Abstract:We show that there is a link between the Kuramoto paradigm and another system of synchronized oscillators, namely an electrical power distribution grid of generators and consumers. The purpose of this work is to show both the formal analogy and some practical consequences. The mapping can be made quantitative, and under some necessary approximations a class of Kuramoto-like models, those with bimodal distribution of the frequencies, is most appropriate for the power-grid. In fact in the power-grid there are two kinds of oscillators: the "sources" delivering power to the "consumers".

In a system of thin alternating layers of superconductors and insulators the equations describing static and dynamic fluxon solutions are derived. The approach, represented by a useful compact matrix form, is intended to describe systems fabricated for example of niobium or niobium-nitride thin films; in the limit of ultrathin superconductor films it may give a model for describing fluxon motion in layered high-T, superconductors. Numerical examples of current versus voltage curves to be expected in such an experiment are presented.

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We have examined the potential of 10 MW superconducting direct drive generators to enter the European offshore wind power market and estimated that the production of about 1200 superconducting turbines until 2030 would correspond to 10% of the EU offshore market. The expected properties of future offshore turbines of 8 and 10 MW have been determined from an up-scaling of an existing 5 MW turbine and the necessary properties of the superconducting drive train are discussed. We have found that the absence of the gear box is the main benefit and the reduced weight and size is secondary. However, the main challenge of the superconducting direct drive technology is to prove that the reliability is superior to the alternative drive trains based on gearboxes or permanent magnets. A strategy of successive testing of superconducting direct drive trains in real wind turbines of 10 kW, 100 kW, 1 MW and 10 MW is suggested to secure the accumulation of reliability experience. Finally, the quantities of high temperature superconducting tape needed for a 10 kW and an extreme high field 10 MW generator are found to be 7.5 km and 1500 km, respectively. A more realistic estimate is 200–300 km of tape per 10 MW generator and it is concluded that the present production capacity of coated conductors must be increased by a factor of 36 by 2020, resulting in a ten times lower price of the tape in order to reach a realistic price level for the superconducting drive train.