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

TL;DR

This work tackles the difficulty of solving large-scale grid topology optimization under nonlinear AC power-flow by introducing a Generative Neural Network (GenNN) that yields a piecewise-linear PF approximation aligned with PF physics. By embedding binary line-status variables in the GenNN and reformulating the resulting relations into a MILP, the approach enables efficient optimization for topology tasks such as Optimal Transmission Switching ($\text{OTS}$) and Restoration Ordering Problem ($\text{ROP}$). A key innovation is area-based sparsification, which achieves linear parameter growth via spectral-clustering-driven partitioning on electrical distance, enabling scalable training and inference for grids with thousands of buses. Numerical results on the IEEE 118-bus and 6716-bus Texas grids show high PF accuracy, strong topology-adaptivity, and substantially faster MILP-based optimization compared to full AC-OPF-based approaches, highlighting practical impact for resilience-oriented grid operation.

Abstract

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.

Figures (9)

• Figure 1: The proposed GenNN model predicts the nonlinear terms in the second layer using trainable weights; it further generates power variables in the third/fourth layers to match the PF equations.
• Figure 2: Each ReLU-based hidden neuron (a)-(b) produces a PWL function with two linear regions. The sum of the two neurons (c) becomes another PWL function with four linear regions due to the combination of two neurons' activation status.
• Figure 3: Error performance versus the number of hidden neurons for the IEEE 14-bus system with either 20 or 15 branches.
• Figure 4: (a) A 4-bus system with two areas and a tie-line; and (b) its sparse GenNN. Two individual GenNNs (blue and yellow) are separately formed for the two areas, while the tie-line is incorporated into the top GenNN by introducing more input variables ($\theta_{23}$ and $V_3$).
• Figure 5: Comparisons of the (a) average and (b) maximum error in approximating the line power flows and (c) RMSE in predicting the injected power vectors for Direct, GenNN_Full and GenNN_Sparse methods using the 118-bus system.