Three Phase Electricity Basics and Calculations electrical engineering

Three Phase Electricity Basics and Calculations electrical engineering

Hey there, guys. Paul here from In this video, we’re
going to be learning more about three phase electricity. We’ll cover how three
phases are generated, how we get two voltages
from a three phase system, what do cycle and hertz mean, where the sine wave comes from, and how to calculate the voltages. Now, we use the power sockets to power our electrical devices. The voltage from these
plugs varies depending on where in the world we are. For example, North America uses 120 volts, Europe uses 220 volts, Australia
and India uses 230 volts, and the UK uses 240 volts. This is the standard voltage set by each country’s government regulations. You can look this up online
or we can just measure it at home if we have the right tools. I’m in the UK and I can read the voltage with my energy monitor. In this case, it reads about 234 volts. It’s lower because there
are some losses in the wire but also the voltage
varies throughout the day. Alternatively, I could
also use a multimeter to take a measurement of this. I can put the probes into the socket and take a reading of 236.8 volts. The readings are slightly different because the multimeter is more accurate. You should be electrically competent and qualified to do this. Remember, electricity is
dangerous and it can kill you. If you don’t have an energy
meter or a multimeter, these are very cheap, very useful. So, I do recommend you get one and I’ll leave a link in
the video description below for where you can pick
one up online for cheap. As I said, the voltages at our sockets do vary throughout the day. You can see here, I’ve
logged the average voltage every five minutes for 24 hours and it varied between 235 and 241 volts. Now these voltages at the
sockets are single phase from a wire connection from either a generator or a transformer. They come from connecting
between a single phase and a neutral line or in other words, just one coil of the generator. But we can also connect to
two or three phases at once. So two or three coils of the generator. This is typical in large
properties, with large equipment and large appliances
which need more power. In North America, you often
find two phase supplies in homes with 120 or 240 volts. That is a completely different system and we’ll cover that in a separate video. This video is only for three phase. Looking at the different
voltages, in the US we get 120 volts from a single phase or
208 volts from three phases. Europe, we get 220 volts single phase, or 380 volts three phase. Australia and India you
get 230 volts single phase or 400 volts three phase, and in UK we get 240 volts single phase or 415 three phase. Again, these voltages vary
slightly throughout the day and it’s unlikely that they
will be exactly this value. We can measure the voltages in
the three phase supply also. You see here, I have a three phase supply going into this breaker. If I use this clamp meter
to measure between phase one and two, I get a reading of 408 volts. If I connect across phase
one and phase three, I get almost the same
reading of 410 volts. So, I’m reading across these two phases to get these readings. You can measure between
any two of the three phases and get the same results. If I use this multimeter
with an inbuilt oscilloscope, and connect the terminals to
a single phase and neutral, you see I get a single sine wave. All three phases are producing a sine wave just at a different time. We can see this if I
connect my power analyzer to the three phase system. Here, I connect to all three
phases and you see it produces these three separate sine
waves, all one after another. Hopefully, you can see
that the yellow phase is a little hard to make out. So what’s happening here? Why do we get different voltages and what do these sine waves mean? So just to recap, we
get useful electricity when lots of electrons move along a cable in the same direction. We use copper wires because
each of the billions of atoms inside of the copper
material have a loosely-bound electron in their outer most shell. This loosely-bound electron
is free to move between other copper atoms and they
do actually move all the time, but in random directions,
which is of no use to us. So, to make them move
in the same direction, we move a magnet past the copper wire. The magnetic field
causes the free electrons to move in the same direction. If we wrap the copper wire into a coil, we can fit more copper atoms
into the magnetic field and we can therefore move more electrons. This gives us an alternating current. Instead of someone moving a
magnet back and forth all day, engineers instead just
rotate it and then place a coil of copper wire around the outside. We split the coil into two
but keep them connected and then place one at the
top and one at the bottom to cover the magnetic field. When the generator starts,
the North and South pole of the magnet are directly
