Total loss sensitivities and allocated losses: Conceptual relations in radial distribution networks

The sensitivity of distribution network losses to the change in net power at the network nodes (and phases of each node for unbalanced distribution systems) conveys key messages about the need to increase or decrease the net power to reduce network losses. Similar information is provided by the total network losses allocated to nodes and phases, determined based on the power flow solution. This paper provides original insights and new analytical formulations of the sensitivity of the total losses with respect to the node current magnitude for balanced and unbalanced radial distribution networks. Two novel fundamental results are presented: (i) the sign of the allocated losses is equal to the sign of total loss sensitivities with respect to the node current magnitudes, and (ii) the increase/reduction of the total losses for small net power changes in a node is identified by multiplying the sign of the allocated losses and the sign of the net node power, to obtain the allocated losses-based product, without carrying out further power flow calculations. Once established the relation between total loss sensitivities and allocated losses, the calculations are carried out by using the allocated losses, avoiding the need for assigning the directions of variation of power in the calculation of the sensitivities. The results are discussed on radial distribution systems with time-varying loads and generations and are used to establish novel losses-based strategies to assist distribution system operation and planning.