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3 Phase: How to Calculate Line Voltage, Phase Voltage, Line Current & Phase Current in Star & Delta



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hello and welcome to this electrical

principals training video this video is

designed to be used in conjunction with

the worksheet that you'll find the link

to in the description below so if you

haven't already done so please click

that link download the worksheet and

then follow through the questions as we

go have a go answering them yourselves

and then check your answers against the

worked example I'll show you on the

board so let's get started by answering

question one so question one tells us

that three identical resistive loads of

25 ohms are connected in star to a 415

volt supply and we're asked to calculate

the phase voltage the line current and

the phase current so let's just put down

the detail of what we already know we

told that it's a 415 volt supply so we

know that the voltage between any of two

of those phases will be 415 volts so

between there and there we've got 415

volts with this kind of question it's

always a good idea to at least sketch

out an image of what you're calculating

it'll just help you to formulate your

thoughts and visualize what you're

trying to do we also need to list what

the resistance of the circuit is so here

we can see that the resistance of this

is equal to 25 ohms so each one of those

is worth 25 ohms so we've got that

clearly on the board it's a good idea

with this kind of question to always

just do a little sketch of what you're

calculating and to write down as much

information on there as you can so in

this case we already know what the line

voltage and the resistance is so we'll

just make a list of the things we know

we already know that the resistance is

25 ohms so R is equal to 25 ohms and we

know that the line voltage VL is equal

to 400 and 15 volts if this is new to

you this idea of line voltage and the

other thing we're going to talk about

phase voltage line current and phase

current then please go and watch a

previous video in this series on

three-phase because it's going to help

you to understand the maths that we're

about to do now so this stage will write

up what we're trying to find so we need

to know what the phase voltage is so

that's one thing that we're going to try

and find we also want to know what the

line current and the phase current is so

we'll write those up as well so we'll

say that the line current and the phase

current are equal to something so we'll

try and find the phase current and we'll

try and figure out what the line current

is going to be also so we'll write that

on there il is equal to so those are the

things that we're trying to find

so what calculations do we need to do to

find those answers well let's try and

figure it out first of all we know the

line voltage and we want to find the

phase voltage so this is really the

first step to answering this question

because we need to know what voltage is

acting across the load so that we can

figure out how much current is being

pushed through the load so here we're

going to say that the phase voltage

let's calculate that so the phase

voltage will be equal to the line

voltage VL divided by the square root of

3 now again if that formula is new to

you then please go and watch a previous

video in this series because it'll help

you to figure out where that's coming

from that's all we've got to do is just

put the numbers in so we'll say that VL

is equal to four hundred and fifteen

volts and the square root of three is

just a mathematical constant that stays

in this calculation so we've got four

hundred and fifteen divided by the

square root of three so we'll put that

into our calculator four hundred and

fifteen divided by the square root of

three and that's gonna give us two

hundred and thirty nine point six volts

so we've got two hundred and thirty nine

point six volts there we go so we

figured out what the phase voltage is

sort of put that in there two hundred

and thirty nine point six volts happy

days now we need to try and figure out

what the phase current is so this piece

of information is absolutely critical

now because we know that the voltage

across that load the phase voltage VP is

equal to two

thirty nine point six volts there and we

want to know how much current is that

pushing through the load remember the

current through the load is the phase

current so that's what we're looking at

there

so let's perform the next stage of the

calculation we want to know what the

phase current is we know what the

voltage being applied to that load is

and we also know what the resistance of

that load is so we can use those with

some nice Ohm's law IP is equal to V

over R bearing in mind that the V we're

going to be using is the phase of

voltage V P because that's the voltage

that is acting on the load by itself so

if we now put the numbers in we've got

two hundred and thirty nine point six

which is the value we just calculated

divided by that resistance of twenty

five so two hundred and thirty nine

point six divided by twenty five I'll

put that into the calculator two hundred

and thirty nine point six divided by

twenty five and that gives us a value of

nine point five eight two ran off to amp

ere's nine point five eight and pairs so

now we know how much current is flowing

through that load it is nine point five

eight amp ere's so we can fill it in

here as our answer nine point five eight

amp ere's and now we want to know what

the line current is going to be now

