Energy and Electricity for Plebs — Plebucation for Bitcoiner’s #1 — Basics and Mining
In this educational series of articles for plebs we will be taking a look at the fundamentals of Electricity, Power and Energy to provide bitcoiner’s an understanding of some of the most debated and controversial aspects of bitcoin and Proof-Of-Work mining.
For most plebs, we probably just want to know if we can run a miner at home. For the entrepreneurial among us, maybe something with a bit more size and scale, or, for those with a general interest of the industry and how bitcoin can potentially solve the big issues of wasted/trapped energy sources, I hope there will be something for everyone in this series.
Within this article we will tackle the Electrical Formula’s 101 and look at an example of how these calculations can be used if considering mining bitcoin at home.
We have to eat our Veges first
We start this series gaining an understanding of the very basics of Electrical Theory looking at Ohm’s Law, Power and AC and DC theory. Electrical theory can get very complicated very quickly, I try to keep the information simple and accessible without diving too far into the complex theory.
The sections below labelled Tech Speak I have included in order to be accurate with the information purveyed. They can be skipped if you are not interested in the nuts and bolts.
Ohm’s Law — One law to rule them all.
As complex as electrical theory can be, the absolute fundamental principles can be explained by an extremely simple formula knows as Ohm’s Law.
V=I*R
Whereby
V= Voltage in Volts (V),
I = Current in Amps (A)
R = Resistance in Ohms (Ω)
To spell this out in words, Voltage is directly proportional to the amount of current flowing through a resistance.
Example 1. If we have 1amp flowing through a resistance of 10ohms, the voltage across that resistance will be 10V. Simple.
V = I*R
V = 1A*10Ω
V = 10V
More often than not, in the real world, we are more interested in calculating what the current draw would be given a set voltage and a fixed resistance. It is a simple case of transposing the equation to make the current the subject of the equation:
I = V/R
Example 2. If we had a supply voltage of 110V and a load with a resistance of 10Ω, how much current would we draw?
I = V/R
I = 110V / 10Ω
I = 11A
In example 2, I introduced the term “load”. This is a more practical wording that can be used to represent a piece of equipment that will do “work”, in other words, a load is anything that requires a power source to operate. When we refer to load, this could be any electrical apparatus we can think of (e.g a bitcoin miner).
AC and DC systems.
There are 2 main types of electrical systems. Direct Current (DC) and Alternating Current (AC). It is common to come across DC within low voltage systems such as batteries, electronics and vehicles. Whereas AC is commonly used where there is a higher power demand such as our houses, machinery, transmission systems.
Direct Current systems are a lot simpler to analyse. They are typically low voltage systems and are typically safe to touch in domestic settings. The voltage of a DC system is normally a steady, consistent level under ideal conditions. E.g The 12V supply in your car is usually a consistent level around ~12V. NB it is often a little higher or lower depending on the state of charge of the battery. DC circuits can be understood by the elements above in ohm’s law; namely voltage, current and resistance.
Alternating Current systems are a little more complex. The voltage in an AC circuit will swing back and forth as a Pure Sine Wave. Figure 2 shows a graphic of one cycle of a sinusoidal waveform. The voltage swings from 0V to a peak value before reversing, crossing 0V again and going negative. This can be a little unusual to think about for new kids.
This back and forth motion of the voltage and current has an effect on the power system that introduces some complexity. It results in us having to think of a term called impedance. Impedance is a term in an AC circuit that replaces resistance (as we saw above). Impedance is made up of a combination of resistance, inductance and capacitance. We won’t dig into all that here just yet, we simply must understand that AC and DC circuits are not entirely the same and that resistance is found in both AC and DC circuits, but AC circuits have some more trickery. It is also important to note that the resistive component of a circuit is the component that performs “real work” which we will talk about soon.
The voltage supply of an AC system is often represented by a figure called RMS (root-mean-squared). For a 230V system, the 230V figure, represents this RMS value, whereas the peak value of the AC waveform is actually closer ~325V, but we never talk about peak values. The RMS value is the value of an AC system that best represents what the equivalent DC value would be, being applied to the electrical apparatus.
