回復效應

回復效應（recovery effect）是電池使用時的一種現象，是指電池可用的能量會小於充電能量和已消耗能量的差。直覺來看，這是因為能量已在電池邊緣消耗，而且電荷還沒有在電池裡均分佈^[1]。

電池若持續的供電，其電壓會平順的遞減，但若電流有中斷，中斷之後會因為回復效應而讓電壓略有提昇^[2]。

可以用KiBaM電池模型^[3]鉛酸電池的回復效應^[1]^[4]。有些電池因著回復效應，若交替的進行放電及不放電，而不是持續放電，其壽命可以延長45%^[5]。回復效應的效果和電池負載、回復時間以及放電深度有關^[6]。

此現象在铅酸蓄电池裡非常的明顯，但在鹼性電池、镍氢电池和鋰離子電池中是否有現象仍有爭議。例如，有一個系統性的實驗個案研究^[7]發現用這些電池進行間歇放電時，可用能量反而比相同平均電流的連續放電要少。這主要是因為相同平均電流的間歇放電，因為高峰值電流造成的過電位增加。

參考資料

^ ^1.0 ^1.1 Boker, U.; Henzinger, T. A.; Radhakrishna, A. Battery transition systems (PDF). Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL '14. 2014: 595 [2025-06-11]. ISBN 9781450325448. S2CID 14690528. doi:10.1145/2535838.2535875. （原始内容存档 (PDF)于2021-10-31）.
^ Fuhs, Allen. Multifaceted Complexity of Batteries. Hybrid Vehicles. 2008. ISBN 978-1-4200-7534-2. doi:10.1201/9781420075359.ch6 (不活跃 2024-11-11).
^ Manwell, J. F.; McGowan, J. G. Lead acid battery storage model for hybrid energy systems. Solar Energy. 1993, 50 (5): 399. Bibcode:1993SoEn...50..399M. doi:10.1016/0038-092X(93)90060-2.
^ Pradhan, S. K.; Chakraborty, B. Battery management strategies: An essential review for battery state of health monitoring techniques. Journal of Energy Storage. 2022-07-01, 51: 104427 [2025-06-11]. Bibcode:2022JEnSt..5104427P. ISSN 2352-152X. doi:10.1016/j.est.2022.104427. （原始内容存档于2024-06-25）.
^ Chau, C. K.; Qin, F.; Sayed, S.; Wahab, M.; Yang, Y. Harnessing battery recovery effect in wireless sensor networks: Experiments and analysis. IEEE Journal on Selected Areas in Communications. 2010, 28 (7): 1222. CiteSeerX 10.1.1.189.3815 . S2CID 18123622. doi:10.1109/JSAC.2010.100926.
^ Rakhmatov, D.; Vrudhula, S.; Wallach, D. A. A model for battery lifetime analysis for organizing applications on a pocket computer. IEEE Transactions on Very Large Scale Integration (VLSI) Systems. 2003, 11 (6): 1019. doi:10.1109/TVLSI.2003.819320.
^ Narayanaswamy, Swaminathan; Schlueter, Steffen; Steinhorst, Sebastian; Lukasiewycz, Martin; Chakraborty, Samarjit; Hoster, Harry Ernst. On Battery Recovery Effect in Wireless Sensor Nodes (PDF). ACM Transactions on Design Automation of Electronic Systems. 18 May 2016, 21 (4): 1–28 [2025-06-11]. S2CID 17666250. doi:10.1145/2890501. （原始内容存档 (PDF)于2024-06-24）.

[boker-1] 1.0 ^1.1 Boker, U.; Henzinger, T. A.; Radhakrishna, A. Battery transition systems (PDF). Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL '14. 2014: 595 [2025-06-11]. ISBN 9781450325448. S2CID 14690528. doi:10.1145/2535838.2535875. （原始内容存档 (PDF)于2021-10-31）.

[2] Fuhs, Allen. Multifaceted Complexity of Batteries. Hybrid Vehicles. 2008. ISBN 978-1-4200-7534-2. doi:10.1201/9781420075359.ch6 (不活跃 2024-11-11).

[3] Manwell, J. F.; McGowan, J. G. Lead acid battery storage model for hybrid energy systems. Solar Energy. 1993, 50 (5): 399. Bibcode:1993SoEn...50..399M. doi:10.1016/0038-092X(93)90060-2.

[4] Pradhan, S. K.; Chakraborty, B. Battery management strategies: An essential review for battery state of health monitoring techniques. Journal of Energy Storage. 2022-07-01, 51: 104427 [2025-06-11]. Bibcode:2022JEnSt..5104427P. ISSN 2352-152X. doi:10.1016/j.est.2022.104427. （原始内容存档于2024-06-25）.

[5] Chau, C. K.; Qin, F.; Sayed, S.; Wahab, M.; Yang, Y. Harnessing battery recovery effect in wireless sensor networks: Experiments and analysis. IEEE Journal on Selected Areas in Communications. 2010, 28 (7): 1222. CiteSeerX 10.1.1.189.3815 . S2CID 18123622. doi:10.1109/JSAC.2010.100926.

[6] Rakhmatov, D.; Vrudhula, S.; Wallach, D. A. A model for battery lifetime analysis for organizing applications on a pocket computer. IEEE Transactions on Very Large Scale Integration (VLSI) Systems. 2003, 11 (6): 1019. doi:10.1109/TVLSI.2003.819320.

[7] Narayanaswamy, Swaminathan; Schlueter, Steffen; Steinhorst, Sebastian; Lukasiewycz, Martin; Chakraborty, Samarjit; Hoster, Harry Ernst. On Battery Recovery Effect in Wireless Sensor Nodes (PDF). ACM Transactions on Design Automation of Electronic Systems. 18 May 2016, 21 (4): 1–28 [2025-06-11]. S2CID 17666250. doi:10.1145/2890501. （原始内容存档 (PDF)于2024-06-24）.

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參考資料