between the coils, so the coil doesn’t experience any
effect and no electrons move. As we slowly rotate the
magnet, the North side passes the top coil and this pushes
the electrons forward. So we get positive values. The strength of the magnetic
field increases as it rotates up to its maximum, whether
most electrons are flowing. The magnetic field then starts to decrease and less electrons flow
until the magnet is again directly between the two coils. Then the South pole rotates in, but this time it pulls
the electrons backwards. So we get negative values. This again increases in
strength up to its maximum and then decreases back
to zero where the magnet is between the two coils. If we plot these values,
then we get a sine wave. The North side pushes
the electrons forward and as the strength of the
magnetic field increases, more electrons flow up to a maximum point. Then we’re leaving the
North magnetic fields, so the number of electrons
decreases down to zero. Then the South pole pulls
electrons backwards, so we get the negative
values out to a maximum and then back to zero. This one circuit gives
us a single phase supply. If we added a second coil
set 120 degrees rotation from the first, then
we get a second phase. This coil experiences the
change in magnetic field at different times compared
to the first phase, so its wave form will be the
same but it will be delayed. The second phase wave form doesn’t start until the magnet rotates
to 120 degrees rotation. If we then add a third
coil, 240 degrees rotation from the first one, then
we get a third phase. Again, this coil will
experience the change in magnetic field at a different
time to the upper two. So, this wave will be equal
to the others except it will be further delayed and we’ll
start at 240 degrees rotation. When the magnet rotates
multiple times it eventually just forms an unbroken three phase supply with these three waveforms. With this design, we need six cables, but we can join them together
in either a delta or Y method. For this example, I’m going
to use a Y or star method because I think it’s easier to understand. With a star configuration,
we need just four cables. One for each of the three
phases and then a neutral. Sometimes you don’t need a neutral, but we’ll look at that in our next video. When the magnet completes
one full rotation, the electrons will have
moved all the way forwards and then all the way back
to their original position. We call this a cycle. We measure cycles in
the unit of hertz or HZ. If you look on your electrical devices, you’ll see either 50 Hertz or 60 Hertz. That’s the manufacturer
telling you what type of supply the equipment needs to be connected to. Some devices are able to
be connected to either, like this charger. Each country uses either
50 Hertz or 60 Hertz. North America, some of South America and a couple of other
countries that use 60 hertz. The rest of the world uses 50 Hertz. 50 Hertz means the magnet
completes 50 rotations per second. 60 Hertz means the magnet
complete 60 rotations per second. If the magnet makes a full
rotation 50 times per second, which is 50 Hertz, then
the coil in the generator experiences a change in
polarity of the magnetic field 100 times per second, so
the voltage changes between a positive value and a negative
value 100 times a second. If it’s 60 Hertz, then
the voltage will change 120 times per second. As voltage pushes electrons
to create electrical current then the electrons change direction either 100 or 120 times per second. We can calculate how long it
takes for a single rotation to complete using the formula
T time equals one divided by F for frequency. A 50 hertz frequency supply
therefore takes 0.02 seconds or 20 milliseconds to complete. A 60 hertz supply takes 0.0167
seconds or 16.7 milliseconds. Now we saw earlier that the voltages from your plug sockets are
different all around the world. These voltages are known as the RMS value or the root means squared value. We’re going to calculate that
a little later in this video, but the voltage coming
out of the plug socket is not constantly 120 or 220
or 230 or even 240 volts. We’ve seen from the sine wave
that is constantly changing between positive and negative peaks. The peaks are actually much higher. For example, in the US, the voltage at the socket can reach 170 volts. Europe reaches 311 volts, India and Australia reaches 325 volts and the UK reaches 339 volts. We can calculate this
peak or maximum voltage using the formula, VRMS multiplied by the square root of two. I’ve already worked these
out for you on screen now. Because the sine wave passes
through the same points in both a positive and then
the negative 1/2 of the cycle, we get the same instantaneous
voltages along the cycle, but they are either positive or negative. If we add these all together
then we would get zero volts. So we need another way to calculate this. Luckily for us, some
intelligent person came up with the idea of using the RMS value. Basically they worked out how much heat an electrical heater could
