Variation of distribution factors with loading

Power transfer distribution factors depend on the operating point and topology of an electric power system. However, it is known empirically that, for a fixed topology, the power transfer distribution factors are relatively insensitive to the operating point. We demonstrate this result theoretically for systems of arbitrary topology with losses, but only for the special case of having reactive compensation sufficient to keep voltages constant at all busses. We also analyze a power to current distribution factor that more closely relates to thermal constraints. We provide empirical corroboration for the theoretical result.