where θ
a
2
y hr
tK R
⋅Δ+ +
is the ambient temperature at time t, Δθ
is the topoil (in tank) temperature rise in steady-state at rated losses (no-load losses and load losses), R is the loss ratio (ratio between the load losses P
LL
and no-load losses P
or
), K is the ratio between the load current at time t and rated current, x is the oil exponent, y is the winding exponent and Δθ
NL
) is the hot-spot to top-oil (in tank) gradient at rated current (H is the hot-spot factor and g
is the average winding to average oil in tank temperature gradient at rated current)