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Applying a negative or positive sign to power factor is an obsolete method of describing whether it is 'leading' or 'lagging'. We no longer do this. These days, a 'leading power factor' indicates that the load is capacitive and the load current is leading the supply voltage, and a 'lagging power factor' indicates that the load is inductive, and the load current is lagging the supply voltage.

Having said that, a 'negative' power factor is also the mathematical consequence of 'negative power' -i.e. the direction of power when it is fed from the load back to the supply (e.g. when the grid feeds energy into a generator, causing it to 'motor'). In this case, the power factor isn't really negative, but simply appears to be so.

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Q: What the negative and positive sign shows for power factor?
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