Promoting Closed-Loop Pumped Storage Hydropower Act (Sec. 2) This bill amends the Federal Power Act to authorize the Federal Energy Regulatory Commission (FERC) to establish an expedited licensing process for issuing and amending licenses and preliminary permits for closed-loop pumped storage projects (in which the upper and lower reservoirs do not impound or directly withdraw water from navigable waters, or that are not continuously connected to a naturally flowing water feature). In establishing the expedited process, FERC shall convene an interagency task force with appropriate federal and state agencies and Indian tribes to coordinate the regulatory process associated with the authorizations required to construct and operate closed-loop pumped storage projects. FERC must assess the safety of existing dams and other structures related to the project before issuing any license for a closed-loop storage project. FERC must hold a workshop to explore potential opportunities for development of storage projects at abandoned mine sites. FERC must also establish criteria that a project shall meet to qualify as a closed-loop pumped storage under this bill, including requiring that the project cause little to no change to existing surface and groundwater flows and uses and that the project is unlikely to adversely affect species listed as threatened or endangered under the Endangered Species Act of 1973. (Sec. 3) Licensees are not required to pay an annual charge for administrative expenses until construction commences.