Magnetic bearings with double crossed loops modelled with T-A formulation and electric circuits

The application of High‐Temperature Superconductor(HTS)coils made of coated conductors has been investigated for many years.A possible configuration for such coils is the jointless loop,also known as the ring coil.The double crossed loop coil(DCLC)has been successfully applied in superconducting magnetic bearings(SMBs).The design of SMBs with DCLCs requires flexible modelling to allow all parts of the device to be represented.This work proposes the T‐A formulation with a thin‐film approximation for modelling SMB with DCLCs in the finite element analysis framework.A 2D representation of the system is coupled with an external electric circuit to model the continuity of the lines that represent the parts of each jointless loop.To couple the T‐A formulation and the circuit,an average of the total electric field,with both resistive and inductive components,is applied to the circuit.The total current computed by the circuit is applied to the T‐A formulation.The proposed methodology was validated by comparison with levitation force experimental data.Two types of tests were simulated:five levitation force tests and three guidance force tests.It is shown that there is a limit to the behaviour of the levitation force related to the high‐loss state.Below this limit,the stack of DCLCs behaves as an equivalent bulk.Beyond this limit,a high‐loss state appears as a linear growth of the levitation force.It is also shown that this high‐loss state in vertical displacement influences the lateral force.

J-A formulation: A finite element methodology for simulating superconducting devices

High‐temperature superconductors are a powerful technological option to be applied in the current scenario of energy transition.Their applications include fault current limiters,power electrical cables,and electrical machines,for example.Due to the non‐linearities of superconductors,it is computationally costly to run real models of superconducting equipment.Therefore,it is of paramount importance to have a reliable and fast formulation to model superconducting devices.This paper proposes a new hybrid J‐A formulation to simulate superconducting devices.The new formulation is validated with 5 case studies,some of which are benchmarks.The J‐A formulation agrees in all cases and has a smaller computation time when compared with the T‐A formulation.Moreover,due to the simple implementation,the proposed formulation allows the possibility of running the J and A formulations in the same order and presents itself as a potential feature to speed up and help the design of the superconducting devices.