Generalized Injection Shift Factors

Generalized injection shift factors (ISFs) are the sensitivities of active-power line flows to active-power bus injections. They are computed without designating an artifactual slack bus in the power network; therefore, conceptually, they reflect sensitivities of power flows more accurately than conventional ISFs, the values of which depend on the choice of the slack bus. This paper derives analytical closed-form expressions for generalized ISFs from a perturbative analysis of the ac circuit equations. In addition, they are computed from a system of linear equations that arise from high-frequency synchronized measurements collected from phasor measurement units. As an application, generalized ISFs are used to predict active-power line flows during the transient period following a contingency by leveraging inertial and governor power flows over appropriate time horizons.