The areas affected were Gariahat, Hazra, Deshopriyo Park, Maddox Square, Rashbehari Avenue, Ballygunge and connected areas in south Kolkata.
The damage occurred at around 3:45 am causing dislocation of around 20 MW of power in aggregate, a CESC statement said.
Two of the three cables feeding power to CESC's Richie Road distribution station were badly damaged at Ballygunge Place due to irresponsible digging, it said.
CESC took up restoration work on a war-footing and could successfully restore supply within 15 minutes, but with increasing power demand in the area, the situation worsened from 9:45 am and rotational shedding had to be resorted to.
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A CESC spokesman expressed serious concern at the recent damage of underground power cables of CESC by other agencies operating in the metropolis.
In March-April this year, there were approximately 15 such incidents of interruption of power cables of CESC.
The issues were taken up seriously with the authorities, he added.