Reactive power equation

Moxica23

Joined Jun 23, 2014
12
Hi,

Here it says that the equation for Reactive power is

$$Q=\frac{E^2}{X}$$​

but in many other places I found that the correct equation is:

$$Q=\frac{E^2}{X}*sin phi$$​

where "phi" is the phase delay between current and voltage.

So, which is the correct version of that equation ?

Regards

crutschow

Joined Mar 14, 2008
27,755
The first equation is correct if X is just a reactive impedance.
The second equation is correct for X being any impedance (often indicated by the complex number Z).

Moxica23

Joined Jun 23, 2014
12
So the first equation describe the situation when in that circuit we have only reactance (capacitive or/and inductive) and no resistance ?

And the second equation describe the situation when in our circuit we have both reactance and inductance ?

If so, why the first equation is included in the calculation methodology for power factor corection for the case when in our circuit we have an electric motor ? An electric motor have both rectance and resistance. They shouldn't use the second equation ?

crutschow

Joined Mar 14, 2008
27,755
If the measured voltage is directly across the reactance and not the complete circuit than the first equation works.

Moxica23

Joined Jun 23, 2014
12
Yes, I agree. But on this page they speak about a circuit in which an electric motor is the only load. Considering that an electric motor has also some electric resistance, I ask myself why they used the equation for the case when the load is only a reactance.

MrAl

Joined Jun 17, 2014
8,479
Hi,

Could that be because they just want to calculate the reactive power, not the total power?

t_n_k

Joined Mar 6, 2009
5,455
The OP's link to the AAC page reveals this is in relation to power factor correction (pfc).

The object is to achieve a load side unity power factor. The value of Q as shown in that case is the leading compensation VARS required from a pfc capacitor placed in parallel with a lagging power factor load connected to a supply E. Since a pure capacitance exhibits a 90° phase shift in its current and applied terminal voltage, the sin(phi) value is unity.

I'm also querying the supposedly "correct" equation

$$Q=\frac{E^2}{X}sin(\phi)$$

I would rather have

$$Q=\frac{E^2}{|Z|}sin(\phi)$$

where E is the voltage applied to a general impedance Z = R±jX and

$$|Z|=\sqrt{R^2+X^2}$$

$$\phi=\mp \arctan(\frac{X}{R})$$

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