Unbalance neutral current in a 3 phase system

[crossman]

Rattus:

Nix on the last post. I did some research, found this http://www.ibiblio.org/obp/electricCircuits/AC/AC_2.html
a simple explanation of polar coordinates and horizontal / vertical components.

I have an elementary understanding of this, but... Why do they call the vertical component "imaginary"? That makes no sense to me, the vertical component is just as real as the horizontal component. Imaginary numbers to me meant the square root of negative one.

Anyway, I have it now. A phasor described with polar coordinates can be broken down into a horizontal component (known as "real") and a vertical component (known as "imaginary" and indicated by "j"). This makes it a simple matter to add phasors by adding the real components to each other and adding the imaginary components to each other.

So it has nothing to do with the square root of negative one.

 

[rattus]

You got my head spinning like them phasors.

Just to make sure: When you say "complex" numbers, we are talking about one component being the square root of negative one?

Yep, the vertical component is multiplied by "j" which is SQRT(-1). The mathmeticians use "i".

The approaches put forth by you and Roger are valid, but are limited to currents separated by exactly 120 degrees. The complex number approach is general and works for any set of angles.

 

[crossman]

The approaches put forth by you and Roger are valid, but are limited to currents separated by exactly 120 degrees. The complex number approach is general and works for any set of angles.

This I understand and feel comfortable with.

Yep, the vertical component is multiplied by "j" which is SQRT(-1). The mathmeticians use "i".

This completely baffles me. Where is the SQRT -1 coming from?

 

[rattus]

Rattus:

Nix on the last post. I did some research, found this http://www.ibiblio.org/obp/electricCircuits/AC/AC_2.html
a simple explanation of polar coordinates and horizontal / vertical components.

I have an elementary understanding of this, but... Why do they call the vertical component "imaginary"? That makes no sense to me, the vertical component is just as real as the horizontal component. Imaginary numbers to me meant the square root of negative one.

Anyway, I have it now. A phasor described with polar coordinates can be broken down into a horizontal component (known as "real") and a vertical component (known as "imaginary" and indicated by "j"). This makes it a simple matter to add phasors by adding the real components to each other and adding the imaginary components to each other.

So it has nothing to do with the square root of negative one.

The mathematicians who thought this up must have used this term because it is hard to visualize SQRT(-1). In general, the roots of a quadratic equation can be complex, therefore "i" is needed.

Now if you multiply complex numbers, you will obtain terms preceded by j^2 which equals -1. Try it.

 

[nakulak]

its just a convention, there are many for handling vectors.
<x,y> cartesian
<r,theta> polar
ai + bj complex

all do the same, some have different applications
if its easier for you to visualize the cartesian or haven't had the math for the latter, use those and the corresponding cartesian projections on to x,y,z axi to add the vectors

so for assumed 120 phases, plase phase 1 on x axis, 2 at 120, 3 at 240
r (radius) = magnitude of vector = I (current value)

converting <r,theta> to <x,y> to make easy addidion of vectors:
x=rcos(theta)
y=rsin(theta)

so you convert the known polar coordinates <current A, 0> , <current B, 120>, <current C, 240> to cartesian, add the x and y values to add the vectors, and get the resultant vector.

that is where the math came from on my earlier post

if this is more intuitive for you, its just one other way of doing the math using simple trig

 

[crossman]

In general, the roots of a quadratic equation can be complex, therefore "i" is needed.

Now if you multiply complex numbers, you will obtain terms preceded by j^2 which equals -1. Try it.

I understand all that. I just don't see that SQRT -1 has anything to do with the vertical component. I would feel more comfortable with "x axis" for horizontal and "y-axis" for the vertical. Unfortunately, I am not the one who gets to decide these things.

 

[crossman]

its just a convention, there are many for handling vectors.
<x,y> cartesian
<r,theta> polar
ai + bj complex

all do the same, some have different applications
if its easier for you to visualize the cartesian or haven't had the math for the latter, use those and the corresponding cartesian projections on to x,y,z axi to add the vectors

if this is more intuitive for you, its just one other way of doing the math using simple trig

Thanks for that info. It reinforces that my understanding of the matter is getting there. The cartesian system seems very close to the complex system in that the phasors are broken down into horizontal and vertical components using trigonometry.

Any takes on why the two systems were invented? And why the complex involves the SQRT -1? Is this a "phasor" versus "vector" thing? A vector represents a set force. A phasor represents a force that is constantly changing. Hmmmmm.......

 

[rattus]

This I understand and feel comfortable with.



This completely baffles me. Where is the SQRT -1 coming from?

Solve the equation,

x^2 + 1 = 0

 

[crossman]

Solve the equation,x^2 + 1 = 0

equals i which is the square root of -1

But convince me why this imaginary number needs to be associated with the vertical coordinate when dealing with phasors. Doesn't it all work out perfectly well on the cartesian plane without the use of i ?

 

[rattus]

equals i which is the square root of -1

But convince me why this imaginary number needs to be associated with the vertical coordinate when dealing with phasors. Doesn't it all work out perfectly well on the cartesian plane without the use of i ?

Crossman, you are making me think, and I hate that! And for the moment, let's think vectors, say a vector of magnitude "A".

We need a method of separating the real and imaginary components in vector algebra. That is what "i" and "j" are all about.

Let, "A" represent a positive number on the real axis--zero degrees.

Now, understand that "j" is an operator which rotates a vector +90 deg. Then jA represents a positive number on the imaginary axis, 90 degrees.

