After spending an embarrassingly long time (Almost a dozen hours) trying to figure out how much each panel provided in kW by manually adding or removing panels until "It just works" (I thought the joules were responsible somehow, not noticing the fuel consumption number until long after) I've finally understood how to calculate how many panels are needed to sustain a single exchanger during the day.

The question however is how does one determine how much is needed to last though the night? The reason I ask this is because I'm playing with Space Exploration and each planet has different day/night cycle lengths. So while I've now learned that joules are a time based unit and not actual power, I imagine it's simply a matter of knowing how many joules are needed per second per MW and just timing the length of the night cycle and adding panels/accumulators accordingly.

Problem is, I didn't know what joules were until now; So rather than spending another dozen hours banging my head against the wall, I'd like some explanation of how to adequately calculate number of panels and accumulators to sustain an exchanger during the night.

My home planet is under 100% brightness for 2:27 minutes, but others can have nights far longer or even shorter. Nuclear is likely preferable for the 20-30 minute long nights, but I'd love to use thermal solar wherever possible for reliable and stable power without needing to regularly send expensive cargo rockets with consumable fuels.

Any help with this would be appreciated.

Let's assume you factory consumes the power P, as shown in the electric network view.
Your day takes X seconds, night takes Y seconds.
So your factory consume P*(X+Y) Joules per day.

Further assume your solar complex produces the power Q.
To supply the factory one cycle, you need Q=P(1+Y/X) solar power and a heat capacity C=PY.

A rectangular solarthermal array of the same tier with nominal power P0 and size NM (both >= 2) produces the power P0(5(N-2)(M-2)+8*(N+M-4)+12).

The heat capacity is determined by solarthermal arrays, heat-pipes, heat-exchangers and most important heat-accumulators. Note that heat capacitance is in J/°C and the usage temperature difference is 500°C (500-1000°C).

With numbers: Lets say the factory consumes constantly 10 MW. Days are 100 seconds, nights are 200 seconds.
Then you need 30 MW solar power or an array size of 6*7 on tier 1 (11.04MW). The required accumulator capacity is 2GJ.

A heat-accumulator stores 5MJ energy per °C. Hence you would need 400 °C temperature difference at one accumulator so one heat-accumulator would be enough for this example if operated between 550 and 950 °C.
If you would need more than 500°C in your case, you would have to add more accumulators.

Also note that a solarthermal array only conducts 5MW heat so you will need 6 heat-pipe taps on the example setup. Heat-pipes conduct 1 GJ so this shouldn't be a problem except for megabases.

Thank you very much, I appreciate the detailed response.

I'll try to create a proper array with this information and if I still get stuck then I'll be sure to drop you a message for further clarification. I found that using heat pipes assisted with keeping the panels at lower temperatures which surprised me at first, but I assume that the low capacitance is why the panels got hot as they were slow to transfer the heat to the destination. I may use pipes to wrap around the panels so they stay cool and keep the heat moving.

I did notice however that the panels do not spawn the fuel based on the brightness on other surfaces. I'm guessing it's tied to the surface of nauvis regardless of what surface it's placed on, as I tried them on a small moon with a day/night cycle of 23 minutes and the panels were sometimes active during the night and sometimes shut off during the day.

It's not a big deal right now since I'm still primarily on the surface of nauvis right now, but it's something I feel I should make you aware of as Space Exploration is gaining more traction and this mod could greatly help others with powering small moon outposts without reliance on nuclear or enormous solar arrays. Support would be greatly appreciated.

Thank you for your time.

The multi-surface bug should be fixed in version 1.2.0.