Minimizing the Expected Cost of Synchronization in Lossless Power Networks

Abstract

The reliable operation of large-scale electric power networks is increasingly challenging, particularly with the integration of stochastic renewable generation. In this work, we address the problem of minimizing network transients by optimally modifying the underlying network. We formulate the problem in terms of graph Laplacian matrices and show that, under certain assumptions, the problem is convex. We derive a linear matrix inequality whose feasibility guarantees the existence and uniqueness of phase cohesive steady-state angles; this condition can be directly incorporated as a convex constraint in the optimization framework and we provide several geometric interpretations of the optimization problem. The proposed method is validated on the IEEE 30-bus test system, where results demonstrate that our approach effectively identifies critical links on the network. Dynamic simulations show a significant reduction in network transients and overall improvements across several performance metrics. We explore the sparsity-optimality trade-off using a reweighted $\ell_1$ heuristic.