COHOES, N.Y. — The number of Americans whose electricity or gas has been shut off for nonpayment of their bills is up sharply in many parts of the country as people struggle to cope with higher prices and a shaky economy.

Shut-offs have been running 17 percent higher than last year among customers of New York state’s major utilities, and 22 percent higher in economically hard-hit Michigan. They are up in all or part of dozens of other states, including Pennsylvania, Florida and California, according to a check of regulators and energy companies.

Despite stepped-up efforts by state and federal governments, utilities and private groups to help people avoid shut-offs this winter, some worry the problem will only get worse in the coming months, particularly with the downturn on Wall Street.

“I just didn’t have the money to pay,” said Marie Williams, a single mother raising four daughters in Cohoes, N.Y., a former mill city on the Hudson River. “Rent had to be paid, and food for the girls.”

Williams’ power was cut off this summer for about a week, forcing her girls to do homework by candlelight. She became one of more than 230,000 residential customers of New York’s 10 major utilities to have their service shut off for nonpayment through August of this year.

Southern California Edison Co., with 4.5 million residential electric customers, reported residential terminations were up 10 percent through August of this year to 228,000; Westar Energy Inc. of Topeka, Kan., said it saw a 19.5 percent increase in residential shut-offs. Tampa Electric Co. reported a 19 percent climb in disconnect orders through June.