hopefully from a previous video you

remember what the relationship is

between line current and phase current

in a star connected load we know that

the phase current is the current flowing

through the load and the line current is

the current flowing through any one of

the supply lines so we can now say we

can perform the calculation I L is equal

to I P and that's pretty much the

simplest formula that you'll ever use in

electrical science because line current

and phase current are the same value in

a star connected load so we can now say

that that is equal to nine point five

eight amperes so that's a nice easy

answer to do we've got nine point five

eight pairs and that is question one on

this worksheet completed so question two

on the worksheet asks the same loads of

25 ohms are now connected in Delta to a

415 volt supply calculate the phase

voltage the line current and the phase

current so we've got the same load 25

ohms connected to the same value of line

voltage of 415 volts and once again

we're going to calculate the phase

voltage the line current and the phase

current so let's follow the principles

outlined in the first question we're

going to fill in what we know on the

drawing so we know that VL again is 415

volts so we've got VL is equal to 400

and 15 volts and we know that the

resistors are each worth 25 ohms so we

know that this resistor here is 25 ohms

so I'll put that in there 25 ohms so

that resistor has a value of 25 ohms and

now we can start to calculate the things

that we need to find so by putting in

the information we already know we know

that the resistance is equal to 25 ohms

so we're happy with that we know that

the line voltage is equal to 400 and 15

volts and once again we're asked to find

a phase voltage VP so the phase voltage

is equal to something we don't know yet

know what the phase current IP is equal

to we don't know what yet and the line

current is equal to again we don't know

what that's going to be so we want to

find that and figure out what that's

going to be so let's do some

calculations so the first thing we need

to figure out is what is the value of

the phase voltage so once again VP is

equal to now again we're in Delta so the

rules have changed and in a delta

connected load we know that VP is equal

to V L so once again we can do that

lovely simple calculation where VP is

equal to VL which is 415 volts so the

voltage that we find across our resistor

is 415 volts so we can put that in

415 volts there and that of course is

your phase voltage is equal to that

value so that's nice and simple as a

starting point the next thing that we

need to find is our phase current so our

phase current IEP once again using a

little bit of Ohm's law

we've got V and divided by R and again

this V is the phase voltage the voltage

across the load

so therefore VP is 415 volts this time

divided by 25 and 415 divided by 25 if

we just put that into our calculator I

should be able to figure out oh my head

I think it's sixteen point six I'm just

quickly verify that 415 divided by 25 is

sixteen point six happy days so we've

got there sixteen point six amperes

sixteen point six amperes so that is the

phase current that's the current that is

flowing through that load there

now obviously the line current is the

current that flows down the supply line

and the current that flows down the

supply line splits off some of it goes

that way and some of it goes that way so

the line current is going to be bigger

than the phase current how much bigger

well if you've not watched the previous

video then we'll tell you now so the

line current will be equal to the phase

current multiplied by importantly that

kind of really important number that we

use for three-phase systems the square

root of three so the phase current times

by root three will give us the line

current so if we perform that

calculation now sixteen point six times

by the square root of three we'll get

our value of phase of line current sorry

so sixteen point six times by the square

root of three gives us a value of twenty

eight point seven five amps so now we've

got twenty eight point seven five

amperes happy days so now if it was me I

just go back and just fill these numbers

in here so the phase voltage was equal

to four hundred and fifteen volts

it's a nice easy calculation that one

the phase current is equal to sixteen

point six amperes so that's that one now

sixteen point six amperes and then the

line current is equal to twenty eight

point seven five amperes twenty eight

point seven five amperes twenty eight

point seven five so that completes

question two we found all the

information that we needed to but just

an interesting little point here if you

look at these systems we've got the same

resistors connected in star and then

connected in Delta and look what happens

to the current that flows into the

system so here we have nine point five

eight amperes and here we've got twenty

eight point seven five or what's the

number that relates those two together

if we lose twenty eight point seven five

divided by nine point five eight now

bearing in mind we've rounded these

numbers off so there might be a little

bit of variance here but if we look at

that you can see that we come out with

practically three so we can say that if

you take the same load and connect it in

star and then connect it in Delta the

amount of current that flows into the

system will be three times as much so

now let's answer question three of this

worksheet so in question three we're

told that we have three identical

resistive loads of 50 ohms connected to

each other in star so here we've got the

