## Measurement-Based Estimation of Linear Sensitivity Distribution Factors and Applications

**Christine Chen with adviser A. Domínguez-García**

Power system operators rely heavily on online studies conducted on a system model obtained offline. The analysis includes the computation of linear sensitivity distribution factors (DFs), which are used, in conjunction with online measurements, to determine whether the system is N-1 secure in near real-time. These studies are not ideal because (1) an accurate model containing up-to-date network topology is required and (2) the results from such model-based studies may not be applicable if the actual system evolution does not match any predicted operating points due to unforeseen circumstances such as equipment failure and faults in external areas. For example, in the recent San Diego blackout, operators could not detect that certain lines were overloaded or close to being overloaded because the network model was not up-to-date. Thus, traditional model-based techniques may no longer satisfy the needs of monitoring and protection tasks. It is important to develop power system monitoring tools that are adaptive to operating-point and system-network changes and to estimate parameters using online measurements. Previously we proposed a method to estimate linear sensitivity DFs that exploits measurements obtained from phasor measurement units in near real-time without the use of a mathematical model. While the method is shown to accurately compute injection shift factors (ISFs), even in the presence of undetected system topology and operating point changes, the least-squares error estimation problem formulation necessitates at least as many sets of synchronized measurements as unknown ISFs. For a large power system, such a restriction may be ill-advised in, e.g., real-time contingency analysis, since power systems are constantly undergoing changes and operators often need to quickly determine whether or not the current system is secure. We propose an accurate and efficient method to recover the ISF solution using fewer sets of measurements than unknown ISFs. To this end, we exploit a sparse representation (i.e., one in which many elements are zero) of the vector of desired ISFs, solve for the transformed sparse representation, and finally compute the original ISFs by applying the inverse transformation.

This research was funded by the U.S. Department of Energy for “The Future Grid to Enable Sustainable Energy Systems,” an initiative of the Power Systems Engineering Research Center.