AC LOSSES

When an AC field is applied to a superconducting cable, the magnetic field generated by the current moves through the cable and generates a so-called hysteric loss, even when the superconductor is below the critical current. The hysteretic losses are proportional to the current to the third, and differ from ohmic losses that are proportional to the current to the second. The physical reason for the ac loss is that the magnetisation of a superconductor shows a hysteresis loop similar to the one seen in ferromagnetic materials, however of opposite polarity (diamagnetic).

Measuring the AC losses

The AC losses can be measured by electrical and calorimetric methods. The loss is given for a specific temperature in watts per m, W/m.

The electrical method is based on measuring the correlated data set I, U, j where I is the current in the cable, U is the voltage over and j is the phase angle between the current and voltage. From this measurement the loss, P, can be calculated by using the expression:

P = I x U x cos(j )

The calorimetric method is based on measuring a temperature gradient and relating this to a heat flow. In practical it can be done by pumping e.g. liquid nitrogen (LN2) through the cable and measure the temperature rise, D T, of the LN2. If the flow rate, dm/dt, is known and the heat capacity of LN2 is c_P, then the loss, P, can be calculated from the expression:

P = D T x dm/dt x c_P

The electrical method is more precise (for low currents) and faster than the calorimetric method, however, under some conditions, the calorimetric method may be the only option.

In the figure, the loss curve is shown for a 10 m cable conductor. The loss curve is measured using the electrical method. The AC loss at 2 kArms was 0.6 W/m. At the time it was reported it was the lowest AC loss measured in the world.

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