Phew….stay with me….
Power
In the above examples of Ohm’s Law we saw a “load” represented by a resistance in ohms Ω. It is actually very uncommon to find a piece of electrical equipment represented by a resistance in ohms. It is more common to find electrical equipment represented by the power output (e.g a 2000W Toaster Oven, or a 3kVA Generator, or a 3250W ASIC miner).
There are 3 terms related to power that we need to introduce:
Apparent Power measured in Volts-Ampere (VA)
Real Power measured in Watts (W)
Reactive Power measured in Volt-Amperes-Reactive (VAR)
When we use Alternating Current (AC) as a supply, we have a phenomenon known as Reactive Power (Volt-Amperes-Reactive (VAR)). Reactive power in an AC supply is caused by either capacitance or inductance (that pesky impedance we introduced above under AC theory) , which we don’t need to get into in this article. For now, we simply need to understand that the amount of VAR in a power system, takes away our ability to do real work. It is energy that gets temporarily stored in a system but doesnt get used, it doesn’t do real work, it takes away our ability to do real work.
The Apparent Power in a power system, measured in Volt-Amperes (VA) is the total capacity in a system. The total amount of Real Power (Watts) that can actually be done is thus limited by the amount of reactive power we have in the system. Think of VA as being the volume (capacity)of a beer glass. The VA is how much beer we can fill that mug with. The Watts are represented by the beer itself (the stuff that will actually get us drunk) and the Reactive Power (VAR) is the froth (Figure 1).
Too much froth and we can’t get as drunk. Too much VAR and we can’t do as much real work (watts). VAR’s become a problem in complex electrical installations and power systems. For us plebs, we simply have to understand that VA and W are not the same thing. It’s importance will become clear in future articles when we talk about transformers, generators and power supplies.
For a quick example, just to hammer the concept home: If we purchased a 5kVA generator, it does not necessarily mean we can drive a 5kW motor, there is a certain amount of inductance in that motor that causes VAR which takes away from our total capacity of 5kVA, we would be able to drive a 4kW motor no problem, as there is plenty of headroom in our capacity of 5kVA to account for any VAR that might be in our system. Inductance is present in an AC electrical apparatus that contains a winding, e.g motors, airconditioner/fridge compressors, speakers.
Tech Speak: The example of a beer glass above is a tad misleading as the relationship between VA, VAR and W is not linear, meaning it is not a simple case of VA = VAR+W.
VA, VAR and W are vectors, meaning they have a magnitude and a direction (angle). We use complex math to solve for VA.
VA = Xangθ = X(cos(θ) +jsin(θ))
Where Xcos(θ) represents the resistive component (Watts) and jXsin(θ) is the reactive component (VAR), θ is the angle corresponding to the power factor of the system.
The formula for power?
To calculate the power for a DC electrical installation we can use the following simple formula.
Power (P) = Voltage (V) * Current (I)
P = V*I
Where P is Power in Watts
V is Voltage in V
and I is current in A
Example. An DC fan draws 5A when supplied with a 12V voltage. How much Power does it draw?
P = V*I
P = 12V*5A
P = 60W
For AC systems the formula becomes slightly more complicated due to that pesky impedance we spoke about.
The formula is still actually still P=V*I, however the P is now Apparent Power in Volt Amperes. These are all vector quantities, having magnitudes and angles. We would have to use complex math now to work it out properly.
Later in this article series when we dive further into complex systems, we will worry about this a bit more. For now we are going to cheat a little bit and use the above formula’s for our DC and AC examples. I’ll explain more further on…
What’s a Watt?
Watts are the base unit for real power. Watts are the real power doing the real work in our electrical apparatus. It is a rate of energy consumption. When we say rate, compare it to the speed when driving in your car e.g km/hour. A Watt is the rate at which we are consuming energy to do work. Watts is simply a unit we use to represent how many Joules (energy) we are consuming per second. But rather than get caught up in Joules, we use Watts to represent Joules/second. I stress this point as people often confuse the fact that Watts is indeed a rate at which energy is consumed. ASIC bitcoin miners, for example, are rated in Watts.