produce when connected to an AC, alternating current circuit and then they connected it to
a DC, direct current circuit and increased the
voltage until it produced the same amount of heat. They then worked out a formula we can use. That being the square root of the squared average instantaneous voltage. I’ve just calculated what
that would be for the wave on screen now and you can
see that the sine wave with 170 volt peaks comes out to 120 volt RMS, which is what we get at the plug socket. So now we’ve seen how to
calculate the basic VRMs. Now, let’s slowly rotate the generator and calculate the voltages, which cause the sine wave
for each of the three phases. Let’s first divide the
rotation up into segments 30 degrees apart, giving us 12 segments. We will cover the
instantaneous voltage at each of these rotation points for
each of the three phases. Now I’m using Excel to calculate these and if you want a copy of my Excel sheet with all the calculations
in, then I’ll leave some download links in the
video description below. For the video worked example
I’m going to use 120 volts VRMs The sheet will update itself, plot the phase wave forms and
give you the calculations. Again, links down below for that. So we first write out a table
showing each of the segments and then the angle of rotation in degrees. First we need to convert each segment from degrees into radians. We do that by using the
formula radians equals degrees multiply by PI divided by 180. so we calculate the radian
value for each segment and fill in the chart. Now we want to calculate
the instantaneous voltage at each of these 30 degrees segments. We calculate the instantaneous
voltage at each segment using the formula V max,
multiply by sin, angular radians. As I said, for this example,
we’ll be using 120 volts RMS and as we calculated earlier, that gives us a Vmax of 170 volts. So just complete that
calculation for each segment until the table is complete
for one full cycle. Now if we plot this,
then we get a sine wave showing the voltage at each
point during the rotation. You can see now how the voltages increases with the rotation of the
magnet and when the polarity of the magnet changes, the
voltages become negative. Now we can calculate phase two voltages and we can do that using the formula Vmax multiplied by sin
angular radians minus 120 times PI divided by 180. This end part 120 times PI divide 180 just takes into account
the delay because the coil is 120 degrees from the first one and then it converts this to radians. So just complete that
calculation for each segment until the table is complete
for one full cycle. We can now plot this to see
the waveform for phase one and two and how these
voltages are changing. For phase three, we need to
use the formula Vmax multiply by sin, angular radians minus
240 times PI divided by 180. So, just complete that
calculation for each segment until the table is complete
for one full cycle. We can now plot this to see
the wave form for phases one, two and three and how the
voltages are changing. So this is our three phase
supply showing the voltage for each phase, every 30 degrees
rotation of the generator. If we try to add these
voltages together, we get zero because they cancel each other out. So instead we’re going to take
the RMS voltage per phase. I’ll just show you this for one phase, but the process is the same
for phase two and three. So, we start by first squaring
each instantaneous voltage for a full rotation. Now take the average of
these values, add them all together and divide by
how many segments you have. In this case, we have 12 segments. Do not include the value at 360 degrees because this is a full rotation. So 360 degrees is back
to start, which is zero. If you include this, you’ll be counting the zero value twice. And your calculation will be higher. Now we take the square
root of that number. This gives us our RMS
voltage of 120 volts. This is the phase voltage. That means if we connect
a device between any phase and the neutral line, then
we get the VRMs of 120 volts. We can do the same for
phases two and three and we’ll get the same value. To get more power, we can
connect to all three phases. We calculate the supply
voltage by squaring each of the instantaneous
voltages on all three phases. We then find the average
for each phase individually, and then we add these
three averages together. Then we take the square
root of that number. You’ll see the three phase
voltages comes out to 208 volts. We call the smaller
voltage our phase voltage, and we get that by
connecting between any phase and the neutral line. We call the larger voltage
our line to line voltage, and we get that by connecting
between any two phases. That’s how we get more
power from the supply. Okay, that’s it for this video, but if you want to continue your learning, then check out one of
these videos onscreen now and I’ll catch you there
for the next lesson. Don’t forget to follow
us on Facebook, Twitter, Instagram and of course


