A breaker's trip curve is a region on a current vs time graph that shows where a breaker may trip when tested under standard conditions. One side of the region shows the fastest the breaker is allowed to trip; the other side shows the slowest it is allowed to trip. So for example, when the current is twice the breaker rating, one trip curve I pulled up shows that the breaker may take anywhere from 25 to 100 seconds to trip.
The breaker's job is to protect the conductors. A conductor will have a withstand curve, which shows for any given current how long the conductor can carry that under standard conditions before the conductor may get hot enough to damage its insulation. So each conductor gets protected by a breaker whose trip curve time (slowest side) is less that the conductor's withstand curve at any current (well, up to some limit; at crazy high currents, a breaker may still take one full AC cycle (66 ms) to trip, so I imagine the conductor could still be damaged.)
Rather than keeping track of all this information, a conductor gets a single rating based on the current it can carry continuously (for arbitrarily long times), called its ampacity. And a breaker's rating is the current it's supposed to carry continuously without tripping, under the standard test conditions of a single breaker in free air with no enclosure and at a standard temperature (I think 40C). When breakers are used used tightly packed inside an enclosure, which is not free air, a continuous load requires a breaker rated at least 125% of the load current to avoid undesired tripping.
The original Powerwall specs already indicated a maximum continuous output current of 24A, which is the most allowed by the specified 30A breaker it is to be connected to. So no after the fact software revision is going to increase that 24A continuous output current; doing that would necessitate increasing the breaker size and likely the conductors from the breaker to Powerwall However, the Powerwall's peak (10s) rating was much less than what a 30A breaker is supposed to allow for a 10s overcurrent. [At least 120A for the trip curve I was looking at, which may not be the appropriate curve to use for these questions; I believe the UL standard for circuit breakers specifies a trip curve.]
So a software revision could allow the Powerwall inverter to boost its power output for short durations while still remaining within the envelope of what a 30A breaker will handle without tripping. That is the only reasonable thing the tweet could be referring to.
Cheers, Wayne
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