Download POWER FACTOR CORRECTION

Power factor correction and the law of conservation of sorrows
by Andrew Williamson Pr.Eng. SMSAIEE
Power factor correction has earned a reputation as something of a black art. While there are some complex and
tricky issues in the design of an installation, the basics of power factor correction are not difficult. Indeed, with
basic engineering know-how, it is possible to assess the benefits of power factor correction equipment, and even
to estimate the savings it will deliver.
Electricity tariffs
Utilities charge for electric power in many different ways, but there seems to be general consensus nowadays that tariffs
should in some way be cost reflective. Obviously, the constraints within the power system affect the perception of
costs, so tariffs can and do change as the network develops. Designing tariffs is an art in itself, so we are not going into
a dissertation on it, but we are simply going to look at some of the cost components, and how the power factor of a load
affects these.
Energy costs
It is obvious that the fuel that is used in a power station directly related to the energy that is sent out from the power
station. Thus, it makes sense that a consumer should pay for the energy that they consume. From a consumer
perspective, there is virtually nothing that can be done to limit or control the energy consumed, except to limit or
control whatever is physically being produced. To make a certain amount of any particular widget or stuff, a certain
amount of energy will be needed. The power factor of the load will not affect the amount of energy needed.
Generation capacity related charges
The cost of a power station is not just the cost of the coal and water it consumes in its lifetime though. There are the
capital and associated costs of the machines themselves. An easy way to recover these costs is as an overhead charge or
levy on the energy charges, and this is quite common. Another form of generation capacity charge, that has been seen
recently in South Africa, and elsewhere, is the time of use tariff. This encourages customers to use existing generation
capacity rather than force the installation of new capacity.
A lower power factor will cause the generator current to increase, and it is possible that the stator current limit is
reached before the power limit is reached. Thus, in some sense, the power factor of the load can affect generation
capacity, but unless the overall power factor of all the loads is very low, this is not usually of major concern. The
power factor of the load also affects the losses in the generator, but again, this is not usually of major concern.
Transmission and distribution capacity related charges
Sending energy out of a power station does not get it to a customer. To do this, either the utility, or the consumer, or a
third party, must provide the wires, which also cost money.
There are various ways of recovering the cost of the wires, but a connection charge, or some sort of demand charge is
commonly used. Demand charges have been based on real power, but this does not accurately reflect the cost unless the
power factor is known and invariant. Therefore, apparent power demand charges have become more common, and
there would even be some justification for a demand charge based on current and not power at all.
A higher power factor saves money
We are going to explain this with the “beer tankard analogy” – something that appeals to electrical engineers.
Anyone who has ever drawn a pint will know that beer has froth on it – if it doesn’t, then it will be flat and tasteless.
But the froth is not a particularly satisfying part of the beer – in a sense it is a necessary evil. It seems self-evident that
for a given size of beer tankard, there will be more satisfaction from 90% beer and 10% froth, than from 60% beer and
40% froth.
It is the same with electrical power. All electrical machines generate or consume real power, and the physics of
operation of most machines compels them to generate or consume some reactive power too. Reactive power, though,
does no real work – it is like the froth on the beer. It is a fact, though, that for a given capacity of wires, there is more
work done by loads that consume less reactive power. Conversely, for a given amount of work to be done, loads
consuming less reactive power need a smaller wires, which cost less. Thus, if you can reduce the reactive power
consumed by your load, you will save on the cost of the wires.
A higher power factor costs money
As most loads are inductive, increasing the power factor is normally done by connecting a capacitor in parallel to the
load. A capacitor consumes no (or very little) real power, so the energy charges are not increased, but by supplying the
reactive power required by the load, the capacitor improves the power factor that is presented to the grid. Obviously,
capacitors do not come for free, though. There is a capital cost, as well as an ongoing maintenance cost. Being static
equipment, the maintenance is, admittedly, very low, but capacitors are not yet completely maintenance free. The
business case for installing a capacitor basically boils down to a trade off between the installation costs and the ongoing
cost savings.
Some formulae
A few formulae to manipulate the figures are always useful. All of the real power, reactive power, and apparent power,
rely on the power triangle and some high school trigonometry. As an example, suppose we wanted to calculate the
reduction in apparent power when a particular capacitor is installed. Assume that the capacitor does not overcompensate the load.
We know that the original apparent power is
Sorig  P
pf
and the original reactive power is
Qorig  P. tan(arccos ( pf ))
so the new reactive power is
Qnew  P. tan(arccos ( pf ))  Qcap
The new apparent power is
Snew 
2
P Qnew
2
and the saving is the difference between the original and new apparent power.
Harmonics
Now we meet The Law of Conservation of Sorrows. This is almost as important as Ohm’s Law. Basically it says that
one can never fix a problem without creating another. Watch it in action!
As we said, most loads are inductive. Most of the components in the “wires” are also inductive. That means that when
a capacitor is introduced into the system, there will be resonant frequencies introduced. If such a resonant frequency
co-incides with a frequency of harmonic currents produced by a non-linear load, then there is a very real possibility of
either very high voltages or very high currents being produced. Obviously, this can damage the capacitor itself, or other
equipment.
Harmonic currents are produced by more loads than one may at first think. Transformers and motors produce third
harmonic currents due to the non-linearity of the magnetisation curve in the steel. Fluorescent lights also produce third
harmonic currents. Variable speed drives produce a whole range of harmonic currents, and so do computer power
suppliers.
If we can’t eliminate the source of harmonics, then the only way to deal with the problem is to make sure that the
resonant frequencies are placed carefully. For a purely inductive network, the resonant frequency is given by
f  50 Hz. Ssc
Qcap
where Ssc is the short circuit capacity of the network in MVA, and Q cap is the size of the capacitor in Mvar.
Normally, if this frequency is above about 500 Hz, the likelihood of a resonance problem is small, unless there is a large
converter based load in the vicinity. If the frequency is below this, then a more detailed study by a specialist engineer
would be needed. The frequency should also not be within about 5 Hz of an exact multiple of 50 Hz.
Voltage rise
Under normal network conditions, energising a capacitor bank will cause the voltage to rise. The size of the voltage rise
is approximately given by
k  Qcap
Ssc
Obviously, this should not be too high, but it should also not be too low, otherwise the capacitor will have little effect
on the power factor. A good rule of thumb would be to limit the voltage rise to between 2% and 4%. With a capacitor
of this size, the resonant frequency would be 350 Hz and 250 Hz. Here comes the Law of Conservation of Sorrows!
The dominant harmonics produced by a six pulse converter are exactly in this range. And the whole range is below the
500 Hz threshold mentioned above.
Switching transients
Another possible problem caused by capacitors relates to their switching transient. At the instant that a capacitor is
switched, it presents a short-circuit to the supply, so the voltage collapses virtually to zero. The voltage recovers very
quickly, but this notch in the supply voltage can cause problems. Perhaps the most common problem is the tripping of
sensitive variable speed drives. By careful design, this problem can normally be overcome, but often the sensitivity of
the drives is only realised the first time that the capacitor is switched! The Law of Conservation of Sorrows again!
Conclusion
Everything in engineering seems difficult until you know how to do it. Power factor correction is no exception.
Hopefully, with the basics covered above, it will be easy to do some simple assessments, and also determine when a
specialist is needed. Never forget the Law of Conservation of Sorrows, though.
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