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Unified Diagnostics for Quantifying AC Operating-Point Robustness Under Injection and Topological Uncertainties with Regime Changes

Laurenţiu Lucian Anton, Marija Ilić

Abstract

In the presence of uncertainties in load, generation, and network topology, power system planning must reflect operational conditions, while operations require situational awareness over credible uncertainty sets. Existing methods screen, analyze, embed, and propagate uncertainty in power flow and optimal power flow settings, but provide only partial insight into how physical constraints, controls, and economic interactions shape steady-state operating-point robustness. By formulating operating-point robustness as a post-solution physical response problem around a solved AC optimal power flow (AC-OPF) equilibrium, this paper presents a unified framework for assessing robustness under injection and topological uncertainty without re-optimization. We construct a primal physical response mapping that accounts for connectivity changes, active power redistribution, generator saturation including $PV \rightarrow PQ$ transitions, and AC network propagation, and introduce quasi-duals that provide a geometric interpretation of shadow prices for off-optimal equilibria. Using these mappings, we develop deterministic screening procedures that generalize $N-k$ contingency analysis to include cost vulnerability $C-k$, and local analogs $N+δ(k)$ and $C+δ(k)$ defined through sensitivity-normalized margins and risk tolerances. The framework is extended to probabilistic screening for distribution- and moment-based uncertainties, with sequentially-pruned mixture modeling and $α$-stressed regime constructions to manage combinatorial branching. A case study on the Puerto Rican bulk power system demonstrates integration with geospatial data to enhance operational and planning awareness.

Unified Diagnostics for Quantifying AC Operating-Point Robustness Under Injection and Topological Uncertainties with Regime Changes

Abstract

In the presence of uncertainties in load, generation, and network topology, power system planning must reflect operational conditions, while operations require situational awareness over credible uncertainty sets. Existing methods screen, analyze, embed, and propagate uncertainty in power flow and optimal power flow settings, but provide only partial insight into how physical constraints, controls, and economic interactions shape steady-state operating-point robustness. By formulating operating-point robustness as a post-solution physical response problem around a solved AC optimal power flow (AC-OPF) equilibrium, this paper presents a unified framework for assessing robustness under injection and topological uncertainty without re-optimization. We construct a primal physical response mapping that accounts for connectivity changes, active power redistribution, generator saturation including transitions, and AC network propagation, and introduce quasi-duals that provide a geometric interpretation of shadow prices for off-optimal equilibria. Using these mappings, we develop deterministic screening procedures that generalize contingency analysis to include cost vulnerability , and local analogs and defined through sensitivity-normalized margins and risk tolerances. The framework is extended to probabilistic screening for distribution- and moment-based uncertainties, with sequentially-pruned mixture modeling and -stressed regime constructions to manage combinatorial branching. A case study on the Puerto Rican bulk power system demonstrates integration with geospatial data to enhance operational and planning awareness.
Paper Structure (60 sections, 101 equations, 3 figures)

This paper contains 60 sections, 101 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Operational Trends on Constraint Margins
  4. Approaches to Incorporating Uncertainty in Steady-State Power Flow and Dispatch
  5. Toward a Unified Framework for Operating-Point Robustness
  6. Contributions
  7. Steady-State Physical Response to Uncertainty Around AC-OPF Equilibria
  8. AC-OPF Primal Formulation and Notation
  9. Modeling Steady-State AC Physical Response
  10. AC Power Flow Bus Conventions
  11. Fixed and Non-Controllable Elements
  12. Generator Active Power Response
  13. Generator Limit Considerations
  14. Generator Reactive Power Response
  15. AC Network Response
  16. ...and 45 more sections

Figures (3)

  • Figure 1: Hierarchical composition of the sequentially-pruned regime tree, illustrating the ordered attachment of sub-trees.
  • Figure 2: $N\!-\!1$ contingency screening on Puerto Rican bulk power system model, around a base operating point representing peak load conditions with dispatch optimized using AC OPF economic dispatch with (a) preset and (b) optimized voltage setpoints.
  • Figure 3: Geospatial visualizations of system-wide screening metrics on the Puerto Rican bulk power system under a peak-load operating point solved by AC OPF with optimized voltage setpoints. Panels (a)–(d) show deterministic $N\!-\!1$, $C\!-\!1$, $N\!+\!\delta(1)$, and $C\!+\!\delta(1)$ screenings, with the ten components exhibiting the highest frequencies highlighted. Panels (e)–(f) present probabilistic single-contingency screening under Gaussian disturbances using the sequentially pruned mixture model and the $\alpha$-stressed regime method, respectively. For probabilistic panels, the 100 largest violation probabilities are displayed, with generator probabilities aggregated to their corresponding buses.