Hydropower Regulatory Efficiency Act of 2013 - (Sec. 3) Amends the Public Utility Regulatory Policies Act of 1978 (PURPA) to increase from 5,000 to 10,000 kilowatts the size of small hydroelectric power projects which the Federal Energy Regulatory Commission (FERC) may exempt from its license requirements.

(Sec. 4) Amends the Federal Power Act to revise the limitation on the maximum installation capacity of qualifying conduit hydropower facilities that are eligible for an exemption from licensing requirements.

Requires any person, state, or municipality proposing to construct a qualifying conduit hydropower facility to file with FERC a notice of intent to do so. Requires FERC, within 15 days after receiving such a notice of intent, to make an initial determination as to whether the facility meets the qualifying criteria.

Waives license requirements for any conduit hydroelectric facility that: (1) uses for electric power generation only the hydroelectric potential of a non-federally owned conduit, (2) has a maximum installed capacity of 5 megawatts, and (3) is not currently licensed or exempted from license requirements.

Redefines "conduit" to specify any tunnel, canal, pipeline, aqueduct, flume, ditch, or similar manmade water conveyance operated for the distribution of water for agricultural, municipal, or industrial consumption and not primarily for the generation of electricity.

Authorizes FERC to: (1) exempt from license requirements any electric power generation facility that utilizes for such generation only the hydroelectric potential of a conduit, and has an installed capacity or 40 megawatts or fewer; and (2) extend the preliminary permit period for up to 2 additional years beyond the 3 years otherwise allowed if it finds that the permittee has implemented activities under the permit in good faith and with reasonable diligence.

(Sec. 6) Directs FERC to: (1) investigate the feasibility of issuing a license for hydropower development at nonpowered dams and closed loop pumped storage projects during a two-year period, and (2) hold workshops and develop hydropower pilot projects.

(Sec. 7) Directs the Secretary of Energy (DOE) to study: (1) the technical flexibility that existing pumped storage facilities can provide to support intermittent renewable electric energy generation, including the potential for such facilities to be upgraded or retrofitted with advanced commercially available technology; and (2) the technical potential of existing pumped storage facilities and new advanced pumped storage facilities to provide grid reliability benefits.

Hydropower Improvement Act of 2013 - Declares the sense of the Senate that the United States should increase substantially the capacity and generation of clean, renewable hydropower which will improve the environmental quality of resources and support local job creation and economic investment across the United States.

Defines "conduit" to specify any tunnel, canal, pipeline, aqueduct, flume, ditch, or similar manmade water conveyance operated for the distribution of water for agricultural, municipal, or industrial consumption and not primarily for the generation of electricity.

Directs the Federal Energy Regulatory Commission (FERC) to: (1) investigate the feasibility of issuing a license for certain hydropower development at nonpowered dams and closed loop pumped storage projects during a two-year period beginning on commencement of the FERC prefiling licensing process (two-year process); and (2) hold workshops on how to implement a two-year process, develop criteria for identifying hydropower development projects at nonpowered dams and closed loop pumped storage projects that may be appropriate for licensing within a two-year process, and develop pilot projects to test such a process.

Amends the Federal Power Act to revise the limitation on the maximum installment capacity of qualifying conduit hydropower facilities eligible for exemption from licensing requirements. Waives such requirements for any conduit hydroelectric facility that: (1) uses for electric power generation only the hydroelectric potential of a non-federally owned conduit, (2) has a maximum installed capacity of five megawatts, and (3) is not currently licensed or exempted from license requirements.

Authorizes FERC to exempt from license requirements any electric power generation facility that utilizes for such generation only the hydroelectric potential of a conduit, and has an installed capacity or 40 megawatts or fewer.

Requires any person, state, or municipality proposing to construct a qualifying conduit hydropower facility to file with FERC a notice of intent to do so. Requires FERC, within 15 days after receiving a notice of intent, to make an initial determination whether the facility meets the qualifying criteria.

Amends the Public Utility Regulatory Policies Act of 1978 (PURPA) to increase from 5,000 to 10,000 kilowatts the size of small hydroelectric power projects which FERC may exempt from its license requirements.

Authorizes FERC to extend the preliminary permit period for up to two additional years if it finds that the permittee has implemented activities under the permit in good faith and with reasonable diligence.

Directs the Secretary of Energy (DOE) to study and report to congressional committees on: (1) the technical flexibility that existing pumped storage facilities can provide to support intermittent renewable electric energy generation, including the potential for those facilities to be upgraded or retrofitted with advanced commercially available technology; and (2) the technical potential of existing pumped storage facilities and new advanced pumped storage facilities to provide grid reliability benefits.

Directs the President to report to certain congressional committees on actions taken by DOE, the Department of the Interior, and the Army Corps of Engineers to carry out a certain memorandum of understanding on hydropower, with particular emphasis on actions taken by the agencies to work together and facilitate the federal permitting process for federal and non-federal hydropower projects at federal facilities.