Last updated 23rd January 2002

A non-mathematical treatment of 'power-factor'
Dr Roy Booth

The type of motor most commonly used in industry is called an induction motor. Induction motors draw electrical power from a supply and do three things with it.
Firstly, they convert part of the electrical power into mechanical power. This is, after all, the purpose of having a motor!
Secondly, they waste some power. Whilst the conversion process is quite efficient, typically 95% at full load, some losses do occur e.g. due to friction, windage and electrical resistance.
Thirdly, and less well known, they give some power back to the supply!
This happens as a consequence of some relatively simple physics but causes tremendous confusion when trying to measure the amount of power a motor is using. To eliminate this confusion we need to understand how an induction motor works.
In a typical induction motor coils of copper wire are wound around a steel structure to form three electromagnets. When an alternating current (ac) is passed through any one of these 'windings' it produces an alternating magnetic field i.e. a field that repeatedly changes direction.
By connecting each winding to a different phase of a three-phase supply we can produce three magnetic fields that pulsate in a rotary pattern. This rotating magnetic field pattern applies a force to the moving part of the motor which causes it to turn.
As each field is built up energy is drawn from the supply and stored in the magnetic field. When the field decays, prior to field reversal, this energy is returned back to the supply system.
Power generation companies don't like this as it causes real problems for their generators. To discourage you from repeatedly drawing then dumping power back into the supply they charge a stiff penalty.
The penalty is based upon the ratio of the amount of power you use as compared to the amount of power you draw. This ratio is called the 'power-factor' with the ideal power factor being 1. This is often referred to as 'unity' power-factor and simply put it means you are using all of the power you are taking.
The amount of power stored and released by the magnetic fields in an induction motor is fixed by the design of the motor. Typically around 20% of the full load power is recycled in this way.
So, when a motor is heavily loaded, its power factor is around 0.8 i.e. 80% of the power drawn is used and 20% is repeatedly stored then released from the magnetic fields.
However, when a motor is lightly loaded its power factor drops dramatically. This happens because the amount of real power being used is relatively small compared with the fixed amount of circulating power. A lightly loaded motor can have a power-factor as low as 0.2 or worse!
In a site that uses a significant number of motors steps must be taken to ensure that large amounts of power are not dumped back into the mains. This is achieved by attaching 'capacitors' to the electrical supply.
When fed with an ac supply these store and release energy in an electrostatic field. The electrostatic field works exactly opposite to the motor's magnetic field and can be used to store the power being dumped out of a motor and then re-supply it when the motor next requires it.
Since the circulating power simply bounces back and forth between the motors electromagnetic field and the capacitors electrostatic field no power needs to be dumped into the mains supply.
This causes a significant improvement in site power-factor i.e. the ratio of power used compared with power drawn is pulled back to near unity. For this reason the capacitors are often referred to as power-factor correction capacitors.
The actual power being used by a motor i.e. that which is either converted into mechanical energy or lost as heat is called the 'real' power and it is measured in kilo-Watts (kW).
The power being stored and released from the magnetic fields of a motor is called either the reactive power, the imaginary power or even the 'Wattless' power. It is measured in kVAr where the lowercase 'r' denotes the fact it is reactive power.
The total power being drawn by a motor is a combination of both the real and reactive powers and is called the apparent power. It is measured in units of kVA.
The apparent power is the easiest to measure. It is found by simply multiplying the current drawn by a motor (Amps) with the voltage supplied to the motor (Volts).
In a circuit supplied with direct current (dc) the product of Volts times Amps is equal to the real power being consumed (Watts). This is because there is no mechanism for storage and release of power i.e. all the power flowing is being used in the circuit.
However, in an ac circuit containing electromagnets there is a storage and release mechanism that produces the effect of reactive power i.e. power that isn't used but rather is repeatedly borrowed and then returned to the supply system.
Most people with an electrical background have a better understanding of dc circuit theory than they do of ac circuit theory. It is easy to see how they fall into the trap of measuring motor current and multiplying it by motor voltage in an attempt to calculate motor power.
Unfortunately this simplistic approach yields the apparent power and makes no account of the flow of reactive power.
To calculate the real power from the apparent power (Volts times Amps) one needs to know either the amount of reactive power flowing or a measure of the power-factor.
For example, we saw earlier that a heavily loaded motor runs with a power-factor of around 0.8. If we multiply the product of Volts times Amps by this factor we will be close to the real power being used.
We also saw earlier that a lightly loaded motor could have a power-factor as low as 0.2. As before the real power being used by the motor is Volts times Amps times the power-factor.
As can be seen, the real power of a lightly loaded motor can be as low as a fifth of the apparent power!
This effect, together with the general lack of understanding of reactive power flow, is used to great advantage by those who peddle 'voltage-optimisers'.
This type of equipment works on the principle of reducing the voltage supplied to a motor when it is not heavily loaded. This causes a significant weakening of the motors magnetic fields and hence reduces the amount of reactive power that is repeatedly stored and released.
Since the apparent power supplied to a motor (Volts times Amps) is made up of a combination of the reactive power and the real power, significant reductions in apparent power can be demonstrated by 'voltage optimisers'.
'Field weakening' can reduce the real power 'lost' in a motor since the reactive current flows through the motor windings which have an electrical resistance. By reducing the current flow one naturally reduces these losses.