resistance of this is equal to 50 ohms

so each one of these has a value of 50

ohms and then the question tells us that

those 50 ohm resistors are connected in

star to a 400 volt supply so that will

be 400 volts there so we've got a line

voltage of 400 volts so here's the

things that we either know or are going

to find so the resistance in this

question is 50 ohms so we can put that

in there we've got 50 ohms and the line

voltage we know is 400 volts so 400

volts and now we need to find the phase

voltage the phase current and the line

current so let's have a look

figuring out what these are so first of

all we need to know what the phase

voltage is going to be so we say that VP

is equal to VL divided by root three so

we end up with four hundred divided by

root three and they should come up with

a reasonably familiar number when we put

this into the calculator so we've got

four hundred divided by the square root

of three which is equal to two hundred

and thirty point nine volts so two

hundred and thirty point nine volts for

that one which is a nice value which is

instantly recognizable is pretty much

the voltage that we state are

single-phase supplies out in the UK so

we've got two hundred and thirty point

nine volts there so we can say we've now

found the phase voltage we then want to

move on and calculate the phase current

so the phase current is found by the

following process we just use a bit of

Ohm's law the phase voltage is obviously

the voltage across the load we know that

from a previous video and we know that

to calculate the phase current we use a

bit of Ohm's law IP is equal to VP over

R notice we're using the phase voltage

because the phase voltage is the voltage

across the load so that's the one that

defines the current flow through the

load so we're going to do two hundred

and thirty point nine which is what we

just calculated divided by fifty for our

values so we're going to do two hundred

and thirty point nine divided by 50 so

two hundred and thirty point nine

divided by fifty and that's going to

give us four point six one eight as an

answer so for 0.618 amp ere's so there's

our answer so how much current is going

to flow through the load four point six

one eight amps and then figure out what

the line current is going to be this

really could not be any easier because

all we've got to do at this point is

remember that in the star connected load

the line current which is the current

flowing into the circuit through any one

of the supply lines is exactly the same

as the phase current which makes sense

because the current flowing

through this load must be coming down

this line here so therefore we can say

that the line current will be equal to

four point six one eight amp ere's happy

days sore volley that in there four

point six one eight amp ere's so that

answers question three of this worksheet

so question four of this worksheet asks

the same loads of 50 ohms are connected

in Delta to a 400 volt supply and then

we're asked to calculate the phase

voltage the line current and the phase

current so once again just as we had in

question three we've got a resistance of

50 ohms so those are resistor value R

equals 50 ohms and the 50 ohm resistor

has now been connected in Delta in this

system and it's connected once again to

that 400 volt supply so the line voltage

the voltage between any two of the

supply lines is 400 volts so listed down

here we've got all of the values that

we're trying to find or that we already

know so we know that the resistance in

this circuit is equal to 50 ohms

connected across each phase and we know

that here we've got VL which is equal to

400 volts so that's 400 volts which is

going to go in there we then need to

calculate the phase voltage the phase

current and the line current so we'll

try and calculate those now and again

the really nice easy part about this to

start with is that the phase voltage is

exactly the same as the line voltage in

the delta connected load so we can say

that the phase voltage is equal to the

line voltage which means that the phase

voltage is equal to 400 volts if only

all maths were this easy you know so we

can put that in there 400 volts we then

need to go on and calculate what our

phase current will be and the phase

current remember is the current that

flows through the load so it's dependent

on the voltage that is applied to the

load and the voltage that is applied to

the load is 400 volts so we're just

going to use some simple Ohm's law

Reagan IP the phase current is equal to

VP that phase voltage the voltage across

the load divided by the resistance of

the resistor so we've got their VP over

R so we're going to do 400

/ 50 and I don't think it's really worth

putting into the calculator is it 400

divided by 50 is gonna give us 8 num

pairs of current flow so now we've found

our current and we can stick that in

here 8 amp ere's next we need to find

our line current and if you remember

from the previous answer the line

current is equal to the phase current

multiplied by that very important number

root 3 so line current is equal to phase

current times by root 3 so we've got 8

times by the square root of 3 and if you

do that calculation 8 times the square

root of 3 you will get the answer to the

line current so 8 times root 3 which is

going to give us 13 point eight six

amperes so there we've got thirteen

point eight two six amperes so that's

the answer to question four we've now

found our line current thirteen point

six eight amps so we can see there that

the resistance is 50 ohms the line

voltage is 400 volts the phase voltage

