Solar Power in Space Age - Definitive Ratios for Planets, Qualities and Throughput-Limits

[Xenothar]

Hey all,

extending on the previous work on solar panels, we are confronted with way more variables in Space Age. Not only are there different planets with different solar power factors, but also different day lengths and additionally five quality levels for panels and accumulators.

One thing which comes into play now is the power output limitation of accumulators (300kW on normal quality) on Vulcanus, because the nights are too short so discharge the stored capacity fully for all qualities starting from uncommon or better. In other words: We have to build more accumulator capacity than necessary to have enough output power available to power through the night. I denoted the new ratio in the table reflecting this but also included the ratio, if no throughput limits were in place. The input power limitations do not come into play on the SA planets, because the daytimes are longer and the charge itself therefore much smaller.

I don't think I need to explain the calucaltion itself, as there are plenty of topics around that. The known value for Nauvis with 0.84 is present, but due to the day-night-cycle being 420s now instead of 416.66, it is slighty different.

I ran all the calculations and sample tested some of them in game, they seem to be correct. I then put everything in nice tables for everybody to reference.

If anyone wants the Python-code to run the numbers yourself, please ask. Please also feel free to report mistakes.

How to read it: Pick your planet, pick your qualities and look up the number. The given number is how many accumulators you need to build per solar panel. So a value of 0.847 means you have to build 0.847 accumulators for 1 solar panel or 847 accumulators for every 1000 solar panels.

On Vulcanus, you can see, that qualities above normal for accumulators only lead to more wasted capacity. You have to decide for yourself if you want to go with prefect ratios and use more space for normal accumulators or waste capacity and have a smaller footprint.

Of course one could now calculate mixed ratios of different qualities, but this becomes unwieldy rather quickly .

Here goes:

SR_Nauvis.PNG (138.73 KiB) Viewed 20855 times

SR_Vulcanus.PNG (160.11 KiB) Viewed 20855 times

SR_Gleba.PNG (140.43 KiB) Viewed 20855 times

SR_Fulgora.PNG (141.77 KiB) Viewed 20855 times

SR_Aquilo.PNG (136.64 KiB) Viewed 20855 times

[JJGG]

Wow, this is really useful and awesome! Nice work!

[mmmPI]

Very interesting. Making it clear why upgrading a 0.84 ratio blueprint several level of quality gives unexpected results compared to nuclear power plant

[Xenothar]

Very interesting. Making it clear why upgrading a 0.84 ratio blueprint several level of quality gives unexpected results compared to nuclear power plant

Very much so. I guess for most people the main diagonals (same quality for both) are the most interesting. Due to the ratio getting smaller on these diagonals, the same footprint could pump out more power than just the quality power increase of solar panels would suggest as you need less and less acc to store the energy hence more panels in the same footprint.

Therefore: If you increase quality, you can replace accs with solar panels in a layout.
Special Rule on Vulcanus: The ratio on the main diagonal only changes once. So you would need a setup for normal/normal and then one for all other four combinations of same-quality. This is because the limiting factor (acc power out limit) increases with the same factor as the power out of the solar panels over quality. So they cancel each other out in the calculations.

Another basic rule you can take from the tables: If you want to keep one layout (per planet), upgrade accs first and then panels or upgrade both at the same time. This prevents brown-outs and black-outs. Upgrading panels only/first is never a good idea coming from a perfect ratio, as you cannot make it through the nights if you reach the power limits.

If one want a single one-to-rule-them-all layout for all planets and qualities, just build one with a 2.117 acc/panel ratio and upgrade however you please. This is very time efficient for the player, but a massive waste of power per footprint and materials/capacity for accs. If you however only ever upgrade according to the rule above, then the Nauvis normal/normal layout is the way to go and as good as it gets for all qualities and all planets. Just never upgrade solar panels first and you're golden, a bit wasteful, but golden.

I would recommend to have at least a single layout for the high output planets Nauvis/Vulcanus/Gleba together with normal/normal ratio (Nauvis 0.847 in this case) and upgrade this one according to the rule above. A second one for the two low output planets Fulgora/Aquilo as the ratios are vastly different, if you want to build solar there anyways. Good compromise of time vs. wasted materials IMHO. Maybe add legendary/legendary layouts next then (keep the normal/normal high output one for Vulcanus or design a special one), as the other qualities might only be transitory in the long run. This would leave you with one or two to five layouts arguably good enough for all situations.

[mmmPI]

That's a lot of interesting observations, i had only limited myself to the diagonals somehow not even noticing there was a nice one for Vulcanus because it uses different quality tier for pannel and accumulators.

I like the rule on how to upgrade, i will keep in mind "accumulator first". Because i used to do the opposite, having usually more accumulator than the golden ratio, "just in case".

I think for Fulgora something similar with lightning may help players. Table that tell you "how many accumulator of X quality" to last 1 day/night for 100 MW ( to make it easy to compute for one's need ) considering the different throughput and the lengh of the storm/no storm cycle.

For "how many lightning collector" , i suppose it require assuming they don't overlap, from which one can measure an average of energy per day per tile. And then factor in efficency due to quality. And finally compute the overlap with X Y or Z tile spacing between them ? I'm not sure it would still be helpfulto represent the game at this point. i'm trying to place them in a grid with substation, so that could work, but if they are placed all around an small island it's difficult then x)

[Xenothar]

That's a lot of interesting observations, i had only limited myself to the diagonals somehow not even noticing there was a nice one for Vulcanus because it uses different quality tier for pannel and accumulators.

