The calculation of high temperature superconductors in feasibility analysis of HTS generators for renewable energies

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Abstract— This paper is presented a simulation setup for the calculation of high temperature superconductors in feasibility analysis of HTS generators for renewable energies from obtained data of a wide bibliographic review, in documents, articles and reports related with critical and operative values of the superconductor material selected for the final simulation in the finite elements software (YBaCuO).

This setup incorporates the magnetic and electric field dependencies as well as the current and temperature dependencies on the electrical resistivity of high temperature superconductors.

The implementation in the software FEMM is shown together with the underlying equations used in the simulation setup and worked in the MATLAB software together with some exemplary simulations.

Index Terms— High Temperature Superconductors, Renewable Energies, Economical Feasibility, FEM

[1] INTRODUCTION

IN the last thirty years it has been demonstrated the existence of a climate change of great impact in the actual society and with a higher impact in the near future. It has been demonstrated too, that the origin of the climate change has been the increasing in the atmosphere due to the excessive use of traditional fossil fuels. It is estimated, fossil fuels, are responsible, approximately, by the 90% of emissions. [1] Recent studies published by the International Energy Agence (IEA) have determined that 80% of emissions by 2035 will come from the industrial and residential sector, so the consequences of the climate change will be every time more terrible for the planet, mainly affecting poor communities [2-3]

Elsewhere, petroleum and natural gas prices are projected to increase in the next 20 years due to increased demand which is expected to grow up 50%: from 87.4 mb/d in 2011 to nearly 99,7 mb/d n 2035 [1]. In that way, emissions will be double times greater in 2050 than actually if we continue with

fossil fuels extensive use. [2-4]

That is the main reason why more and more countries, and in general, all the societies, are demanding the increasing of the use in renewable energies, and although exist interesting developments nowadays, there is so much to advance, and research. Consequently, there are a lot of opportunities to the different fields of science and engineering. One of them and it is where this document is focused, is the implementation of electrical generators using superconductor materials. They have taken so much importance with the discovery of elements with a critical temperature (that one where the superconductivity disappears) higher than 77 K (boiling point of liquid Nitrogen), where this element could be used as refrigerant to meet the superconductivity conditions.

[2] THEORETICAL CONSIDERATIONS

High temperature superconductors.

These are materials that behave as superconductors at high temperatures. Superconductivity was discovered in 1911 at the Leiden Laboratory when H. Kamerlingh discovered a resistance specified of a sample, this suddenly drops to zero when the material is cooled below its critical temperature and remained unmeasurable at all attainable temperatures below. Kamerlingh stated the sample had undergone a transformation into a novel, as yet unknown, state characterized by zero electrical resistance. This state was named “Superconductivity” [5] In that way the development of superconductor materials and their applications history began.

Superconductors can be classified according to their physical behavior:

- Type I superconductors:

They are superconducting in the presence of a magnetic field establishing surface currents which prevent said field to penetrate the material; this phenomenon is known as the Meissner effect. They were the first superconductors to be discovered, and their behavior is largely explained within the framework of the BCS theory, proposed in 1957.

They are all pure elements, they also have a single critical temperature Tc above which they cease to behave like abruptly, and therefore begin to have electrical resistance. In addition, their critical temperatures are very lows, not exceeding 7 Kelvin, They have a unique critical magnetic field Hc which are relatively low, typically no greater than 0.2 Tesla.

- Type II superconductors:

They are materials that instead of passing abruptly from superconducting to normal state (as do the other type I), gradually from one to another.

In contrast to the type I (which are all pure elements) superconductors of this type are a heterogeneous group. They are alloys, ceramics or pure elements. If we apply a magnetic field we see a range of temperatures, Tc1 and Tc2 between, wherein the material is in a mixed state in which the superconducting state coexist and normal. If we increase the magnetic field, these two temperatures will be lower each time, and if the field is large enough, the material is non-conductive even at absolute zero.

On the other hand, if we set the temperature when the substance is in the superconducting state and apply a magnetic field, we find a similar situation: after a certain value Hc1 field starts to penetrate the material, and if we increase to a value Hc2 the superconducting state disappears completely.

Until 2008, only certain compounds of copper and oxygen, usually named as “Cuprates”, were believed to have high temperature superconductors properties (HTS). However, several iron based compounds (pnictides) are known to be superconducting at high temperatures. [6]

Nowadays, materials can exhibit superconductivity at temperatures above 77 K, which can have interesting electrical power applications [7]

Selection criteria of liquid nitrogen as a coolant in HTS generators.

A coolant bath is a mixture used at lower temperatures required, for example for cold traps. Generally consists of a solid that melts or sublimes at low temperature, or a liquid which boils at low temperature, mixed with some other substance that modulates the bath temperature or heat conduction improves.

The simplest and cheapest cooling bath is the ice / water mixture, which maintains a temperature of 0 ° C. For lower temperatures, it is common to use four types of cooling baths, ice, dry ice, liquid nitrogen and liquid hydrogen.

The

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