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Batteries in our laptops and phones eventually wear out after thousands or tens of thousands of discharge cycles over the lifetime of the product, maybe a cycle ever few days.

The ISS and other satellites in LEO very often are eclipsed perhaps fifteen times a day.

What management strategies are used to maintain their battery life? For example, do they discharge a different subsection of the battery for each eclipse rather than cycle the whole thing between say 90% and 100% every 90 minutes? Do they use types of cells that are very different than those used in consumer electronics?

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Partial answer - addressing the questions about managing the system for the ISS

tl;dr it's done manually by the ground

If the Primary Power System batteries are not discharged, they can overcharge, thereby causing damage to the batteries. Or, they can develop a memory, meaning the full depth of discharge (i.e., time that a rechargeable battery can last on a single discharge) would not be available. Ground controllers must actively manage battery states of charge during high beta operations by reducing the current used to charge batteries and occasionally deactivating batteries to prevent them from overcharging. As a result, some of the power that is generated is wasted and cannot be used by the EPS. Annually, batteries must be reconditioned by taking each battery off-line and completely discharging it to remove any memory buildup and allowing the state of charge (SOC) software calculations to be updated

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From a planning perspective, the operations team plans for the batteries to fully recharge each orbit and is limited to a maximum discharge down to 65% SOC to prevent excessive wear on the battery hardware and maintain contingency reserve power in case of a failure preventing a battery from recharging.

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All these operations are carefully defined in the flight rules, which detail under what conditions the batteries can be discharged below the nominal limits.

From The International Space Station Operating an Outpost in the New Frontier page 161

Note: NASA does not make the ISS Flight Rules publicly available.

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