# Circuit Analysis for Power Transmission Network Question

1. Apr 19, 2012

### Constantinos

Hey!

Below you will find a piece of text I found on a paper. There are some things I don't get, perhaps you could help me.

What it means for the network to be lossless?
Also, why is the power flow equal to Re[Vi(t) Ii,k(t)*] and not outright Vi(t)*Ii,k(t) ? Why the complex conjugate?

I get the math, but not the definitions really!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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2. Apr 20, 2012

### Staff: Mentor

A lossless network contains no resistances, so no real energy can be lost by that network (remember that reactances only store and release energy without loss).

The complex conjugate of the current is used in order to get the phosor angle correct for the power. It has to do with how phasors are multiplied.

Suppose:
$V = |V| \angle \phi_v$
$I = |I| \angle \phi_i$

Multiplying:
$V I = |V||I| \angle \phi_v + \phi_i$

However, for the power we should have the angle corresponding to the power factor:

$\phi_v - \phi_i = \phi~~~~$

So we need to invert the sign of the current angle, hence the complex conjugate is taken.

3. Apr 20, 2012

### Constantinos

Ah yes I see, having susceptance means it also has reactance (I forgot about that).

I'm not sure I understand. Why would we need the angle of the power factor and not the angle of power itself? By power factor I assume you mean this correct?

4. Apr 20, 2012

### Staff: Mentor

If you expand VI* then:

$V I^* = |V||I| \angle \phi = |V||I| cos(\phi) + j|V||I| sin(\phi)$

But this is just the sum of the real and imaginary power P + jQ.

$VI^* = P + jQ$

5. Apr 20, 2012

### Constantinos

Yes I think I get it now, thanks for the clarifications!