is 400 volts phase current 8 amps and

line current 13 point 6 8 amps so now

let's answer question 5 and our

worksheet question 5 states that three

identical resistive loads of 220 ohms

are connected in star to a 440 volt

supply so let's fill in the information

that we already know we know that we've

got a resistive value here are equal to

220 ohms and we know that we've got that

connected to a three-phase supply so we

know that VL is 440 volts V L is equal

to 440 volts bearing in mind that's the

voltage between any two of the supply

lines so we'll fill out information up

here as well

we know that VL is 440 volts and we know

that the resistance is also equal to 220

ohms and the question asks is to go on

to state the phase voltage the phase

current and the line current so let's

work through this question and get our

answers so

first of all we need to find that the

phase voltage so we're going to say that

VP bearing in mind that this is a star

connected load and we know that in a

star connected load VL divided by root

three will give us our phase voltage so

therefore we need to be able to stick

these numbers in accurately so 440

divided by the square root of 3 will get

us to our answer so put that into the

calculator

we've got 440 divided by the square root

of three and four hundred and forty

divided by the square root of three

gives us two hundred and fifty four

volts 254 we'll leave that if we run off

to one decimal place that's a zero so

254 volts is perfectly acceptable as an

answer so there's our number 254 volts

for our phase voltage bearing in mind

that the phase voltage is the voltage

across the load and therefore that is

the voltage that we'll need to figure

out what our phase current is the

current through the load because the

current through the load is dependent on

the voltage across the load so we move

on now to start calculating the phase

current and that's really nice and

easily done because for the phase

current we're just gonna use a little

bit of Ohm's law I P the phase current

is equal to the phase voltage VP divided

by the resistance R so we're just going

to put this into the calculation now and

we know that that will be 254 this value

here divided by 220 so 254 divided by

220 gives us an answer of 1.15 amp ere's

one point one five amperes now that we

know that the phase current is 1.15 amps

we can use that now to calculate what

the line current is going to be and

again if you haven't got the idea by

this stage hopefully we'll be able to

correct you now we know that the line

current in a star connected system so I

L is equal to I P and that's the end of

the statement

those values are the same a star

connected system so therefore our line

current il will be

- 1.15 amp ere's so we now know that the

line current is 1.15 amps

nice and simple okay so now let's

workout question 6 on our worksheet in

question 6 tells us that the same load

from question 5 of 220 ohms are

connected in Delta to a 440 volt supply

so we know we've got resistances here of

220 ohms so we can just put that on the

drawing and we know that our line

voltage VL is 440 volts the only

difference in this question being that

we've got it connected now in Delta

instead of in star so VL is equal to 440

volts there so again we'll put that in

fee information here this is the part

where I record what I already know from

the question 440 volts for the line

voltage and 220 ohms for the resistance

and then I just make a note of the

things that I'm trying to find so that

when I've completed all my calculations

I can fill this in and I've got my

answers laid out nice and neatly and if

you can manage the structure you're

working that nice neat way then your

lecturer will love you forever so let's

have a look now at finding the first

part of our question which is the phase

voltage it's always nice to start off

with an easy calculation and a delta

connected load V P and V L have exactly

the same value so there we've got the

phase voltage will be equal to 440 volts

nice simple couch there no problem then

we move on to start calculating the

phase current and the phase current we

rely on Ohm's law to find that so I P

the phase current is equal to V over R

but bearing in mind that the amount of

current flowing through the load which

is the phase current will be dependent

on the voltage that is applied to the

load the phase voltage so that's going

to be 440 divided by 220 so I've

realized that there's a reason that I

chose these numbers because it makes

this calculation really nice and easy so

we can see there that forward and 40

divided by 220 gives us 2 amperes for

our phase current in the Delta connected

system what we don't need to do

once we filled that in on a list of

definitive answers is find the line

current and the line current is a very

simple relationship between a phase

current and a line current in a delta

connected system the line current il is

equal to the phase current IP multiplied

by the square root of three so il is

equal to IP times root 3 so we've got

two M pairs for our phase current times

by the square root of 3 and once again

if we put that into our calculators 2

times root 3 so 2 times root 3 that

gives us three point four six amperes

three point four six and pairs so I'll

put that onto our list of definitive

answers three point four six and there

you can see that we've answered question

six now we've got our phase voltage our

phase current and our line current so

all that remains in this video is to say

thank you very much for watching

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