Field hysteresis losses

These balanced enclosure currents also induce electric fields into nearby structures, RCC beams and columns in the same way as the main conductors, and hence nullify most of the space magnetic fields. These space fields (fields outside the enclosure) are otherwise responsible for causing eddy current and hysteresis losses in the metallic (magnetic) structures, RCC beams and columns in the vicinity. The electrical bonding of enclosures thus... 

When a critical field (Ec) is reached, which is near to the coercive field, the domains switch direction as a whole involving considerable hysteresis loss. This loss is proportional to the area of the loop, so that for the single crystal in Fig 2.46(a) it amounts to about 0.1 MJm-3. At 100Hz the power dissipated as heat would be 100 MW m-3, which would result in a very rapid rise in temperature. The dissipation factor (tan (5) is also very high at high field strengths, but becomes small at low field strengths, as described above. Modifications to the composition diminish the loss still further. 

FIGURE 2. Schematic curve illustrating the B vs. H dependence for hard and soft magnetic materials. Hard materials have a larger remanence and coercive field, and a correspondingly large hysteresis loss. 

The main energy loss is attributed to the creation and annihilation of the domain wall surface during its displacement (Guyot Globus, 1976). Hysteresis loss decreases by decreasing the coercive field, by means of the various mechanisms discussed in this section. An approximate, general expression for hystersis loss as a function of frequency is simply ... 

Magnetically soft materials have a low coercivity H < 1000 A/m) and high permeability because of their reversible magnetization and correspondingly low hysteresis loss. They are largely used in field... 

The anisotropic continuum approach to losses in multifilament conductors was first conceived by Carr, who developed the model assuming that the inductor is a continuum material with anisotropic resistivity. He applied this approach to the special case of losses in cylindrical conductors for applied transverse sinusoidal fields in the absence of transport current [ ]. Those losses resulting from pJ in the conductor are classified as eddy current or saturation hysteresis losses, depending upon the level of /. Eddy current losses result from J below Jc, with the implicit assumption of rapidly rising resistivity in the flux-flow regime with currents saturated at Jc. The magnetization loss for the continuum is essentially the magnetic hysteresis loss for the filaments times the fraction of the composite occupied by the filaments. 

As current is increased through a filament that is situated in a transverse changing magnetic field, the hysteresis loss appears to increase in a manner that depends upon the shape of the filament and its orientation in the applied field. The increase in loss is accompanied by the appearance of a resistive voltage drop across the sample, so that the transport current source delivers real power to the filament, and the filament is thus effectively resistive because of the dynamics of the applied field. At the same time, the hysteretic magnetic moment associated with the applied... 

Calculations of hysteresis losses in filaments or solid conductors with transport current have implicitly or explicitly included the effect of the dynamic resistivity. Several researchers have calculated losses for magnetic field changes parallel to the surfaces of flat-slab filaments or flat conductors and Morgan noted the dis-... 

A general solution for the hysteresis loss for arbitrarily shaped filaments with transport current in full penetration transverse fields has been provided by Walker and Murphy [ ]. For the case of cylindrical filaments, dynamic resistivity increases with transport current. Dynamic resistance has been observed in several experiments conducted to examine the effect of transport current on losses... 

The hysteresis loss in the filaments may be calculated precisely for the limiting case I/Ic = 1 for all magnetic fields, and also for large magnetic fields and any value of ///c. Other cases are complicated by variations in the permeability, and by factors which depend upon whether the filament is fully or partially penetrated for the given ac field and transport current. Therefore, it is desirable to develop some semiem-pirical interpolation formulas which will give a smooth connection between limiting values for the hysteresis loss. 

In another limiting case, the value of the hysteresis loss at I/Ic = 1, denoted by Pfi(l), is given for any magnetic field amplitude [ ] by... 

Fig. 2. Dependence of hysteresis loss on the amplitude of alternating field for no transport current O, measured point , measured point with calculated eddy current loss subtracted.

The data in Fig. 5 also cover measurements in the region of partial penetration of the field into the filaments (Ho < H ). The effective field for full penetration, Hp, decreases with increasing transport current and full penetration occurs at ///c = 0.4. In Fig. 6, full penetration exists over the complete range of ///c. The eddy current loss in Fig. 6 is a small part of the total, and the measured loss is predominantly hysteresis loss. The overall agreement between measurement and calculation is quite good, indicating that the interpolation formula (16) may be used with some confidence. It is not known whether the observed discrepancies are due to errors in the formula or to imprecision in the material constants. 

Fig. 6. Effect of dc transport current on the predominant full-penetration hysteresis loss. The solid curves give the total measured loss. The dashed curves give the theoretical total loss, most of which is hysteresis. At these larger amplitude fields, the eddy current contribution is nearly independent of ///<..

If the material is initially unmagnetized at O it will reach saturation at P as H is increased. As the field is reduced and again increased the loop PQRSTP is formed (see graph). The area of this loop is proportional to the energy loss (hysteresis loss) occurring... 

---