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A problem reads "A single phase 50 Hz generator supplies an inductive load of 5000 kW at a power factor of 0.707 lagging ... " How can there be real power loss from an inductor?

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Pure inductors don't dissipate power. However, look at the problem statement carefully. Note the 1/sqrt(2) power factor, meaning 45°. A pure inductance would be 90° and a power factor of 0. This load therefore has both a resistive and inductive component. The overal load is drawing 5 MW, which of course is all going into the resistive part of the load.

The term "inductive load" was used only to point out that the load has a significant inductive component. Giving the specific power factor then provides all the details.

Added:

In electric power engineering, the term reactive power is often used for the voltage times the current drawn by the inductive component of the load. Since the voltage and current of the reactive power are always 90° out of phase, no actual power is transferred. For utilities, thinking of any load demand as a combination of real and reactive powers is a useful abstraction since the two are often dealt with sepearately. For example, a bank of capacitors is a reactive power generator.

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With a 5 GigaWatt generation of power, caused by heavy industry with motor driven inductive loads it raises the reactive current which doesn't get counted as "real" power consumption but is a cost to the provider, as it reduces the capacity limited by current in distribution losses. Motors have inductance but do work (consume real power) and have losses and dissipate heat from many causes, such as winding resistance.

To resolve this, switchable capacitor banks are manually or automatically adjusted near the sub-stations to raise the power factor and reduce the peak current back to the source. They select +VARS of phase leading current from banks to offset some of the -VARS from the loads to reduce distribution losses and improve capacity for real power to be sold.

So even though as consumers we are measured by real power, with all our fridge and air condition motors running, power providers need to raise the power factor when additional capacity is required or to reduce the distribution losses which can be as much as 10% in cable resistive loss. But in large hydro power stations this is still the most efficient power source.

      • the above answer was intended to offer a bigger picture of what power factor means to a 5GW power station. We obviously are not dealing with just inductors here but in general "inductive loads". Inductive Power factor is different from power Factor caused the growing issues of SMPS effects of current pulses before peak voltage. Olin has already clearly stated the theory & fundamentals already. So maybe this should just be a side comment to put it in perspective on a large scale power network. I was not trying to compete with a better answer, just add practical value.
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