# Reactive power, RL RC circuits

1. Nov 5, 2011

### Bassalisk

Trying to understand the power network and synchronous machines, led me to the fact that I am not sure about the basics.

The terms the generator is delivering or consuming reacting power made me halt.

So I went back to my old course(which I allegedly passed) where the reactive power is addressed. I couldn't understand that back then(1 year) because I barley handled the phase angle, let alone problems of reactive power and its true meaning.

Consider a RL circuit. Plain. (or real inductor).

Solving the differential equation(which I didn't know how to do back then) gives me this:

for $u(t)=U_m\cdot sin(\omega t+\theta _u)$

I get that the current is changing like:

$i(t)=I_m\cdot sin(\omega t+\theta _u-\phi _L)-I_ m\cdot sin(\theta _u -\phi _L)\cdot e^{-\frac{R}{L}t}$

Lets discuss this:

We have 2 components. First component represents a steady-state current.

Second component represents a transient-state which slowly fades.

My question here is:

Do we say for an inductor, that is consuming reactive power?

If we make the angle of the voltage source u(t) such that it cancels the transient-state, did we in fact, "configured" that voltage source, to give OUT reactive power, and give it out just SO much that it cancels the "needs" of that inductor?

These are the questions for now, tons of other are awaiting, but first I have to make a clear distinction between giving out and consuming reactive power.

2. Nov 6, 2011

3. Nov 7, 2011

### gerbi

It's all a agreement how we call that.. consuming means that the current is lagging. There is no power consumption - the reactive power is stored in inductiors magnetic field (stored in one period and moved out in another period).

First of all.. where from comes the transient state ? Tranient occurs when You start from "u(t=0) not eq amplitude". Why ? When U is at it's peak I is equal to 0 (90deg phase shift, obvious). But what about reactive power ? When "q(t=0) is eq to 0" the circuit starts with no transients. At point (t=0"-") the total energy stored in inductor is zero, and there can't be a discontinous energy change.

4. Nov 7, 2011