The effects of mode coupling in multimode fibers have been reported using coupled power equations of power flow equations, and the good agreement between theoretical and experimental results provides further evidence that the power flow equation is a useful description of the power distribution in a multimode optical fiber. This paper develops a simple formalism to analyze power flow equations with the help of a variational principle. The results can treat not only any mode coupling mechanism involving the previous works and the experimental results but also any input modal distribution, and the good agreement between theoretical and experimental results shows the validity of our theory. As an example of applications, mode coupling due to random bends of the fiber axis is studied in detail, and the mode coupling-induced losses and the steady-state pulse width are calculated.