# Complex power

1. Oct 8, 2015

### Passionate Eng

Why does a load consume reactive power?
How can we produce reactive power?
And what is the relationship between instantaneous power and complex power?

2. Oct 8, 2015

### Svein

• You do not consume reactive power, you "borrow" it and then "pay it back".
• You do not produce reactive power. You supply power, the load may be more or less reactive.
That depends very much on the application. I have seen examples (CRT scanning) where the peak voltage and the peak current were both quite high - but never simultaneously.

Last edited: Oct 8, 2015
3. Oct 8, 2015

### milesyoung

In the framework of steady-state AC analysis, the OP's lingo is correct.

Assuming use of the passive sign convention, the complex power is given by:
$$\mathbf{S} = \mathbf{V}\overline{\mathbf{I}} = P + jQ$$
where $\mathbf{V}, \mathbf{I}$ are RMS phasors for voltage and current, respectively, and $P, Q$ is the active and reactive power consumed, respectively.

$Q$ will, for instance, be positive for an ideal inductor, i.e. it is said to consume reactive power.

$Q$ will, for instance, be negative for an ideal capacitor, i.e. it is said to produce reactive power.

There is none. Complex power is defined in terms of phasors.

4. Oct 8, 2015

Homework questions?

5. Oct 8, 2015

### Baluncore

Real power is the product of voltage and the in-phase component of the current.
The product of voltage and the quadrature-phase current is reactive circulating energy.

Since cables have real resistance, real power is needed to circulate a reactive current. That power is the product of the reactive current by the voltage drop along the wires due to the reactive current, not the voltage between the conductors as with real power.

6. Oct 9, 2015

### Passionate Eng

Thx for all ^_^

7. Oct 9, 2015

### William White

hmm- thats being a bit picky.

Power stations generate reactive power to balance the grid

8. Oct 9, 2015

### Svein

Properly speaking: They introduce a reactive load in order to "balance the grid".

9. Oct 9, 2015

### William White

like I said, you are being picky; everybody knows what is meant by generating reactive power.

Dont be pedantic - it does not help.

Power stations generate power. Some of it is VARS, some is VAs. The ratio can be changed by the power station manager.

I understood the OPs question, and the manager of the power station would too.

10. Oct 9, 2015

### Svein

I am a mathematician - in my world there is no such thing as "everybody knows". A power station generates voltage and supplies current to the load. The phase of the load current is determined by the load, not by the generator.

11. Oct 9, 2015

### William White

The generator itself and all its associated gubbins is a load. When everyday people talk about the generator in a power station, they are talking about the plant that burns fuel and produces electricity.

- lets say it is widely known (rather than everybody knows).

yes - it is acceptable to "produce reactive power" and the manager of the power station would ask the plant technician to do so when required without any argument.

Last edited by a moderator: Oct 9, 2015
12. Oct 9, 2015

OK so this blew up a little - I wanted to post earlier. I disagree, they do not "generate" reactive power they provide it! Providing reactive power decreases the amount of real power they can provide (if they are maxed out) because you are "pushing" current and not delivering anything. Conversely - and on the face counter-intuitively, - you DO CONSUME reactive power - because the system providing the POWER has to supply enough POWER to deliver the current (in and then out). If your house is a pure inductor - the utility has to supply current, the generator has to supply that current through the system - it takes energy to supply that current.

Consider this - you buy a gold ring - the vendor has to supply it - they ship it to you, you send it back - the vendor sees"cost - but you received nothing - and they do not charge for shipping. If you did this everyday - the vendor would say they have to stop. But they are not generating a new gold ring every day.

13. Oct 9, 2015

And the utility does measure it KVARH - is measuring it.

14. Oct 9, 2015

### Staff: Mentor

Thread closed temporarily for some cleanup...

15. Oct 9, 2015

### Staff: Mentor

I am learning from the discussion in this thread, and don't think it's a bad thing to clarify the terminology.

16. Oct 11, 2015

### Hesch

That's not right. In a grid ( connected to several power stations ) you can control the production of reactive power in a single power station by over/under-magnetizing the generator, thereby distributing the production/consumption amongst the power stations in a way, that leads to minimum conducting power losses in power lines.

17. Oct 11, 2015

### Svein

Yes. I do not quite see how you control the current phase in that way, unless you introduce an output impedance in the generator that is (partly) reactive. What staggers me, however, is the problem of doing any control at all on a high voltage transfer line (think 700kV)...

18. Oct 11, 2015

### Hesch

Say you have this 700kV transfer line, and you magnetize a single connected generator to yield 800kV ( transformed ), the generator cannot change the voltage of the 700kV ( too many competiting power stations ), so the 800kV ( which is there as for the single power station ) must be vectorially folded, so that the sum of the folded vectors are kept within a radius of 700kV from 0V, and when you fold the 800kV vector, a transverse vector must be created, resulting in a reactive power.
Well, the 700kV and the power is created by power stations. They ( and the consumers ) are the ones to control it.

Last edited: Oct 11, 2015
19. Oct 11, 2015

### Baluncore

You can make the concept of VAR as difficult as you like by making the situation more complex. KISS.
But once you have the concept of the grid being an “infinite bus”, with many sources and sinks, you will realise that the VAR on the grid must be satisfied by generators providing a current slightly out of phase with the local voltage.

Generators are adjusting the phase of the current they produce to satisfy the bus. On average they must balance the grid VA + VAR, or the power frequency would change.
http://www.openelectrical.org/wiki/index.php?title=Infinite_Bus

20. Oct 12, 2015