Take the Fuel Array
Start with a survivor who arrives in an Escape Pod, such as Commando. MUL-T, Acrid, Void Fiend, and False Son do not arrive in a pod, so they cannot obtain it this way in a solo run. Artifact of Command cannot directly supply a Fuel Array.
After leaving the pod, walk around its back and open the panel. Take the Array and check that it is in your equipment slot. It is not ordinary equipment you activate on demand.
Keep it from exploding
When the carrier reaches the half-health threshold, Fuel Array starts a 3-second countdown, explodes, and is destroyed. Avoid blood shrines, falls, and obvious bursts of damage. Prioritize staying above the threshold.
Surviving the explosion through invulnerability does not preserve the Array for the hand-in. Do not give it to an Equipment Drone, and do not accidentally leave it behind when replacing equipment.
Repair REX in Abyssal Depths
Reach Abyssal Depths in the fourth environment group and find Broken REX on the high platform. If you get a different map, continue to the fifth environment, align the teleporter to the planet, and loop while keeping the Array intact.
With Fuel Array equipped, interact with Broken REX. The repair consumes the Array, completes Power Plant, and unlocks REX. Simply reaching the platform is not enough.
If the Array is destroyed, start a new run and take another from an escape pod.