# Reactive power

Discussion in 'The Projects Forum' started by Peytonator, Mar 24, 2011.

1. ### Peytonator Thread Starter Active Member

Jun 30, 2008
105
3
Hi there,

How do you measure reactive power in the presence of non-sinusoidal waveforms due to non-linear loads? Obviously we can't use S^2=P^2+Q^2, and Q ≠ Ssinθ since P and Q are not orthogonal.

Thanks

2. ### CDRIVE AAC Fanatic!

Jul 1, 2008
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Do you think a Thermocouple would do?

3. ### Peytonator Thread Starter Active Member

Jun 30, 2008
105
3
Are you referring to active/real power? I'm looking for reactive power...

4. ### CDRIVE AAC Fanatic!

Jul 1, 2008
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Yes I was. Sorry.

5. ### GetDeviceInfo Senior Member

Jun 7, 2009
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Could you measure reactance by applying a square wave and measuring the resultant time constant.

6. ### Peytonator Thread Starter Active Member

Jun 30, 2008
105
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Reactive power is not reactance...

7. ### CDRIVE AAC Fanatic!

Jul 1, 2008
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I think what I'm having trouble getting my head around is this.. Since reactive power isn't real then wouldn't it always be zero?

8. ### Peytonator Thread Starter Active Member

Jun 30, 2008
105
3
Reactive power (in sinusoidal systems) is VIsinθ. In a resistive load, θ=0, so reactive power = 0. In an inductive/capacitive load, θ≠0.

In a non-linear system, the power triangle no longer holds due to the presence of harmonics, and reactive power ≠ VIsinθ. How to find it?

Even though it's not real, we still have to find it

9. ### CDRIVE AAC Fanatic!

Jul 1, 2008
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Is your instructor expecting an instrumentation solution or a mathematical one?

Where are all the AAC math-heads when we need them?

Apr 5, 2008
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11. ### Peytonator Thread Starter Active Member

Jun 30, 2008
105
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Please can you critique my attached solution? I have a new question: how do I phase shift one of the signals (voltage or current by 90deg)?

Btw, the solution has to be theoretical and practical...

Thanks again

Last edited: Mar 26, 2011
12. ### Peytonator Thread Starter Active Member

Jun 30, 2008
105
3
I see that if you use a low pass filter, you get a 90deg phase, but the amplitude attenuates dramatically... which is not exactly what I want...

Anyone know how to use Hilbert's transform? I can't find much on the internet.

Jul 1, 2008
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15. ### The Electrician AAC Fanatic!

Oct 9, 2007
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What happened to your attached solution? Did you delete it?

If your load has no capacitors or inductors, but just a non-linear resistive load, such as a light dimmer might provide:

Is it really proper to speak of "reactive power" or "VARs"? The fundamental component of the current is phase shifted with respect to the fundamental component of the applied voltage due to the time delay in turning on the triac, not due to any reactive circuit elements in the load.

There are meters on the market (such as the Fluke 43B) that measure the power drawn by a non-linear load and indicate the real power, volt-amperes and VARs even though there are no reactive elements in the load.

For example, here are a couple of images showing the circumstances of a light dimmer set to 50% conduction angle into an incandescent bulb.

The first image shows the applied line voltage in orange, the current in blue and the instantaneous power in red. Notice that the instantaneous power never goes negative as it would with, for example, a sine wave of voltage applied to a capacitor.

The numbers on the right are from the power analysis module plugged into the scope. The "reactive power" is 37.1 VAR, even though the load has no capacitors or inductors; it's just an incandescent light bulb.

I measured the same setup with a Fluke 43B and got essentially the same numbers. The Fluke also gave a number for volt-amperes (VA, apparent power) of 53 watts, and a displacement power factor of .86

The grid voltage is somewhat distorted (flat topped) so the numbers are not exactly what one would expect with a perfect sine wave and a conduction angle of 45°, but close enough.

In the second image are shown the harmonics of the current waveform.

The three components of the power triangle are called real (or true) power, apparent power and reactive power (VARs). The term "reactive power" derives from historical reasons, back when loads were mostly linear and the current drawn by a load was nearly sinusoidal.

Notice that the relationship S^2=P^2+Q^2 still holds, according to the meter (37 watts, 37 VARs and 53 VA), even though there are a lot of harmonics due the non-linear nature of the load, and no reactive circuit elements at all.

To answer my own question, even though there are no reactive elements in the light dimmer load, and it would seem incorrect to speak of one component of the load power as "reactive power", that is in fact the convention. It is the third component in the power triangle along with "real power" and "apparent power", and everybody refers to it as "reactive power".

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16. ### Peytonator Thread Starter Active Member

Jun 30, 2008
105
3

I was originally under the impression that VAR is reactive power (regardless of what the load it). True, there need not be reactive elements in the load - diodes are not reactive, but non-linear - but as you say, they do introduce a phase shift between harmonics.

The problem I'm still having is that each harmonic has a different phase shift, which is not neccessarily equal to the fundamental displacement angle. Thus you can only draw up the power triangle for the FIRST HARMONIC. So is your multimeter reading not misleading, or accurate only for the first harmonic? Further, displacement power factor is by definition that of the FIRST harmonic.

A significant amount of literature shows that in the presence of harmonics,

S^2 = P^2 + Q^2 + D^2.

Since no right angle exists between P and Q, D (distortion power) is used to compensate.

To summarise, there has to be a new way of defining reactive power for ALL harmonics, which I've shown in the attachment... do you agree? (Note that U_h and I_h refer to RMS harmonics).

Last edited: Mar 30, 2011
17. ### sharma@vivek New Member

May 2, 2010
9
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You should use any power meter ( watt meter)

18. ### sharma@vivek New Member

May 2, 2010
9
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use a watt meter

19. ### Peytonator Thread Starter Active Member

Jun 30, 2008
105
3
A wattmeter measures watts not VAR...

Just another question: Assuming I can get the magnitude of the displacement power factor for a load, by using S/P (real power/apparent power), how would I tell (in software) whether it is leading or lagging? Is there some way to look at instantaneous values? Btw, I don't explicitly have the angle, but only power factor...