  1. ⚠️ Found this video super useful? Buy Paul a coffee to say thanks: ☕


  2. At 2:15 you mentioned “2 phase” US system will be covered in another video but I cannot find it. Is it still in work?

  3. In the US most residential dwellings are 120/240 volt SINGLE phase and most large commercial and industrial building use 277/480 volts THREE phase.

  4. Great video, but I have a question. In your previous video the maximum peak of the voltage falls together with the 'side' of the bar magnet. In this video it falls together with the tip of the N or S side of the magnet. What is correct?

  5. The two prong plugs in the US are no longer used, they are all grounded or 3 prong like everyone else, been that way since the 90s

  6. I dont get it. If they cancel eachother out then why we can conect a device to all 3 phases? The no Current should flow in my opinion

  7. I thought in the U.S., 3 phase provided 277V/480V normally and only 208 when 3 phase power was used to provide power to a residence in the absence of single phase, thus giving the home 120V/208V. the 208V is a result of using only 2 of the 3 phases instead of 120/240 from a single phase. Am I incorrect?

  8. Square root of 2 works for the RMS of a single phase and the square root of 3 works for line to line.

  9. Actually in Canada, you can have 120v/208v (basic distribution and lighting) and 347v/600v for bigger demand (commercial/industrial such as drives or lighting). Hydro-Quebec by default in industrial or commercial applications actually only supplies 3phase 600v. Its on the customer side that we drop down tension to 120v/208v. Residential is fed 120v/240v (single phase) from Hydro. Heavy commercial/industrial, Hydro can supply 14.4Kv/25kv 😛 Actually did a [email protected] entrance this winter…50mW of pure power! 😛

  10. At 3:05, I was like "wtf is wrong with his hands?!" before I realized they were rubber gloves a moment later. Wow xD

  11. I'm newbie and this video unlike the first video,how electric generator work. In this video, all the free electrons supposed to be move faster at the strongest part of magnetic field and vtg must increase but in this video why minimum point of magnetic field keeping making vtg higher. I dont understand.

  12. How three phase electricity is distributed, Because there will be 6 wires, just like in 1 phase there are two wires on poles.

  13. Anyone answer please actually vrms= 1.11vav
    Vrms =0.707vpeak
    Then how vrms =squre root( (vavg) squre)

  14. It is really interesting to see how other countries handle the electrical installation / infrastructure! But the most countries in Europe (for example Germany) also use 230 / 400 Volt 😃

  15. This video really cleared up most everything. 👏🏽👏🏽👏🏽👏🏽👏🏽👏🏽👏🏽👏🏽👏🏽👏🏽👏🏽👏🏽👏🏽👏🏽👏🏽👏🏽

  16. RMS Voltage is the Voltage, where the area between the graph and 0 line of the voltage is the same size for either AC or DC. That is a mathematical function and results in a factor of root 2 ~1.41 between the voltages

  17. In the following video
    You explain in a way that when the magnet inside a rotor is perpendicular to the coils you get maximum current, but in the above video you explain this ideo when magnet is parallel
    Which one is the correct? 🤔

  18. The voltages, in this video, are primarily residential voltages. All have the same relationship, for 3-phase power, the Phase-Phase voltage must always be Square Root of 3 times the Phase-Line voltage, that is true for all the voltages shown @2:30.
    Industrial and larger commercial users usually get higher voltages than those shown, with 277/480 as one common example, and generate the common voltages in-house.

    North America, uniquely, has dual voltages in all residences. All homes have either 120/240 or 120/208, and have also slowly been drifting from 110V to 120V and above.

  19. Hello. Thanks so much for making these. The visual aid's are very helpful. I'm having problems getting the same values for "Vmax x sin (radians)" I see it work for the 30 degrees calculation at 85 volts, but the others have me perplexed. I.E. How does Vmax (170V) x 1.571 at 90* end up 170V?

  20. you sir, are the fucking man. Studying Electrical engineering, this video was incredibly clear and helpful! Downloading the excel sheet and will use that to study along with my ac circuits class.

  21. Love your videos. You explain things well! I think you should have kept all the calculations for a different video though. It didn't mix well with the explanation of what 3 phase actually is.

  22. Mate in Australia we have 240/415V not 230/400V please correct your video, if you want I can provide documentation stating this!



  24. No EU uses 230 V. Britain is officially 230 V but in practice it in many places s 240 V an they play with tolerances.

    Norway has 133 V but they do not use it, they use 230 V between two phases.

  25. Another way to think about it is that RMS is unusually 70% of the peak value. So that is why you get 120v if the peak to peak is 170.

  26. Knowledge being taught must be as in this active and readable way , not just those fixed graph and vague words !

    Anyway , thanks for your brief but elaborate teaching !

    Chuck from Taiwan

  27. This channels teaches you things within few minutes …whereas in colleges or educational institutes it take almost 3 to 4 years to get concept clear ..Great channel .

  28. How electricity turns back to its source in tree phase motor, where there is no neutral wire connected to it. Also how one phase appliance si connected in tree phase system where there is not an neutral wire?

  29. i think there is a problem in phase 2 and phase 3 voltage calculation …
    i think phase 2 should be = vmax * sin(rad – (150*π / 180))
    phase 3 should be = vmax * sin(rad – (210*π / 180))

    in phase 2 at 60degree value should be 0
    in phase 3 at 120deg value should be 0

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