Material Parameters T c J c B irr v J E We can pass a current until the Lorentz force pulls flux lines off pinning centres. Max force BJ c /vol and E=Bv
Consequences Maximum force/ vol is BJ c. This is what drives a motor. When the field changes there is a loss EJ c /vol This determines AC losses.
AC Losses, Field amplitude b, or current I Self field at I c Loss/cycle/length o I c 2 /4 2 Independent of material, fairly independent of shape, reduces with cube of current, so subdivide conductors and work below I c for low loss.
External field, (relevant to motors) Loss= bJ c d J/cycl/vol d is width perpendicular to field. Since field is also proportional to Jc, loss for given field in given volume does not depend on Jc or conductor material, only on conductor width. Maximum Possible (Based on perfect diamagnetism and square hysteresis loop). Aspect ratio x applied field 2 o J/vol/cycle
Material Limits for Conventional Machines Nearly all conventional machines can be approximated by a hollow cylindrical iron stator containing a solid iron rotor. There are current sheets fixed to each, either in the gap or in slots. A sinusoidal current sheet allows simple analytic expressions for torque and dissipation
NS N S Max B 1T, Fe saturation Max j 800 kA/m, 0.1 T (Thermal and appoximate) Max torque Bj /vol of rotor Max power at 50Hz 25MW/ cubic metre of rotor.
EFFICIENCY Loss/Power is ( /R) 2 where is the skin depth of copper (1 cm at 50 Hz) and R the rotor radius. Large machines are very efficient, (98% for utility generators) Superconductors are attractive for small machines, but small coolers are expensive and inefficient which cancels advantage
Now compare superconductors Limits depend on maximum pinning force
Force BJ c S Integrate the moment of the force to get torque. Torque/vol=RBJ c /3 Power x 2 frequency Torque/vol proportional to J c and radius.
Using YBCO we get 100 times the power/vol, or 1/1000 volume for a given power. (Weight even better)
HOW TO ACHIEVE THIS? Maximum BJ c is at 2 tesla Rotor can be solid or wire Stator needs wire, and AC losses are high. Only possible with YBCO coated conductors
Realities We can come down from the ideal in many different ways and still have major benefits A factor of 100 is possible, a factor of five can be economically attractive.
Motor Types Conventional motor types tend to merge using superconductors. Think in terms of force on flux lines and E-J characteristics. E I Induction (viscous) Hysteresis (friction) Induction Reluctance, Permanent Magnet
How do we provide a large rotating field? Firstly a large field Secondly without large losses?
B j A/m Free space o j=0.1 T, thermal limit. B=0.05 T (approximately) Iron on outside (or inside) doubles B B=0.1 T (May be needed for screening) Narrow air gap. B=0.1Tx(radius/gap) up to saturation 2T
A superconducting rotor is a large air gap so only small fields can be applied with a normal stator. A hybrid iron/superconducting rotor does not increase the B at the right place so is not helpful (But it is useful in reluctance machines)
Cooling Start with Carnot,work proportional to 1/T:- T 300 : 77: 20: 4 K Power 1: 4: 16: 80 Inefficiency, multiply by 10-50. Large coolers are more efficient Efficient coolers cost more
Coolants Liquid Nitrogen Liquid neon Liquid Hydrogen He
Materials YBCO wires, ideal but expensive and not yet available. BSCCO tape, must be shielded from field at 77K, good properties at 20-30K YBCO bulk. Good for rotor, especially as permanent magnet- but then may need to be remagnetised.
Magnesium Diboride Magnesium Diboride, comparable with BSCCO at 20K, still improving. Cheaper and easier. Low Tc, still the cheapest per kA m, but AC losses in stator an expensive cooling a barrier.
CONCLUSIONS Superconducting motors and generators can increase the power per unit volume by several orders of magnitude compared with copper and iron. Efficiency gains are also significant.
YBCO Only YBCO wires can realise the full benefits Significant improvements can be obtained with a wide variety of different materials, temperatures, and machine designs.