  The power-flow sensitivity coefficients (PFSCs) are widely used in the power
system for expressing linearized dependencies between the controlled (i.e., the
nodal voltages, lines currents) and control variables (e.g., active and
reactive power injections, transformer tap positions, etc.). The PFSCs are
often computed by knowing the compound admittance matrix of a given network and
the grid states. However, when the branch parameters (or admittance matrix) are
inaccurate or known with limited accuracy, the computed PFSCs can not be relied
upon. Uncertain PFSCs, when used in control, can lead to infeasible control
set-points. In this context, this paper presents a method to quantify the
uncertainty of the PFSCs from uncertain branch parameters and noisy grid-state
measurements that can be used for formulating safe control schemes. We derive
an analytical expression using the error-propagation principle. The developed
tool is numerically validated using Monte Carlo simulations.
