In the Rockaways, where nearly 14,000 customers still had no power as of Monday morning, volunteers set up a makeshift solar charging station between a car roof and a shopping cart. A multipanel, battery-tied system is helping fuel a relief center’s operations.

In the storm’s wake, solar companies have been donating equipment across New York and other stricken areas to function as emergency power systems now and backups in the longer term. It is important, executives say, to create smaller, more decentralized ways of generating and storing electricity to help ease strain on the grid in times of high demand or failure.

“The grid won’t evolve into something more distributed and fault-tolerant overnight — it’s still dependent upon a centralized system,” said Ben Tarbell, vice president for products at SolarCity, a leading installer that has donated generators after Hurricanes Katrina and Sandy and is developing a battery backup system for its customers. “But the components are starting to come together.”

Generally, home systems like Mr. Antonio’s are engineered to feed electricity from the roof array through an inverter and into the home’s electrical panel, sending the excess to the broader electric grid. But during a failure, the inverter automatically shuts down the system to guarantee that no electricity is flowing into equipment that workers will be trying to fix. The shutdown also ensures that the system’s current will sync with the grid when power is restored and guards against damaging the lines.

Certain systems allow solar panels to run a household directly during prolonged power failures, generally combined with battery storage to keep the power functioning around the clock. Those require installing a separate electrical panel and a more complicated inverter that would switch the flow of electricity entirely over to the house, perhaps to a few critical circuits to run, say, the refrigerator, some lights, television and minimal heat.