AC-Informed DC Optimal Transmission Switching Problems via Parameter Optimization
Babak Taheri, Daniel K. Molzahn
TL;DR
This work addresses the gap between DC-OTS and AC-OTS by tailoring the DC power-flow model to OTS through parameter optimization. It introduces an OTS-focused loss L(b, ψ) that aligns DC line flows with AC flows and a bias term ψ to capture reactive effects, optimizing these parameters online for a given loading condition. The approach uses a bilevel-inspired scheme with a DC-OPF lower-level and a gradient-based upper-level solver, implemented via differentiable convex optimization (e.g., CVXPY layers) and solved with Conjugate Gradient and Wolfe line search. Numerical results on PGLib test cases show that the optimized O-DC-OTS achieves significant cost reductions and higher AC feasibility compared to DC-OTS, LPAC-OTS, and QC-OTS, while delivering favorable computation times, especially on larger networks.
Abstract
Optimal Transmission Switching (OTS) problems minimize operational costs while treating both the transmission line energization statuses and generator setpoints as decision variables. The combination of nonlinearities from an AC power flow model and discrete variables associated with line statuses makes AC-OTS a computationally challenging Mixed-Integer Nonlinear Program (MINLP). To address these challenges, the DC power flow approximation is often used to obtain a DC-OTS formulation expressed as a Mixed-Integer Linear Program (MILP). However, this approximation often leads to suboptimal or infeasible switching decisions when evaluated with an AC power flow model. This paper proposes an enhanced DC-OTS formulation that leverages techniques for training machine learning models to optimize the DC power flow model's parameters. By optimally selecting parameter values that align flows in the DC power flow model with apparent power flows -- incorporating both real and reactive components -- from AC Optimal Power Flow (OPF) solutions, our method more accurately captures line congestion behavior. Integrating these optimized parameters into the DC-OTS formulation significantly improves the accuracy of switching decisions and reduces discrepancies between DC-OTS and AC-OTS solutions. We compare our optimized DC-OTS model against traditional OTS approaches, including DC-OTS, Linear Programming AC (LPAC)-OTS, and Quadratic Convex (QC)-OTS. Numerical results show that switching decisions from our model yield better performance when evaluated using an AC power flow model, with up to $44\%$ cost reductions in some cases.