Data-driven Modeling of Linearizable Power Flow for Large-scale Grid Topology Optimization

Effective power flow (PF) modeling critically affects the solution accuracy and computational complexity of large-scale grid optimization problems. Especially for grid optimization involving flexible topology to enhance resilience, obtaining a tractable yet accurate approximation of nonlinear AC-PF is essential. This work puts forth a data-driven approach to obtain piecewise linear (PWL) PF approximation using an innovative neural network (NN) architecture, effectively aligning with the inherent generative structure of AC-PF equations. Accordingly, our proposed generative NN (GenNN) method directly incorporates binary topology variables, efficiently enabling a mixed-integer linear program (MILP) formulation for grid optimization tasks like optimal transmission switching (OTS) and restoration ordering problems (ROP). To attain model scalability for large-scale applications, we develop an area-partitioning-based sparsification approach by using fixed-size areas to attain a linear growth rate of model parameters, as opposed to the quadratic one of existing work. Numerical tests on the IEEE 118-bus and 6716-bus synthetic Texas grid demonstrate that our sparse GenNN achieves superior accuracy and computational efficiency, substantially outperforming existing approaches in large-scale PF modeling and topology optimization.