HARTFORD, Conn. (AP) — Hundreds of more crews from out of state were arriving in Connecticut on Thursday to help restore power to nearly 580,000 homes and businesses that remained in the dark after Tropical Storm Isaias, as state officials announced an investigation into electricity utilities amid mounting criticism of their response.

Gov. Ned Lamont also announced Thursday that he deployed the Connecticut National Guard to help with power restoration.

A spokesman for the state’s largest electricity provider, Eversource, meanwhile, said there likely would have been many more outages if the company had not made hundreds of millions of dollars worth of upgrades under an agreement with the state following storms in 2011 and 2012 that cut power to hundreds of thousands of customers.

Eversource and United Illuminating said it could be several more days until power is fully restored. Nearly 580,000 outages remained in the state late Thursday afternoon, down from about 611,000 during the late morning and down from more than 700,000 outages on Wednesday morning, the day after the storm.

The state Public Utilities Regulatory Authority, or PURA, announced Thursday that it will investigate the utilities’ response to determine if they were adequately prepared, adhered to laws and regulations and whether civil penalties should be imposed. PURA also will look into failures of the utilities’ outage response systems.

Gov. Ned Lamont had requested an investigation Wednesday, calling the restoration efforts “wholly inadequate.” He also expressed confidence Thursday that all polling places will have power for Tuesday’s primary election.

“I think we’re going to be in good position by Tuesday, or else there will be hell to pay,” Lamont said.

During an afternoon briefing, Lamont said officials were monitoring outages at nursing homes in the state, about a third of which were without power but operating on backup generators. He also said the Department of Labor is running on an old generator, and if it fails it could affect the distribution of unemployment benefits to 300,000 people. Many wastewater treatment plants also are operating on generators, and some cell phone towers were running on batteries.

The governor announced a second storm-related death in the state, a person fatally wounded in a chainsaw accident in Newtown. The person’s name hasn’t been released. A 66-year-old Naugatuck man, Raymond Schultz, died when a tree fell on him as he was clearing branches from a road. Five other people were seriously injured, Lamont said.

Eversource expected several hundred crews from other states and Canada to arrive in Connecticut on Thursday, after several hundred came to the state Wednesday. Eversource said it expected most of its outages to be restored by the end of the upcoming weekend. United Illuminating said it expected to have the majority of outages restored Saturday and restoration substantially completed by Monday.

Eversource underestimated the severity of Isaias, but United Illuminating did not, said Marissa Paslick Gillett, chairwoman of PURA.

“There are disturbing reports emerging about the coordination, or lack thereof, between our electric utilities and the communities which they serve,” Gillett said. “This is simply unacceptable. There will be a full, transparent investigation.”

Criticism mounted against the utility companies on Thursday, in Twitter posts by government officials.

U.S. Sen. Chris Murphy, a Connecticut Democrat, called their response “unacceptable.”

State Treasurer Shawn Wooden said, “The utility companies reaping huge profits from consumers must be held accountable for being unprepared for a natural disaster and looking out for the best interest of the people they serve.”

And Mayor Mark Boughton in Danbury, where more than 15,000 customers remained without power Thursday, posted a picture of people looking through binoculars with a caption saying, “Waiting on @eversourceenergy.”

Two storms that caused massive power outages in 2011 led to a new state law aimed at increasing the accountability of utility companies. An October snowstorm caused more than 830,000 outages which took nearly two weeks in some places to restore. That followed Tropical Storm Irene in August, which knocked out power to nearly 800,000 customers.

In October 2012, superstorm Sandy caused nearly 690,000 outages.

State Senate Republican Leader Len Fasano, of North Haven, and state Republican Sen. Paul Formica, of East Lyme, called on state lawmakers to be part of the PURA investigation.

“After Irene, the October storm and Sandy, how could Eversource not be prepared for a tropical storm with weeks of notice?” they asked, in a statement.

In January 2013, state regulators approved a $300 million plan for Eversource’s predecessor, Connecticut Light & Power, to strengthen its electricity system to help avoid extended storm-related outages. Under the plan, the company trimmed scores of trees, strengthened utility poles and equipment and installed coated, thicker-gauge wire.

Eversource spokesman Frank Poirot said Thursday that those upgrades likely prevented scores of additional outages this week.

“The damage would have been much worse,” he said. “Despite the number of outages we experienced with this storm on Tuesday, I think there was still a benefit — a resilient and hardened electric system.”

Despite Eversource’s tree-trimming efforts, insects, disease and drought left trees across the state vulnerable to high winds, Poirot said.

A United Illuminating spokesman, Edward Crowder, said the company will fully cooperate with the PURA investigation. He said UI’s preparation and response to the storm were consistent with its emergency plan that is filed with the state.