Let me try explain what I think is happening.
On a freighter the main power comes from the
AIRLCKCONNECTOR, which is the open doorway where you actually enter the freighter base, just up the last stairs. This provides energy storage of 1000 with a rate of 10000. This is similar to the free power connected to a base computer on a planet in creative mode when ‘free power’ is activated. However, instead of a huge range to cover the full base range (1000u), it only covers 4.1u radius, enough to just overlap with the next rooms/hallways connected.
Each room/hallway has a 4.1u radius in which it looks for a power connection and if available, passes it on using this same radius, like a bubble or sphere. Now with the ‘airlckconnector’ having all the power, the connected rooms towards the bridge, each have their own bubble of 4.1u radius. This works like a chain, where these bubbles overlap and are passing on power. The
BRIDGECONNECTOR is an odd one out, as it has a bubble looking for and passing on power at a radius of 35u instead. This is why power is never an issue when building close to the bridge.
Now move further away from the bridge and you will fully rely on the bubbles from each room/hallway of 4.1u radius. Each room is 8u*8u*4u (l*w*h) with their bubble at the center of the floor. Each hallway has the same bubble radius of 4.1 and is either straight, l-shaped, or x-shaped, acting the same as a room.
Each object that is related to power use, has a bubble of its own as well. The radius of this bubble as well as origin (location relative to the object) can vary. These values can all be found in the source files however. A small coloured light for example, has a value of 0.447u for a radius to look for and pass on power. A large hydroponic tray has a value of 1.5u, a small one a value of 1u. A health station has a value of 0.63u, and a shield station a value of 0.62u. And so on for other objects.
Now when you try to visualize all these bubbles for each object placed, to see if it connects to a bubble that ‘produces’ power in the chain, you will find there are edge cases. These edge cases are actually quite easily found once you realise how it works. I will try to show an example below, where the bubbles looking for and passing on power are shown in green. The white objects are a representation of room and connected hallway:
Now let’s add the Health Station (0.63u) and you will see how this bubble does not connect to other bubbles to receive and/or pass on power.
Another example that explains why a large hydroponic tray is not receiving power when placed right in the middle of 4 rooms.
These edge case issues appear to be consistent with the values and calculations after having done quite a bit of research on this with the release of Beyond. I have reported this in full detail to Hello Games and am hoping they will fix this with a future update. It actually (no longer) amazes me how they had not foreseen this issue to begin with.
Hope this explains it all. I could be wrong though, but I doubt it in this case.
Edit: Including the default freighter layout, where the small blue sphere is the
AIRLCKCONNECTOR and the large blue sphere is the