In the current energy scenario, due to the increment in power generation from renewable sources, the importance of electrical storage systems has increased significantly, and as a consequence, the study of the improvement of its efficiency and the design of new storage systems also increased. Superconducting material permits the design of Superconducting Magnetic Energy Storage (SMES). The main problem of SMEs is the low energy density they have, what make the optimization of design to be one of the keys for inclusion of this elements in the power grid and other specific applications as, for instance, flux pumps. As the only basic forms for SMES, and with the objective of its mathematical optimization, this work (i) evaluates the mathematical equations for a real solenoidal winding, and (ii) develops the equivalent equations for a toroidal winding, from the electromagnetic laws. Then, (iii) a practical structure formed by short solenoids connected in series along a circular axis (quasi-toroidal structure) is studied. Due to the large number of equations involved in this case, the finite-element method in used here. Finally (iv), in order to validate the results without building the complete solenoid (impossible at the time), one of the magnetic coupling between two solenoids in the quasitoroidal winding was developed according with the theoretical method, and experimentally tested. The study was carried out by programming different dimensions in order to make conclusions for a further development of an optimization algorithm. These conclusions are presented. This work is the first stage for the optimized design of a SMES, and presents the complete equations of the real toroidal winding as the base of the outline dimensions of a practical quasi-toroidal SMES.

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One of the most interesting applications of superconductors in power systems is the so called "Superconductor Fault Current Limiter (SFCL)". This is a device that makes the lines exhibit a variable short-circuit impedance: very low (almost null) under normal operation, and high when the current increases above the security limit of the line. There are two types of SFCL: resistive and inductive. The first one consists of a superconducting element in series with the line. The element is designed with a critical current equal the security limit of the line. When the current in the line is higher, the element transits and a high resistance arises, protecting the line. The second type is connected in series with the line too. It consists of an inductor with the magnetic core shielded by a superconducting screen. The screen is designed to transit by magnetic field when the current in the coil (line current) is higher than the security limit of the line. At this time, a high reactance arises protecting the line. The PhD thesis we are working on is a new concept of SFCL with two stages (resistive and inductive) in series designed to solve some problems of each type separately. In this case, the resistive stage is located in the gap of the inductive stage magnetic core. Firstly, the objective is to make the magnetic screen transit. When this happens, the magnetic field penetrates the core and surrounds the resistive stage provoking its transition. In this paper, we present the work philosophy of this novel device, which does not have equivalent in conventional (nonsuperconducting) technology.