Development of Power Flow Sensitivity Analysis for Experimental Data Using Virtual Point Transformation

The equations for a power flow sensitivity analysis are developed by means of describing the coupling interface between substructures with virtual points. This analysis describes how power flow between source and receiver structures changes with respect to modifications made to the real and imaginary components of the receiver impedance; termed the real and imaginary sensitivities, respectively. Previously developed power flow sensitivity equations have been applied to analytical and numerical models, but assume source and receiver interfaces have identical meshes, and both translational and rotational dynamics are accounted for. In an experimental setting, translational dynamics can easily be measured by use of accelerometers, but rotational measurements are more difficult to make as an array of accelerometers is often needed. However, the equations derived for numerical models are cast onto a domain in which physical and virtual coordinates are accounted for, where the virtual coordinates define the coupling interface with three translational and three rotational degrees of freedom (DOFs). It is shown that the properties of the real and imaginary sensitivity still hold after this coordinate transformation. Finally, retaining internal DOFs, and the need for defining a “synthetic impedance” in the derivation of the sensitivity equations, is discussed.