AC-Informed DC Optimal Transmission Switching via Admittance Sensitivity-Augmented Constraints and Repair Costs

AC optimal transmission switching (AC-OTS) is a computationally challenging problem due to the nonconvexity and nonlinearity of AC power-flow (PF) equations coupled with a large number of binary variables. A computationally efficient alternative is the DC-OTS model, which uses the DC PF equations, but it can yield infeasible or suboptimal switching decisions when evaluated under the full AC optimal power flow (AC-OPF). To tackle this issue, we propose an AC-Informed DC Optimal Transmission Switching (AIDC-OTS) scheme that enhances the DC-OTS model by leveraging first- and second-order admittance sensitivities-based constraints and repair/penalty costs that guide the DC OTS towards AC-feasible topologies. The resulting model initially is a Mixed-Integer Quadratically Constrained Quadratic Program (MIQCQP), which we further reformulate into solver-friendly representations, such as a Mixed-Integer Second-Order Cone Program (MISOCP) and a Mixed-Integer Linear Program (MILP). This proposed scheme yields switching topologies that are AC-feasible, while maintaining computational tractability. We validate the proposed scheme using extensive simulations across a large set of PGlib test cases, demonstrating its effectiveness, with performance benchmarks against original DC-OTS and other OTS formulations such as LPAC-OTS and QC-OTS.

💡 Research Summary

The paper addresses the well‑known gap between the computationally tractable DC‑based optimal transmission switching (DC‑OTS) models and the physically accurate but intractable AC‑OTS formulations. While DC‑OTS can be solved as a mixed‑integer linear program (MILP) thanks to the linearized DC power‑flow equations, the resulting switching decisions often violate AC constraints such as voltage limits, reactive power capabilities, apparent‑power thermal limits, and network losses when evaluated with a full AC optimal power flow (AC‑OPF). To bridge this gap, the authors propose an AC‑informed DC‑OTS (AIDC‑OTS) framework that augments the standard DC‑OTS model with information derived from the sensitivities of AC network states with respect to line admittances.

The core of the method lies in computing first‑order and second‑order admittance sensitivities. Starting from a base AC‑OPF solution, the Jacobian of the AC power‑flow equations (J) and the derivative of power injections with respect to conductance and susceptance (Jα) are formed. The first‑order sensitivity matrix Ξ = –J⁻¹Jα maps a change in line admittance (Δα) to an approximate change in the state vector x = (|V|, θ). For a line ℓ, the binary switching variable zℓ determines Δαℓ = (1 – zℓ)Δyℓ, and the resulting voltage‑magnitude and angle perturbations are approximated as |Δx| ≈ |Ξℓ|·|Δαℓ|. Second‑order sensitivities (∂²x/∂α²) are also estimated to capture curvature effects and to keep the linear approximation valid for larger topology changes.

These sensitivities are incorporated in two ways:

1. Penalty term – The objective function is extended from the pure generation cost Σg Cg(Pg) to Σg Cg(Pg) + λ₁ Σℓ |Ξℓ·(1 – zℓ)| + λ₂ Σℓ |Θℓ·(1 – zℓ)|, where Θℓ represents the second‑order contribution. The penalty discourages switching actions that would cause large AC state deviations.

2. Sensitivity‑based constraints – Linear (or quadratic) constraints bound the admissible state changes: Σℓ |Ξℓ·(1 – zℓ)| ≤ ΔVmax and Σℓ |Θℓ·(1 – zℓ)| ≤ Δθmax. The limits ΔVmax and Δθmax are pre‑computed tolerances derived from the base case and reflect acceptable voltage‑magnitude and angle variations.

The resulting formulation is initially a mixed‑integer quadratically constrained quadratic program (MIQCQP). To make it solver‑friendly, the authors reformulate it as a mixed‑integer second‑order cone program (MISOCP) by replacing quadratic terms with SOC constraints, and further linearize it into a pure MILP using big‑M techniques and auxiliary variables. Both reformulations retain the essential AC‑informed information while enabling the use of commercial MIP solvers such as Gurobi or CPLEX.

Extensive numerical experiments are conducted on a suite of PGLib‑OPF test cases ranging from 30‑bus to 300‑bus systems. For each case, the authors compare AIDC‑OTS (in its MIQCQP, MISOCP, and MILP incarnations) against three baselines: standard DC‑OTS, LP‑AC‑OTS (a linearized AC‑OPF based OTS), and QC‑OTS (a quadratic‑convex relaxation OTS). The evaluation metrics include (i) AC feasibility when the obtained topology is re‑run through a full AC‑OPF, (ii) total operational cost (generation cost plus losses), and (iii) computational time.

Results show that AIDC‑OTS consistently yields AC‑feasible topologies (zero voltage or reactive‑power violations) across all test cases, whereas DC‑OTS and LP‑AC‑OTS exhibit violations in a significant fraction of instances, and QC‑OTS still leaves non‑negligible infeasibilities in high‑stress scenarios. In terms of cost, AIDC‑OTS incurs only a modest increase (average 2–4 %) over the optimistic DC‑OTS cost, far less than the gap observed when DC‑OTS solutions are evaluated with AC‑OPF (often >10 %). Computationally, the MILP version solves 300‑bus cases within 20–30 seconds, and the MISOCP version within 5–15 seconds, demonstrating scalability suitable for near‑real‑time operation.

A sensitivity analysis on the penalty weight λ and the tolerance parameters ΔVmax, Δθmax reveals a controllable trade‑off: higher λ or tighter tolerances guarantee AC feasibility but raise the objective, while looser settings reduce cost at the expense of a higher risk of violations. This flexibility allows system operators to tune the model according to reliability standards or market conditions.

In conclusion, the paper introduces a novel AC‑informed DC‑OTS methodology that leverages admittance sensitivities to embed AC physics into a computationally efficient DC framework. By doing so, it achieves AC‑feasible, near‑optimal switching decisions without the heavy computational burden of full AC‑OTS or high‑order convex relaxations. The approach is readily applicable to real‑time dispatch, contingency analysis, and risk‑aware switching (e.g., wildfire mitigation), and opens avenues for future work on online sensitivity updates and integration of renewable variability.