Optimizing energy consumption with productivity modules

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Cilya
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Optimizing energy consumption with productivity modules

Post by Cilya »

Depending on the objectives you chose for your game, you might want to optimize different aspects of your factory. You might want to optimize the growth of your factory by choosing the highest return on investment possible. At some point though, you might want to just improve the productivity of your factory to its maximum. It means using productivity modules 3 everywhere possible. This has several advantages.
  • First, your factory will obviously consume less resources, thus reducing the amount of time needed to maintain mining sites and increasing the period between the construction of new mining sites. If your resources settings implies scarce resources, it might be crucial.
  • The second advantage, is that you'll need less intermediate products. This implies that the logistic in your factory will be a bit easier. For instance, the advanced circuit assembling machine has a slow output but a fast input. If you use a blue fast belt to convoy the output, you'll need several fast belts to provide the input. With productivity modules, if you manage to keep the same output, you would need much less inputs. Thus, it requires a bit less belts to convoy the building materials without having a congestion somewhere. If you use robots though, you'll need also much less robots to feed your assembling machine.
Productivity modules though, drastically reduce the building speed of your assembling machine. With 4 productivity module 3, the base assembling speed falls to 40%. This means that the input is 40% of the normal input. If you add the 40% of productivity, the output speed is 56% (1.40 * 0.40) of the unmoduled factory. This means the moduled assembling machin is almost two times slower than the original one. To keep the same output speed, you'll have to double the number of assembling machines. This does not only cost in size, but also in energy. The Assembling machine 3 costs 210W, but with 3 productivity modules, it increase the power consumption to 882W. This very large increase of energy consumption will cause even more problems : the space and the material cost of the additional power generators needed.

This is when beacons starts to be interesting. It is not possible to use productivity modules in beacons. But it is possible to use speed modules. A beacon is usually not very effective due to it's very high energy consumption. But compared to the 882W, the 480W of power input for beacon is not prohibitive. Using two speed module 3 in a beacon will give a 50% speed bonus to any assembling machine in the range of the beacon. For our assembling machine, the base speed goes form 40% to 90%, thus almost doubling the production. The total energy consumption increases to 1509W, that is, much less than the double. This advantages come from the fact that, the slower your factory is and the more power consuming it is, the better speed modules are. The advantage can grow much higher if you use multiple beacons on multiple assembling machines. This is what I want to calculate.


Optimizing the energy consumption with productivity modules and basic beacons.

Let's say the power efficiency of an assembling module is the energy cost needed to build one item of building time 1. If some assembling machine/furnace/mining dirll, requires a power P and craft/mine/smelt at a speed S, it's power efficiency is

power efficiency = P / S (in watts per production units)

Now, let's say this production unit is influenced a number a of speed modules, b of efficiency modules, and c of productivity modules and let's note p and s their base power consumption and speed.

P = p * (1.0 + 0.7*a - 0.5*b + 0.8*c)
S = s * (1.0 + 0.5*a - 0.15*c) * (1.0 + 0.10*c)


For us, c is given by the type of production unit we use. (4 for assembling machines, 3 for drills, 2 for furnace, etc.) We won't use any efficiency modules, so b=0. The number of speed modules will be defined by the number of influencing beacons n, every of each is covering m distinct production units. Each beacon costs a power p'. This cost can be amortized on the cost of every production unit, by a factor n/m.

P = p * (1 + 0.7*n - 0.8*c) + (n/m) * p'
S = s * (1 + 0.5*n - 0.15*c) * (1.0 + 0.10*c)


Thus, we can estimate the power efficiency this way :

power efficiency = [p * (1 + 0.7*n + 0.8*c)+ (n/m) * p'] / [s * (1 + 0.5*n - 0.15*c) * (1.0 + 0.10*c)]

We can use this formula to calculate the power efficiency in some relevant case. For instance, for assembling module 3 :

p = 210W, p' = 480W, c = 4 productivity modules, s = 1.25

Image

and for electric furnaces :

p = 180W, p' = 480W, c = 2 productivity modules, s = 2.0

Image

I've done the assumption that n + m <= 13 as i don't believe it's possible to cheat this law. n increases downside, and m increases right.

From this numbers, you can try different patterns for your factory. I personally use very often a very simple pattern with rows of beacons and rows of production units, with usually something like n=4 and m=4 or even n=4 and m=8. I'll show some examples of this later.

We can see that it is really interesting to increase the number of beacons in these two cases. One beacon for 12 assembling machines/furnace is possible, but it's more complicated and not optimal when we use productivity modules. The inverse, 12 beacon for 1 assembling machine is possible, and not that bad, though far from optimal.

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Re: Optimizing energy consumption with productivity modules

Post by Apotheosis »

The simple fact that you only need to affect one level 3 assembler with full productivity modules with a basic beacon in order to make the beacon useful--and not only does it assemble items faster (90% speed vs. 40% * 2) and use less power (1509 kW vs. 1764 kW), but also generates far less pollution (26.46 vs. 45.36!) than two assemblers--is quite a revelation to me. I've always been under the impression that you need to affect a large number of devices before a basic beacon actually makes its large power consumption worth it, but this is a really cool exploit.

