The Massachusetts Department of Public Utilities said Thursday it would investigate National Grid, after about 20,000 South Shore customers of the utility were without power for days following the Dec. 26 snowstorm. The DPU said it would evaluate National Gridâ¿¿s preparation for the storm and its efforts to restore power in regions that suffered outages. The department also plans to investigate whether the utility complied with DPU regulations and with its own Emergency Response Plan. Attorney General Martha Coakleyâ¿¿s office said Thursday that it had requested the investigation. The AGâ¿¿s petition cites National Gridâ¿¿s â¿¿apparent failure to fully implement the Emergency Response Plan it filed with the DPU,â¿ the office said. National Grid issued a statement saying that its â¿¿top priority in any storm is public safety and the safety of our employees, and restoring power to our customers as quickly and safely as possible.â¿ â¿¿Within 36 hours of the storm ending, we restored service to more than 30,000 customers across the state at the peak of the storm, and thousands more in the days after, when high winds caused additional outages,â¿ National Grid said in the statement. If the DPU finds that National Grid has violated any of its standards for restoration of service, the DPU may levy penalties of up to $250,000 per violation, up to a total of $20 million for any related series of violations, Coakleyâ¿¿s office said. National Gridâ¿¿s Emergency Response Plan requires the company to activate local Emergency Operations Centers prior to a storm â¿¿ which are staging areas to conduct restoration of service â¿¿ and to communicate with municipal officials, public safety providers and customers during a storm event, according to Coakleyâ¿¿s office. The petition accuses National Grid of failing to activate the staging areas in order to adequately deploy repair crews and failing to coordinate with local officials, in response to a severe winter storm that had been forecasted days in advance, Coakleyâ¿¿s office said.