What’s a Kilowatt?
Just like the relationship between meters and kilometers is 1000m to 1km. The same is true for watt and a kilowatt. 1000W = 1kW. No brain-busters there.
What’s a Kilo-watt-hour?
A Kilo-Watt-Hour (kWh) is a measure of how much energy we have consumed. A kWh is the base unit by which most electrical utilities will charge for energy consumption.
But what does it mean?
Remember above how we said a Watt is a rate at which we consume energy? if we ran a fan rated at 1000W for 1 hour, we have consumed 1kWh of energy. Make sense? Let’s look at a better “bitcoiner” example:
If we had an ASIC miner that was rated at 3250W, and all things being equal we ran it for 24hours straight in perfect conditions with a perfect ambient temperature, cooling system and steady/stable supply voltage(these things are important), then we can work out how much energy we consumed for that period with very simple math.
The energy rating(watts) * time used(hours) / 1000 = Energy consumed
Therefore: 3250Watts * 24hrs / 1000 = 78kWh
NB: We must divide by 1000 to convert the W into kW.
Knowing our energy usage we could then refer to our electrical utility bill and work out how much it would cost us to run this miner per day.
For me, my base tariff rate for energy is 27c/kWh (I know right…. it’s robbery). So this ASIC would cost me 78kWh*$0.27/kWh=$21.06/day.
Now do you understand the need for miners to find the cheapest source of energy they can?
Tie it all together.
How do we use what we have learned above in a practical sense?
Say I wanted to buy an Antminer 219 Pro to run at home in my garage. There are a few things I need to know.
- What is the power rating of the equipment?
- What is the required voltage supply of the equipment
- What is the voltage supply at my house?
- What is the current draw?
- What is the rating of my electrical installation at home?
- Am I likely to burn my house down? (joking….not joking)
Figure 3 provides the specs for the Antminer s19 Pro
- We can see that the rating is 3250W.
- The equipment can operate with a voltage between 190–240V AC
- My supply voltage at home is 230V (Australian standard)
- What is the current draw? ………..Math time.
We are going to use our DC power formula. Why? Because we are going to cheat. Even though this is an AC supply, the rating of these ASIC’s is in Watts. They have inbuilt switched mode power supplies which convert the AC to DC. I also know (because I am a nerd) that the load of the ASIC is mostly resistive. I can safely assume then that my VA and my W figures would be near identical in reality. Don’t worry if that is a little confusing. Just know that for a simple miner at home in a simple installation, we can safely approximate the current draw using the the DC power formula.
Therefore P=V*I
Rearranging to make I the subject >>>> I = P/V
Therefore I = 3250/230V (make sure you use your actual supply voltage at home)
I = 14.13Amps.
5. I check the rating of my standard general purpose outlet (GPO’s) in my garage. It is only rated for 10A? “Uh ohhhh!!” This is common practice in Australia. Standard GPO’s are only rated for 10A.
Knowing the above, I may have to have a new dedicated 15A circuit installed. I would probably err on the side of caution and go to a 20A circuit while I am going to the trouble. Lucky I am an electrician…for you, it might be time to call in a favour from your bestie or get a local in. Pay ‘em in sats using a lightning wallet.
Luckily however for us, the S19’s do come with dual power supply chords meaning the power can be drawn from 2 separate standard GPO outlets. I may still experience nuisance tripping if they run a little hotter than your typical power circuit breaker of 16A, especially if those circuits share other appliances within your home (see below for more detail) . You are best to try and identify 2 separate GPO’s on 2 separate circuits if you can manage it. Otherwise a dedicated circuit still might be the best option.
6. Would I burn down my house? I would definitely not recommend you running the above scenario off a single standard 10A GPO. You may melt your GPO, or cause a fire with your wiring, posing a significant safety risk to you or your family. In most modern electrical setups chances are you would overload your circuit breaker before doing any significant damage, however in saying that, one should always stick to the recommended ratings, and never rely on something mechanical to save the day.
