## A Quasi-Newton Algorithm for Solving the Power-Flow Problem in Inverter-Based Power Systems.

*PhD student Temitope Amuda with Advisor A. D. Domínguez-García.*

Commercial power-flow solvers compute the solution to the single slack-based power-flow problem using conventional approaches such as the Newton-Raphson or the Gauss-Seidel methods. In the conventional power-flow formulation, a single bus with a fixed normalized voltage and angle is dedicated to carrying all the slack in the network. Alternatively, a distributed slack-based power-flow formulation, which does not depend on a single bus to carry the slack in the network, has gained importance in inverter-based power systems. The power-flow formulation for the inverter-based system utilizes distributed slack, where the generator buses in the network all share the slack according to their participation factors. Commercial solvers cannot be utilized directly to implement and solve the distributed formulation. To this end, we propose Quasi-Newton methods to implement and solve distributed slack-based power flow formulation on commercial solvers. The proposed Quasi-Newton methods use modified Jacobian matrices in order to simplify the formulation into sub-problems which can then be solved by the commercial solvers. The result of the Quasi-Newton algorithm developed is shown in Figure 1 below. The convergence rate of the algorithms developed was compared to the classical Newton’s method on a modified IEEE 14-bus test feeder.