm{EES}}}{ p _{\textrm{imp}}{{\,\mathrm{\cdot }\,}} r _{ p }\left( {\eta }_{\textrm{ch}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}\right) {{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}}= \frac{ r _{\textrm{inv},\textrm{EES}}}{ r _{ p }\left( {\eta }_{\textrm{ch}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}\right) {{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}} \end{aligned}$$

With Eqs. (16) and (19d):

$$\begin{aligned} m ^{*}&= \frac{ p _{\textrm{inv},\textrm{EES}}}{ p _{\textrm{imp}}{{\,\mathrm{\cdot }\,}} r _{ p }\left( {\eta }_{\textrm{ch}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}\right) {{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}}\\ &= \frac{ p _{\textrm{inv},\textrm{EES}}}{ p _{\textrm{imp}}{{\,\mathrm{\cdot }\,}}\left( \frac{1}{{\eta }_{\textrm{imp}}}-\frac{ r _{\textrm{exp}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{exp}}}{{\eta }_{\textrm{ch}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}}\right) {{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}}\\ &= \frac{ p _{\textrm{inv},\textrm{EES}}}{\frac{ p _{\textrm{imp}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}}{{\eta }_{\textrm{imp}}}-\frac{ p _{\textrm{exp}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{exp}}}{{\eta }_{\textrm{ch}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}}}\\ &= \frac{ p _{\textrm{inv},\textrm{EES}}}{\frac{ p _{\textrm{imp}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{ch}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}}{{\eta }_{\textrm{imp}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{ch}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}}-\frac{ p _{\textrm{exp}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{exp}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{imp}}}{{\eta }_{\textrm{imp}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{ch}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}}}\\ &= \frac{ p _{\textrm{inv},\textrm{EES}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{imp}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{ch}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}}{ p _{\textrm{imp}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{ch}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}- p _{\textrm{exp}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{exp}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{imp}}}\\ &=\frac{ p _{\textrm{inv},\textrm{EES}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{ch}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{imp}}}{ p _{\textrm{imp}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{dch}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{ch}}- p _{\textrm{exp}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{exp}}{{\,\mathrm{\cdot }\,}}{\eta }_{\textrm{imp}}} \end{aligned}$$

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Fellerer, J., German, R. (2025). Analytical Solution for the Cost Optimal Electric Energy Storage Size Based on the Effective Energy Shift (EfES) Algorithm. In: Jørgensen, B.N., Ma, Z.G., Wijaya, F.D., Irnawan, R., Sarjiya, S. (eds) Energy Informatics. EI.A 2024. Lecture Notes in Computer Science, vol 15272. Springer, Cham. https://doi.org/10.1007/978-3-031-74741-0_15

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