Last Week of October Question...

[happysteve]

Well, I'm trying to post the answer to this, but I keep getting the anti-spam thing. Seems a bit harsh, in the trainee section. Maybe I'll try splitting it up (if it lets me post anything!)

 

[happysteve]

Part 1:

Right, y'bugger.

Instead of L1, L2, L3 let's call the 3 points a, b, c.
So Ra = 100, Rb = 120, Rc = 150.

Ia+Ib+Ic = 0 (Kirchoff's current law) (eqn 1).

Expressing the resistances as conductances (or, more generally, admittances):

Ya = 1/Ra, Yb = 1/Rb, Yc = 1/Rc.

Let "0" be the floating neutral point, so "Va0" is the voltage between Va and the floating neutral, i.e. the voltage across resistance Ra (or, to put it another way, across admittance Ya)

Ia = Va0 x Ya, Ib = Vb0 x Yb, Ic = Vc0 x Yc

So substituting those into the KCL equation:

(Va0 x Ya) + (Vb0 x Yb) + (Vc0 x Yc) = 0 (eqn 2)

Let "n" be the neutral point (if neutral was still connected to Earth).

Va0 = Van + Vn0
Vb0 = Vbn + Vn0
Vc0 = Vcn + Vn0 (equations 3a-3b)

Substituting these into (eqn 2):

(Van+Vn0)Ya + (Vbn+Vn0)Yb + (Vcn+Vn0)Yc = 0

Therefore:

V0n = ((Van*Ya) + (Vbn*Yb) + (Vcn*Yc)) / (Ya + Yb + Yc) (equation 4)

(... to be continued...)

 

[happysteve]

But we have to be careful, because we have to take phase into account. I do this using complex numbers, but you can think of this as

resolving your voltage plus phase angle into "x" (the "real part") and "y" (the "imaginary part")

 

[happysteve]

Let's define "a" as zero phase. So Van is easy:

Van = 230

In complex form, Vbn = -115 + 199j

 

[happysteve]

Sorry, won't let me post any more.

 

[happysteve]

Oh, apparently it will let me post inanities, but not maths. Great.

 

[happysteve]

I'll resort to taking a screen shot then:


Sorry about that. Best I could do.

 

[happysteve]

Practical application of all this: If you find yourself the victim of a floating neutral (as I once did... well, one with a high resistance to Earth), put the kettle on (and any other loads you can). You will reduce your voltage so there's less chance of stuff blowing up or a fire... but your neighbours won't be so lucky.

 

[pennychew]

Damn! i was just about to post all that and you beat me to it!

Seriously though, top work fella :coolgleamA:

 

[Silly Sausage]

I knew you'd be first to answer this Steve!
I was considering barring you.

Haven't checked your answer yet, I still need to work it myself, got 7 days left.

What was that battery thread, I've got to own up on that one!

 

[happysteve]

I knew you'd be first to answer this Steve!
I was considering barring you.

Haven't checked your answer yet, I still need to work it myself, got 7 days left.

What was that battery thread, I've got to own up on that one!

I don't tend to pipe up unless it's a question I struggle with myself. There is a lot to be gained by struggling on and working stuff out for yourself, so if I reckon it's a fair question I'll generally stay out of it (unless no-one's volunteered an answer for ages).

But this was on another level. That's not a Level 3 question (well, not any more, dunno if it used to be taught). I'd be interested to hear from our overseas trainees what they thought of that!

And the battery thread is this one: Tonight. I noticed Tony went quiet on that one, too...:angel_smile:

Cheers for posting it up... I certainly learnt summat! I also learnt about wye-delta and delta-wye transformations in my research (though it turned out ultimately to not be useful for this question). And it's good to be able to put numbers in.

 

[Baker1988]

i honestly do not remember doing this in college i could be wrong but i do not remember ant of that

 

[Simonslimline]

If this was taught it would come under unit 309 on the 2357 C&G. We never did anything regarding floating neutrals. There was a question on the 309 written exam asking for the neutral current of unbalanced loads on a 3 phase 4 wire system.

 

[happysteve]

I didn't come across it on my 2365 unit 305, either (like Simon, we also did neutral currents in unbalanced star).

I looked back through my old uni notes, I found this from the first year (Level 4):


"Calculation of the line currents can be done using mesh analysis but we shall not enter that here."
Couldn't find it in my Level 5 notes either.

Saying all that, it's an interesting problem! Summat that looks so simple, a problem that's so easily stated and understood, yet takes a page of maths to sort out.

So cheers