I'll never waste my resources on multiple assemblers and productivity units when I want to increase my output again.

However, it is important to note in all these energy considerations that the assumption is that your devices are constantly being used in order to offset a basic beacon's 480 kW constant power drain. When they aren't in use that's just wasted energy and may not end up making the setup more power-efficient than without the beacon.

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Re: Optimizing energy consumption with productivity modules

Post by Cilya »

Apotheosis wrote:However, it is important to note in all these energy considerations that the assumption is that your devices are constantly being used in order to offset a basic beacon's 480 kW constant power drain. When they aren't in use that's just wasted energy and may not end up making the setup more power-efficient than without the beacon.
Yes, I should have mentionned it. I believe it's not so bad if you decided to dimension your energy production to power all assembling machines anyway. Even if your production changes over time, (building capsules, then building modules, then building research, and so on) most intermediate prodcts are used in all recipes. This means its likely that your beacons will always be usefull. On my factory, i believe, at least 70% of them are used when my factory is consuming the most power. This means 30% of them is using power for nothing. I could add this value to the base power consumption of beacons in the calculations. I don't think it would change the result drastically : beacons use only 480kW of power when some of my assembling machines uses up to 1.5MW.

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Re: Optimizing energy consumption with productivity modules

Post by MeduSalem »

Thanks for putting the effort into calculating this Cilya!

I never was quite sure if the Beacons will pay off or not. For stuff where there's a constant workflow (without long idle times) this is quite interesting. I started using the approach in my smelter banks feeding my evergrowing storage system because of that and my throughput increased vastly while my overall power consumption is a little bit better now. ^^
Cilya wrote:I've done the assumption that n + m <= 13 as i don't believe it's possible to cheat this law.
Are you sure about that?

I think there are 8x8 setups possible... when using rows of assemblers/furnaces and beacons alternately. I think this is the absolute maximum possible amount of assemblers/furnaces and beacons effecting each other. ^^

Thereby the other combinations like 6x8, 7x7 and 7x8 are also possible by just leaving some of the assemblers/furnaces/beacons in each row out.

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Re: Optimizing energy consumption with productivity modules

Post by n9103 »

MeduSalem wrote:
Cilya wrote:I've done the assumption that n + m <= 13 as i don't believe it's possible to cheat this law.
Are you sure about that?

I think there are 8x8 setups possible... when using rows of assemblers/furnaces and beacons alternately. I think this is the absolute maximum possible amount of assemblers/furnaces and beacons effecting each other. ^^

Thereby the other combinations like 6x8, 7x7 and 7x8 are also possible by just leaving some of the assemblers/furnaces/beacons in each row out.
So long as beacons have 3 range, and beacons and AMs are 3x3 size, then yes, any one AM cannot be affected by more than 12 Beacons, and 1 Beacon cannot affect more than 12 AMs (or furnaces, drills, etc.).
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MeduSalem
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Re: Optimizing energy consumption with productivity modules

Post by MeduSalem »

n9103 wrote:So long as beacons have 3 range, and beacons and AMs are 3x3 size, then yes, any one AM cannot be affected by more than 12 Beacons, and 1 Beacon cannot affect more than 12 AMs (or furnaces, drills, etc.).
Basically I don't doubt that this is true for the edge cases... since I can't fit more than 12 assemblers around a single beacon and vice versa.

It's more because Cilya wrote that he believes it's not possible to cheat around this limitation. My question is more about if the rule still holds true for other setups like the following:
020.JPG
020.JPG (106.64 KiB) Viewed 16437 times
(the pattern can be repeated endlessly thereby reminding me of 8x8, since this how many beacons & assemblers/furnaces are effecting each other.

Or is this a case where complete patterns or entire setups have to be normalized to make any sense in comparison at all?

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Re: Optimizing energy consumption with productivity modules

Post by n9103 »

The table of values doesn't apply to all AMs or Beacons in a system, but a single selected one.
One of those beacons is affecting, at best, 8 AMs. One of those AMs is affected by, at best, 8 Beacons.
You would need to apply the relevant values in the table to each of the AMs (or beacons), in order to come up with your expected consumption/efficiency.
Colonel Failure wrote:You can lose your Ecologist Badge quite quickly once you get to the point of just being able to murder them willy-nilly without a second care in the world.

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Re: Optimizing energy consumption with productivity modules

Post by Cilya »

MeduSalem wrote:It's more because Cilya wrote that he believes it's not possible to cheat around this limitation. My question is more about if the rule still holds true for other setups like the following:
020.JPG
(the pattern can be repeated endlessly thereby reminding me of 8x8, since this how many beacons & assemblers/furnaces are effecting each other.

Or is this a case where complete patterns or entire setups have to be normalized to make any sense in comparison at all?
You are right. For most AU and beacons, the number of beacons affecting an AU is 8 and the number of AU affected by a beacon is also 8. So we have n = m = 8, and the rule is broken. I should give the entire array.

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Re: Optimizing energy consumption with productivity modules

Post by The Lone Wolfling »

Can you do a separate chart that has the percentage of the time the machine has to be working for it to be worth it, power-usage wise?

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