AMARILLO—Xcel Energy customers in Texas will receive a one-time, $39.4 million refund in their June billing cycle related to a continued drop in prices for power-plant fuel and the increased use of low-cost wind-energy resources.

If approved by the Public Utility Commission of Texas, Texas residential customers using 1,000 kilowatt-hours a month would see a bill credit of $35.60 based on the amount…