Not to mention, that a standard GPO circuit will have other GPO’s on the same circuit, maybe your TV, fridge, microwave, all of the above. If you ran your miner at full noise and turned on the kettle you would trip the breaker right away. Typcially, in Australia at least, a standard power circuit would be protected with a 16A breaker, it doesn’t take much to encroach upon that trip curve when running a miner at full noise. The higher the load from other appliances sharing that circuit, the quicker the breaker trips and the more often it will occur. Most of the time, there will be a protection device (e.g a circuit breaker) on the circuit, if there isn’t….run. The protection device, if installed as per current standards, will be rated lower than the wiring it is protecting. Meaning it should operate before you get to a point where you will cause a fire. If it is an older installation, or god-forbid a “home-job”, or if you are simply unsure, call your local electrician to come have a look. Failure to adhere to electrical safety standards is very unforgiving and simply not worth the risk.
Realistically, you have dropped significant $$ on the miner in the first place, what is a couple more hundred $$ to add piece of mind to your installation and your investment to ensure that it is safe and confirm that it will run without interruption when wifey turns the clothes dryer on. Hmmmm, what about an Antminer S19 clothes dryer? Now there’s a thought…..
Going Big
What about if you want to run more than one miner? Now you really do need to call in the big guns, call in a sparky (Australian for electrician).
If you want to run a semi sophisticated setup from home, you will have to consider your whole electrical installation. You will need to assess your circuits as well as the consumer mains from your metering point to the connection point of the utility company. You will need to assess whether a single phase supply from the utility will be sufficient (which is what most domestic installations are) or a 3-phase system supply (typically used in commercial/industrial settings). Your first point of call would be to contact the local utility to see if you can actually get a 3phase installation (this may not be available), this would limit your options for mining at home at the outset.
An electrician would need to then perform a maximum demand assessment on your installation. Depending on the existing wiring to your premise, this may need to be upgraded which can become quite expensive. Electrical wiring is selected according to safety standards and can depend on a number of factors to determine what the rating of current we are allowed to run through it would be. Factors like the conductor metal (copper or alluminium), insulation type, is it surrounded by thermal/acoustic insulation, is it buried direct in the ground or within a conduit, just to name a few. Your electrician will be able to determine your maximum current draw allowable with your existing installation, and may suggest alternatives should you require more current that your installation will allow.
The utility company may also have metering limitations to the amount of supply you can have, e.g in QLD Australia you are limited to a maximum of 100A per phase. Should you wish for more and you may require CT (current transformer) metering which can become very expensive. At this sort of level of installation I would argue you really are beyond the home garage scenario anyway.
Conclusion
Hopefully this article was able to introduce you to some of the fundamentals of electricity and energy and how they relate to bitcoin.
Once the above concepts are known and understood it is easy to then integrate this knowledge with the myriad resources out there to assess if bitcoin mining is profitable to do from home. As is well known, the biggest barrier to entry is your cost of energy. It is thought that unless you are able to obtain sub 8c/kWh for energy then it is often not profitable to mine (this of course is subject to the network hash rate, the cost of setup and your time horizon for expected returns).
When running a miner from home, you will benefit more from contributing to a pool of miners. Trying to go-it-alone is akin to trying to win the lottery with a 1 in several million chance of being the successful miner to solve a block. All of this is well documented in other places and I need not dwell on this too greatly. A fantastically thorough resource has just been posted at Bitcoin Magazine entitled : The Plebs Guide To Bitcoin Mining At Home.
In future articles we will look at power generation, large scale mining considerations, sources of trapped energy and we will dive into what makes bitcoin mining such an attractive proposition for utility companies, power generation facilities and energy markets.
I hope you found this useful and any feedback, questions or suggestions can be sent to me via DM on twitter @dazbea1.
Thanks for reading and happy stacking.
Daz Bea
@dazbea1
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