However, the power 'lost' in a motor through electrical resistance is deliberately made small and is typically around 5% of the motors full load power. Since the real savings produced by field weakening are a small part of this the actual value of 'voltage optimisation' is minimal.
Unfortunately there appears to be a number of charlatans who are willing to trick people into believing that 'voltage optimisation' can produce savings as high as twenty, thirty, even forty percent!
Such percentage savings can genuinely be demonstrated on very small (fractional horse-power) motors in unloaded conditions. This is simply because small motors are particularly inefficient and when unloaded the amount of real power being consumed is very small.
As a consequence of their gross inefficiency 'voltage optimisation' can produce real savings of the order of tens of Watts for small motors. This is not worth much but when compared against the amount of real power being consumed under such conditions, also of the order of tens of Watts, the savings appear as a large percentage.
The problem comes when the results of such contrived examples are extrapolated to larger motors, which are inherently more efficient, and generally never work in totally unloaded conditions. Under these 'real' conditions such levels of savings are simply not possible. However the charlatans are able to demonstrate savings of this magnitude by playing upon the general misunderstandings surrounding the measurement of motor power consumption.
They do this by measuring the 'power' a motor is using without the 'optimiser' connected. They then hook up their 'optimiser' and measure the new 'power'. The difference in 'power' between the 'before' and 'after' measurements is passed off as the 'power' saving.
This would be fine if what was being measured in the experiment was the real power the motor was using i.e. its 'kilo-Watt-hour' consumption. Unless the motor was extremely lightly loaded the result would be small, typically less than 5%.
However, the charlatans measure apparent power by simply taking current readings and multiplying them by line voltages. When the 'optimiser' is deployed the reactive power is significantly reduced and hence the apparent power is reduced even though the real power being consumed is hardly affected at all!
Using this technique people are tricked into believing they really are saving a lot of power and hence a lot of money. It looks real because the current readings, and hence the product of Volts times Amps, are significantly reduced.
Intuitively a current reduction feels like a power reduction. Intuition is correct, there is a power reduction, but only a reduction in reactive power which doesn't cost anywhere near the same as real power!
Recently I saw a fax that was sent from a well-established UK producer of 'optimiser' equipment. It was addressed to a client who had queried the level of savings measured by his own experiment. The fax contained the statement '..if the current is going down you must be saving money!'.
The same company insisted that the client was wrong to measure motor power consumption in kWh as this took into account local power-factor and his electricity bill was based upon site power-factor. (Cunning or what?)
Their proposal was to measure motor current with a clamp, multiply this by supply voltage and multiply this by the site power-factor. This approach nicely converted all the reactive power flowing between the motor and the power-factor correction capacitors into real power and allowed their contraption to show a tangible saving.
Fortunately the client was perceptive enough to see through the bullshit!
If it were possible to identify which fraction of the total current entering a site was going to a particular motor it would be feasible to multiply this current by the site voltage and the site power-factor to obtain the real power being used by the motor.
However, since this is not possible for all but the simplest of sites, the only 'sure-fire' way one can accurately measure motor power consumption is to use an instrument that measures the relationship between current flow and supply voltage and separates out the reactive power from the real power.
Simply put, there are three things you need to know about a motor to understand how much power it is using: kiloWatts, kiloWatts, kiloWatts!
Measuring only the magnitude of the current a motor draws tells you very little indeed. It's a bit like trying to work out how much beer is left in a barrel by weighing it when you don't know the weight of an empty barrel!
I recently observed another example of a claim of significant motor power reduction that later turned out to be false. This time it was with a variable speed drive!
The supplier measured the current drawn by a motor under normal load and converted this into 'power' by assuming a power-factor of 0.8. The motor actually had a dynamic load with an average power-factor closer to 0.6. This meant the overestimate of power-factor converted a portion of the reactive power into real power.
Then, a variable speed drive (vsd) was fitted and set to run in an 'optimiser' like mode. The current was measured at the input terminals of the vsd and found to be significantly smaller than before.
When the alleged power reduction was calculated a saving of 23% was claimed!
Unfortunately when I repeated the experiment using an instrument capable of measuring real power the saving magically vanished!
Variable speed drives contain a large capacitor bank which is charged by the mains. When a vsd is fitted to a motor the internal capacitors act like power-factor correction capacitors. The reactive power flows back and forth between the fields in the motor and the capacitors but does not show up on the input terminals of the drive.
The alleged saving was achieved by first converting some reactive power into real power by an overestimate of power-factor. The reactive power was then removed from the supply leads by fitting the vsd i.e. making use of the internal capacitor bank.
Bingo! A 23% power reduction!
Unfortunately not, when the real power entering the drive was monitored with a meter capable of measuring kWh, and the 'optimiser' mode switched on and off, the change in real power consumption was found to be negligible!
A moral can be drawn from both of these real world examples of the misinterpretation of motor current:
'If you are being offered a system that claims to reduce motor power consumption and the seller doesn't use an instrument that directly measures true power (kiloWatts) then the seller is either lacking in understanding or lacking in integrity'.
My personal belief is that there are plenty who fall into the second category!!
For those interested in a more conventional explanation of the concept of power-factor I recommend you Click Here.
An alternative explanation can be found by Clicking Here.
Finally, a less than scientific explanation but one I particularly like because of the 'mother-in-law' references can be found by Clicking Here.
Please e-mail me if these links stop working or if you come across other references which you think might be of interest.