Power-flow sensitivities in DC distribution systems

We examine the steady-state behavior of DC distribution systems with arbitrary topologies that couple a heterogeneous collection of power-electronic circuits modeled as parallel connections of resistances, and constant current and power sources (or loads). For this system, we provide analytical closed-form expressions for sensitivities that capture variations of line power flows due to: i) changes in nodal power injections, and ii) line outages. Our results follow from a perturbative analysis of the network power-balance expressions, and the approach leverages contemporary results from circuit theory and structural properties of the network conductance matrix. Simulations from illustrative networks confirm the validity and accuracy of the analytical expressions in estimating the impact of nodal power injections and line outages.