A party in interest dissatisfied with an order of the commission may appeal to the Supreme Court or court of appeals as provided by statute and the South Carolina Appellate Court Rules. No right of appeal accrues to vacate or set aside, either in whole or in part, an order of the commission, except an order on a rehearing, unless a petition to the commission for a rehearing is filed and refused or considered refused because of the commission's failure to act within twenty days. The commission must not be a party to any action.