Tracing the flows of electricity

Consider an electrical power system and let G denote the set of nodes with net generation, L the set of nodes with a net load and assume the DC model of the network. Our aim is to determine how much power is each node of G sending to each node of L in such a way that the flow decomposition arising from this assignment is such that each branch flow is broken in parcels of the (as much as possible) same orientation in order to provide a sensible tool for transmission cost allocation.