Towards AC Feasibility of DCOPF Dispatch

TL;DR

The paper tackles the gap between fast DCOPF solutions and the need for AC-feasible operation by introducing a DCOPF→ACPF pipeline that combines loss-aware DCOPF variants with a structured AC feasibility layer. It evaluates four DCOPF formulations (including LLLF, LQCP, and LLOA) and four AC feasibility variants (BASE, BTS, DS, SPF), demonstrating that the DC_LQCP→AC_SPF pipeline most effectively restores AC feasibility while minimizing violations and cost. The study reports substantial improvements on large-scale networks (e.g., a 13,659-bus system) with mean reductions in cost differences and mean absolute error by 93% and 75%, respectively, and large reductions in inequality constraint violations under extreme loading. The results underscore the practical value of loss-aware DC dispatch paired with a structured, distributed-slack AC recovery, offering a scalable pathway for AC-feasible operations in DC-operated markets; future work points toward end-to-end self-supervised learning to further enhance efficiency and scalability.

Abstract

DC Optimal Power Flow (DCOPF) is widely utilized in power system operations due to its simplicity and computational efficiency. However, its lossless, reactive power-agnostic model often yields dispatches that are infeasible under practical operating scenarios such as the nonlinear AC power flow (ACPF) equations. While theoretical analysis demonstrates that DCOPF solutions are inherently AC-infeasible, their widespread industry adoption suggests substantial practical utility. This paper develops a unified DCOPF-ACPF pipeline to recover AC feasible solutions from DCOPF-based dispatches. The pipeline uses four DCOPF variants and applies AC feasibility recovery using both distributed slack allocation and PV/PQ switching. The main objective is to identify the most effective pipeline for restoring AC feasibility. Evaluation across over 10,000 dispatch scenarios on various test cases demonstrates that the structured ACPF model yields solutions that satisfy both the ACPF equations, and all engineering inequality constraints. In a 13,659 bus case, the mean absolute error and cost differences between DCOPF and ACOPF are reduced by 75% and 93%, respectively, compared to conventional single slack bus methods. Under extreme loading conditions, the pipeline reduces inequality constraint violations by a factor of 3 to 5.

Figures (6)

• Figure 1: Pipeline of the $\text{DCOPF}\!\rightarrow\!\text{ACPF}$ model. The DCOPF gives $\mathbf{{p}}_{\mathrm{g}}^\mathrm{sp}$ and $\boldsymbol{\theta}^{\mathrm{dc}}$ from input $\mathbf{p}_{\mathrm{d}}$. The ACPF performs feasibility checks with distributed slack using participation factors ($\boldsymbol{\pi}_{\mathrm{g}}$). Voltage initialization ($\mathbf{v}_{\mathrm{}}^{\mathrm{int}}$) aids in convergence. ACOPF constraints are marked with red.
• Figure 2: The generator bus-type switching logic. The blue curve is the discrete logic. The bus transitions between $\mathbf{PQ}^{\mathrm{max}}$, $\mathbf{PV}$, and $\mathbf{PQ}^{\mathrm{min}}$ states, based on ${q_g}_i$ and $v_i^{\mathrm{sp}}$. The blue dashed lines are infeasible regions where the generator cannot maintain voltage control while obeying reactive power limits. The orange curve is the tolerance-based control, with tolerances $\mathrm{\epsilon}_q$ and $\mathrm{\epsilon}_v$ on reactive power and voltage.
• Figure 3: Comparison of the sum total of violations in different AC power flow formulations across various cases: case_118, case_1354, and case_2869 (with mean and min–max error bars). The pipelines shown have different DC setpoints: (top) $\mathrm{DC}_{\text{BASE}}$ and (bottom) $\mathrm{DC}_{\text{LQCP}}$. The plots are taken over load uncertainty with ${\sigma}=15\%$, for $\mathrm{1000}$ samples per case. Shown are the active power, reactive power, voltage, and thermal violations, with y-axes on log-scales. Results are reported for $\mathrm{AC}_{\text{BASE}}$ (orange), $\mathrm{AC}_{\text{BTS}}$ (blue), $\mathrm{AC}_{\text{DS}}$ (green), and $\mathrm{AC}_{\text{SPF}}$ (red).
• Figure 4: Boxplot comparison of different AC variants' metrics across test cases: case_118, case_1354, and case_2869 (with mean and min–max extremes). The AC variants shown have different DC setpoints: (top) $\mathrm{DC}_{\text{BASE}}$ and (bottom) $\mathrm{DC}_{\text{LQCP}}$. The plots are taken over load uncertainty with ${\sigma}=15\%$, for $\mathrm{1000}$ samples per case. Metrics shown (left to right): cost difference, mean absolute error, iteration count, and solving time. Results are reported for $\mathrm{AC}_{\text{OPF}}$ (purple), $\mathrm{AC}_{\text{BASE}}$ (orange), $\mathrm{AC}_{\text{BTS}}$ (blue), $\mathrm{AC}_{\text{DS}}$ (green), and $\mathrm{AC}_{\text{SPF}}$ (red).
• Figure 5: Pipeline comparison across different DC and AC variants, over load uncertainty with ${\sigma}=5\%$. (a) Slack-bus active power using $\mathrm{100}$ per case, for: case_500, case_1354, case_2869, and case_13659 under $\mathrm{DC}_{\text{BASE}}\!\rightarrow\!\mathrm{AC}_{\text{BASE}}$ (orange), $\mathrm{DC}_{\text{LQCP}}\!\rightarrow\!\mathrm{AC}_{\text{BASE}}$ (blue), $\mathrm{DC}_{\text{BASE}}\!\rightarrow\!\mathrm{AC}_{\text{SPF}}$ (green), and $\mathrm{DC}_{\text{LLOA}}\!\rightarrow\!\mathrm{AC}_{\text{SPF}}$ (red). Dashed (red) line is the active power violation. (b) Cumulative density factor (CDF) plot of unit-wise active-power deviation $|\mathbf{p}_\mathrm{g}^{\mathrm{DC}\rightarrow\mathrm{AC}} - \mathbf{p}_\mathrm{g}^{\mathcal{O}}|$ across generators in case_1354, using $\mathrm{1000}$ per case, with an x-axis log-scale.