ESTIMATION OF MINIMUM CORE LOSSES [HYSTERSIS LOSSES AND EXCESS LOSSES]BASED ON GRAIN SIZE.

1. CORE LOSSES = HYSTERSIS LOSSES +
EXCESS LOSSES;
HYSTERSIS LOSS =
REF: Combining Mager and Steinmetz: The Effect of Grain Size
and Maximum
Induction on Hysteresis Energy Loss
EXCESS LOSSES =C√L;
CORE LOSSES = A/L+B√L----------------(I)
FOR MINIMUM CORE LOSSES
DIFFERENTIATING ABOVE EQUATION
WITH RESPECT TO L AND EQUATING TO
ZERO,WE HAVE
dC/dL= [-A/L2
]+[B/2√L]

2. EQUATING dC/dL=0;
ON SIMPLIFYING AND RE-ARRAGEMENT
WE HAVE
B=[2A/L3/2
]
ON SUBSTITUTION IN MAIN CORE LOSS
EQUATION WE HAVE
CORE LOSS=A/L+[2A/L3/2
]*L
CORE LOSS= 3A/L
GENERAL MINIMUM CORE LOSS
EQUATION IN TERMS FO GRAIN SIZE IS
GIVEN BY
MINIMUM CORE LOSS=
[3* ]