Hawaiian Electric Industries Inc.’s earnings rose sharply in the second quarter, largely reflecting the timing of a rate increase at its main utility subsidiary that wasn’t in effect for the comparable quarter a year earlier.

HEI earned $38.8 million, or 40 cents a share in the April-to-June quarter, up 43 percent from $27.1 million, or 28 cents a share during the same period in 2011, the company reported Thursday.

Hawaiian Electric Co. and affiliates Maui Electric Co. and Hawaii Electric Light Co. earned a combined $29.4 million in the second quarter, up 73 percent from the $17 million they earned during the second quarter of 2011. The most recent quarter included revenue from a 3.4 percent rate increase that HECO began collecting from Oahu customers on an interim basis in the third quarter of 2011.

When compared with the first quarter of 2012, the earnings of HECO and its affiliates rose 8 percent in the second quarter.

Thursday’s financial report included results for American Savings Bank that HEI originally reported Tuesday. American Savings earned $14.2 million in the second quarter compared with $15.2 million in the year-earlier period.

The utilities are the biggest part of HEI’s business, generating more than twice as much in net income than American Savings Bank.

The HECO companies spent $74 million in the second quarter on upgrades to the electrical grids as part of a move to increase its use of renewable energy, said Constance Lau, HEI’s president and CEO.

"Reducing our dependence on oil is critical to the future of Hawaii, our company and our customers," Lau said in a news release. "With the ongoing impact of high oil prices on customers’ bills, our utilities rate of renewable integration remains a critical priority to help stabilize customer bills," she said.

HEI’s utilities provide electricity to about 95 percent of the state’s population. They generate about 80 percent of their power by burning oil. The average cost of for fuel oil rose to $145.27 a barrel in the second quarter, a 17 percent increase from $123.69 a barrel a year earlier.

Hawaii’s electricity rates are the highest in the country, largely because of the dependence on oil for power generation.

Electricity sales at the HECO companies fell to 2,257 gigawatt-hours in the second quarter, a 4 percent decline from a year earlier, HEI said.

HEI also reported that return on equity, a measure of profitability, rose at HECO but fell at HELCO and MECO. On a consolidated basis, return on equity increased to 8.73 percent at the end of the second quarter from 5.83 percent a year earlier. The Public Utilities Commission allows the HECO companies to earn a return on equity of up to 10 percent.