Minimizing the Expected Cost of Synchronization in Lossless Power Networks
For power system operators, this work provides a convex optimization framework to enhance grid stability by identifying critical network modifications, though validation is limited to a small test system.
The paper addresses minimizing network transients in power systems by optimally modifying the network structure, formulated as a convex optimization problem. On the IEEE 30-bus test system, the method effectively identifies critical links and significantly reduces transients in dynamic simulations.
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.