Perfect so long as inverter is 100% efficient and voltage after IR drop in cables never goes below 24V.
Fuses are supposed to be small enough to blow before cables overheat.
Fuses should be large enough that they never blow simply due to expected load (only if there is a short circuit or malfunction in inverter).
To avoid nuisance trips (of breakers) or blowing (of fuses), they are sized 25% higher than maximum continuous load.
They will tolerate brief higher surges (so long as not of the "fast blow" variety.)
What is the inverter efficiency? It may say "peak efficiency 95%", but at 100% load will be lower. I'll assume 90%.
What is the lowest battery voltage, under load? I'll assume 20V for a 24V battery.
How much voltage drop in cable at max current? (I'll include that in the 20V)
2000W/20V = 100A
100A x 1.25 = 125A
So 125A would be a common recommendation for this case.
I have determined that when driving a heavy AC load with an inverter, rather than steady 100A DC from battery, the current follows AC sine wave going higher and then dropping near zero. Same power is delivered to inverter but heating of wire and fuse (which goes as square of the current) is 12% higher.
125A x 1.12 = 140A
Although 2 awg in a cable or conduit would get too hot, individual conductors with free air to cool them are OK.
Wire Size Chart: Allowable Ampacities of Conductors in Free Air - 30C
wiresizecalculator.net
So I would recommend 150A fuse.
You can get away with 100A if you don't draw 2000W except briefly (e.g. microwave for a couple minutes.)
But better to design it so fuse just provides protection against overloads, never leaves you in the dark otherwise.
If you can use 2/0 rather than 2 awg, that is better for reduced voltage drop, and keeps them cool.
I used 2/0 for 6000W at 48V (equivalent current to 1500W at 12V)
Other thing to consider is type of fuse. You haven't mentioned type of battery in this thread. Lead-acid? or Lithium?
If a cable short-circuits, lead-acid batteries can typically dump 3000 to 5000A. Lithium batteries have lower internal resistance, can dump 20,000A (I think.)
Fuses have an AIC (amps interrupting capability) rating. Class T is rated 20kA AIC up to 125V. Various other types have ratings such as 2kA at 48V & 5kA at 12V.
Depending on your battery, select a fuse that can handle its short-circuit current at 24V.
Here's an ANL fuse rated 5000 AIC at 32V
Use with ANL Fuse Blocks for many applications with 35-750 Amp loads
www.bluesea.com
MRBF 5000 AIC at 32V
Space-saving ignition protected fuse for 30 to 300 Amp loads. Must use with Terminal Fuse Block.
www.bluesea.com
Class T 20,000 AIC at 125V
Use with Class T Fuse Blocks for circuit protection of devices including inverters. high interrupt capacity for large battery banks including Lithium-ion and TPPL batteries.
www.bluesea.com