When a synchronous generator is running at lagging power factor the current it supplies lags its terminal voltage.
The Power factor of a utility depends on the type of load it supplies. Usually the Loads on utility are inductive loads (where the current lags behind the Voltage) and hence the power factor at which the utility operates is lagging. Most loads connected to utility are inductive loads like motors, fans, rolling mills which cause the power factor of the utility to be of lagging in nature.
Hope this helps
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