OLYMPIA, Wash. — Washington state hauled in $541.1 million in its fourth cap-and-trade auction, as the cost of carbon allowances rose high enough to trigger another safety-valve auction to try to tame energy costs.

More than 8.5 million allowances sold for $63.03 each at the Aug. 30 auction, the Department of Ecology announced Wednesday, bringing the state’s take to $1.46 billion since cap-and-trade began Jan. 1.

For the second time, the allowance price surpassed the $51.90 threshold for a special auction closed to investors, who are competing with oil and natural gas companies for the limited pool of allowances.

Investors bought 14.5% of the allowances sold last week, betting prices will continue to climb. The settling price was 30% higher than at the first cap-and-trade auction in February and 12.5% higher than in May.

At $63.03, allowances can be expected to add about 50 cents a gallon to gasoline and 63 cents to diesel, according to a formula cited by the California Air Resources Board.

State Sen. Mark Mullet, D-Issaquah, said Wednesday he will introduce a bill to increase the supply of allowances, refund cap-and-trade surcharges to farmers and cut vehicle license fees to offset high fuel costs.

Mullet, a candidate for governor and who voted for cap-and-trade, said the program needs changes, or else Washington will set a bad example.

“I really worry we won’t see other governments following Washington’s leadership on climate if we can’t show that it’s possible to fight carbon pollution while still balancing it with affordability,” he said in a statement.

Washington emulated California in adopting cap-and-trade. The early results have differed, however.

Allowances in California, which hold auctions with Quebec, Canada, in August sold for $35.20, a record-high for the decade-old program.

Washington plans to cut the number of allowances available by 7% a year, doubling California’s pace. If energy companies don’t acquire enough allowances, they face penalties beginning next year.

“In these early auctions, risk-averse businesses are eager to out-bid each other and acquire allowances sooner rather than later,” the Environmental Defense Fund commented in a statement.

California and Washington are the only states where the average price of regular unleaded gasoline topped $5 a gallon on Wednesday, according to AAA.

California, after slipping to No. 2 for about a month this summer, had the most-expensive gas at $5.34 for a gallon of regular unleaded. The average price in Washington was $5.08 a gallon.

Washington had the third most-expensive diesel at $5.61 a gallon, trailing California and Hawaii.

In the past year, gas prices have risen 41 cents a gallon in Washington, compared to 2 cents in Oregon. A year ago, diesel was a penny a gallon cheaper in Washington than in Oregon. It’s now 46 cents a gallon more expensive.