And, jjA = -A, a negative number on the real axix--180 degrees

Then -jA is a negative number on the imaginary axis--270 degrees.

And, -jjA = A--zero degrees again.

The same rules apply to phasors.

That is a simple answer to a complicated question.

 

[crossman]

I can go with that. It is basically just a convention, like nakaluk said and the numbers work regardless of which convention we use as long as we are consistent.

Thanks for helping me along, I understand more now than I did.

 

[Gary Shumaker]

I finally have the solution

I finally have the solution

(delta phase A - phase B) divided by 1.732 = I1
(delta phase A - phase C) divided by 1.732 = I2
(delta phase B - phase C) divided by 1.732 = I3

(I1+I2+I3) divided by 1.73 = neutral current

This method proved out in the lab.

Thanks guys

 

[crossman]

Rattus, I did some research last night. What I found is that vectors in three dimensions used in physics are typically designated by i in the horizontal direction, j in the vertical direction, and k in the third direction. Since we only need two dimensions with the electrical stuff, we use i and j, but apparently they do away with the i on the horizontal. So it seems it has nothing to do with the SQRT -1. This sound reasonable?

 

[rattus]

Yes it does:

Yes it does:

Rattus, I did some research last night. What I found is that vectors in three dimensions used in physics are typically designated by i in the horizontal direction, j in the vertical direction, and k in the third direction. Since we only need two dimensions with the electrical stuff, we use i and j, but apparently they do away with the i on the horizontal. So it seems it has nothing to do with the SQRT -1. This sound reasonable?

Here is a simple example:

Consider a current,

I = 10 + j10 Amps

through an impedance,

Z = 10 + j10 Ohms

What is the voltage across Z?

V = I x Z = (10 + j10)A x (10 + j10)Ohms

= (100 + j200 - 100) = j200V = 200V @ 90

j^2 must equal -1 for this to work!

 

[rattus]

(delta phase A - phase B) divided by 1.732 = I1
(delta phase A - phase C) divided by 1.732 = I2
(delta phase B - phase C) divided by 1.732 = I3

(I1+I2+I3) divided by 1.73 = neutral current

This method proved out in the lab.

Thanks guys

Where do you measure neutral current in a delta system?

 

[Gary Shumaker]

Where do you measure neutral current in a delta system?

Delta represents the difference in current between phases.
Gary Shumaker

 

[crossman]

(delta phase A - phase B) divided by 1.732 = I1
(delta phase A - phase C) divided by 1.732 = I2
(delta phase B - phase C) divided by 1.732 = I3

(I1+I2+I3) divided by 1.73 = neutral current

Gary, there is no way this can work. Doing a little figuring on the numerator of what is in bold:

(A - B) + (A - C) + (B - C) = 2A - 2C

Notice the B current dissappears and has no bearing on the result. This means that B current could be anything between 0 and infinity and you would get the same answer. In other words, B has no bearing on the outcome.

 

[crossman]

What is the voltage across Z?

V = I x Z = (10 + j10)A x (10 + j10)Ohms

= (100 + j200 - 100) = j200V = 200V @ 90

j^2 must equal -1 for this to work!

Rattus, I am still struggling with the above, but I will get it, I am doing research right now.

I did figure out that my post above referring to i, j, k, the unit vectors of 3 dimensional systems does not apply because these are electrical PHASORS. Electrical phasors don't show an actual "direction" in 3 dimensional space.

As an example, take current. Current only flows one way or the other in a wire which can be considered as one dimension. So, the vertical axis in the comlex plane is not representing an actual direction, but rather it helps define the magnitude and "polarity" of the current at any given point in time on the sine wave.

With your patience and help, I will get there.

 

[roger]

Gary, that does not work out.

Try your method using the values below

A = 20 amps
B = 20 amps
C = 0 amps

and for a second example use

A = 20
B = 20
C = 10

Roger

 

[charlie b]

I am getting into this late, so I won’t really get into it. I will just point out three things.

First, the letters i, j, and k are used as unit vectors in a 3-dimensional system. The letter i (for mathematicians) and the letter j (for electrical engineers) are used to represent one specific number. These are two completely different uses of the letters, and are not related in any way.

Secondly, in a Cartesian Coordinate System, we often use terms such as, “3X + 2Y” to represent a point on a plane. For this example, the point would be 3 units along the horizontal direction and 2 units along the vertical. But in Electrical Engineering, we use terms that look like, “3 + j2” to represent the same point. It also means a point 3 units along the horizontal and 2 units along the vertical. The “j” is the square root of -1. We really do need to use that number, and not just an X/Y style coordinate, because the “j” is part of the math. If you have to multiply two values, let us say a current value times a voltage value, which will give you a power value, you will wind up with on “j-term” times another “j-term,” and the j^2 will give you a -1, which as I say will be part of calculating the final answer. In the Cartesian system, when you multiply two terms you end up with an X^2 and a Y^2 and an XY, all of which is just letters. The j^2 is a number, not just a letter.

Third, when I first learned math, I was taught that any number multiplied by itself will always give you a positive answer. It was sometime later that the notion of multiplying a number by itself, and getting a negative answer, was (attempted to be) explained to me. I was told that I simply had to imagine that such a thing could happen, and try to work with whatever that number turned out to be. So it was no stretch for me to accept the number as being called an “imaginary number.” That may have been the basis for the original use of the phrase. It may also have been the reason they chose the letter “i” as the symbol for the number “the square root of negative one.”