Electrodynamic tethers (EDT) are a promising alternative for producing the energy required in any scientific exploration mission to Io and its plasma torus, which are generally handcuffed by a scarcity of power. We propose two alternatives using EDT working in the generator regime: 1) a bare self-balanced electrodynamic tether in equilibrium position in the synodic frame Jupiter-Io, and 2) a rotating EDT orbiting around Io to generate permanent power and to provide propellantless orbital maneuvering capability. For the first alternative we derive the necessary orbital and tether design conditions for equilibrium and the system performances in terms of power generation. For the second alternative, we investigate two mission scenarios both involving a 25-km-long 5-cm-wide tape tether placed on a stable retrograde equatorial orbit around Io capable to provide kW-level useful power extracted from the fast rotating Jupiter plasmasphere. In the first scenario the tether current is controlled to provide maximum power generation. The amount of power produced and the impact on the orbit stability is investigated numerically. In the second scenario the current is controlled in order to reduce or increase the orbital energy of the system with the possibility of reaching escape velocity. Results show that EDT can be used as a permanent power production system in exploration missions to Io and the surrounding plasma torus without compromising the orbital stability.