I like the rule on how to upgrade, i will keep in mind "accumulator first". Because i used to do the opposite, having usually more accumulator than the golden ratio, "just in case".

I think for Fulgora something similar with lightning may help players. Table that tell you "how many accumulator of X quality" to last 1 day/night for 100 MW ( to make it easy to compute for one's need ) considering the different throughput and the lengh of the storm/no storm cycle.

For "how many lightning collector" , i suppose it require assuming they don't overlap, from which one can measure an average of energy per day per tile. And then factor in efficency due to quality. And finally compute the overlap with X Y or Z tile spacing between them ? I'm not sure it would still be helpfulto represent the game at this point. i'm trying to place them in a grid with substation, so that could work, but if they are placed all around an small island it's difficult then x)

Weeeeell, I can look into it, once I reach Fulgora . I am on a rather slow first playthrough (Co-Op, finding times together proves difficult). Have only reached Vulcanus so far.

[mmmPI]

I run some tests and thought i could share the datas in case it helps and as i'm not sure i can run properly the other calculations :

Lightning Rod [normal]
1 hour average production when no overlap => 12 MW
reach => 15 + lightning
efficency 20 %

Lightning Rod [Uncommon] 1 hour average production when no overlap => 19.6 MW
reach => 19.5 + lightning
efficency 26 %

Lightning Rod [epic] 1 hour average production when no overlap => 49.8 MW
reach => 28.5 + lightning
efficency 38 %


Lightning collector[normal] 1 hour average production when no overlap => 43.8 MW
reach => 25 + lightning
efficency 40 %

Lightning collector[uncommon] 1 hour average production when no overlap => 89.1 MW
reach => 32.5 + lightning
efficency 52 %

Lightning collector[legendary] 1 hour average production when no overlap => 490 MW
reach => 62.5 + lightning
efficency 100 %

[Frightning]

Glad to see my hard work deriving the basic cases across the different planets has been noticed and expanded upon (I was rather surprised when I first went looking for that kind of information that there seemed to be just about nothing out there on it for Space Age).

Those charts are really nice (I kept to exact ratios in my original post because I wanted to always be able to math exactly how many accumulators were needed without potential error propagation).

One interesting observation about Accumulators and quality is that their capacity grows faster than their throughput, this actually impacts how many Accumulators you need to pair with the Solar Panels and store enough energy (I hadn't considered this when I first decided to math this out). Interestingly, on Vulcanus the charge/discharge rate of Accumulators isn't enough at Uncommon and above qualities on Vulcanus to take advantage of 100% of their storage capacity, so you instead have to actually look at Accumulator throughput to figure out how many you need.

[MBas]

Ou this is a good one! Nice and clean.

Btw, let me present general formula (note: this does not include Vulcanus limit)

D = daylight time (relative for whole day cycle)
N = nightlight time (realitive for whole day cycle)
T = day cycle in seconds
P = full power of solar panels (in kW)
A = one accumulator capacity (in kJ)

Solar panel efficiency = ( 1 + D - N ) / 2
Energy needed to store = ( 1 + D - N ) * ( 1 - D + N ) * ( 1 + D + N ) * P * T / 8
Number of accumulators = Energy needed to store / A

And because D,N parameters are currently same for all planets, you can also be more specific and use more simple

Solar panel efficiency = 7/10
Energy needed to store = (21/125) * P * T

As example for "old" game with no quality and one solar panel there was

D = 0.5
N = 0.1
T = 25000 / 60
P = 60 kW
A = 5000 kJ

Solar panel efficiency = 0.7 (with 60 kW the efficient output is 60 * 0.7 = 42kW)
Energy needed to store = 4200
Number of accumulators = 0.84

Note: The model assumes constant daylight, followed by a linear drop to zero power during nightime, and then a linear rise back to full power. Sunrise and sunset do not necessarily need to have the same duration.

[MBas]

About Fulgora.

I think the final formula for the number of accumulators needed would be something like:

Number of accumulators = constant_1 * lightning_rods + constant_2 * sqrt(lightning_rods)

Here, you derive constant_1 and constant_2 from theory (these would be constant parameters for Fulgora) and then apply them to the actual number of lightning rods in your base. The first term accounts for the average output, while the second term (which might be very small—I’m not entirely sure yet) represents the fluctuation component.

[Mr Wednesday]

For accumulator power on Fulgora, I think the limit is more likely to be the amount of power storage than the feed from the lightning rods (so far I've easily capped charge well before the end of the charging period), though maybe I'll find I have issues with amount of lightning with more high-draw equipment.

I did some testing and calculations.

Based on my power graph, the time during which lightning is striking and recharging the accumulators is 1.2 minutes (or 108 seconds) out of the 3 minute (180 second) overall cycle.

Assuming zero ramp-up time as a lower bound, I found the following by dividing total energy stored by discharge time:
Base quality - 46.3 kW output during the discharge period - 21.6 accumulators per MW of power
Uncommon - 92.6 kW - 10.8 accum / MW
Rare - 138.9 kW - 7.2 accum / MW
Epic - 185.2 kW - 5.4 accum / MW
Legendary - 277.8 kW - 3.6 accum / MW

In practice, the ramp-up time is non-zero, so if you're right at the bleeding edge, there may be short unpowered periods early in the evening before the charge has started to build up again. For my own purposes, I'm aiming for about 24 accumulators / MW. I figure it's close enough that I don't need to try to figure out the ramp too.