For the first time, we derive efficient modeling equations for the average
power analysis of Raman amplifiers (RAs) from the standard propagation equa
tions. Applications of these equations to the numerical analysis of practic
al RA-based systems show a reduction in computation time of over two orders
of magnitude compared with the direct integration approach based on ordina
ry coupled differential equations, while reproducing all the essential syst
em performances precisely. In addition to enhanced computational efficiency
, derived equations also give deeper insights into the detailed dynamics of
RAs.