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Dynamic Line Ratings in AC Optimal Power Flow: Transient Temperature, Decomposition, and Large-scale Evaluation

Baptiste Rabecq, Thomas Lee, Andy Sun

TL;DR

The paper tackles grid congestion under rising renewables by embedding transient conductor-temperature dynamics into a multi-period ACOPF via Dynamic Line Rating (DLR). It develops a closed-form solution to the line heat equation and a finite reformulation, enabling a space-time decomposition solved with a provably convergent bi-level ADMM, scalable to a 2000-bus network. In large-scale ERCOT-like simulations, transient DLR achieves around 2% generation-cost reductions and 1–3% higher renewable output compared with static or ambient-based ratings, while offering localized headroom during rapid weather changes (5–20 minutes). The study also shows that transient DLR provides additional flexibility over steady-state DLR, particularly for short-lived, localized congestion, with convergence and computational costs comparable to steady-state approaches.

Abstract

As power grids experience increasing renewable penetration and rapid load growth from AI data centers and electrification, alleviating line congestion becomes critical to unlocking additional grid capacity. This work investigates Dynamic Line Rating (DLR), a congestion mitigation method that adjusts power line current limits in response to meteorological conditions. Unlike traditional approaches that impose predefined time-varying limits, we propose a novel optimization framework that embeds the transient-state heat equation governing conductor temperature dynamics, enabling direct constraints on conductor temperature rather than simplified steady-state approximations. We derive a closed-form solution to the heat equation, enabling a finite-dimensional reformulation of the dynamics. We then leverage a distributed decomposition method, a bi-level Alternating Direction Method of Multipliers (ADMM) algorithm with provable convergence, aided by regularity properties of the heat equation solution. These modeling and algorithmic innovations allow us to conduct the first large-scale evaluation of DLR using multi-period AC optimal power flow. Numerical experiments on the 2000-bus Texas grid demonstrate that DLR allows significant reduction in generation cost in congested systems over Static Line Rating (SLR) and Ambient Adjusted Ratings (AAR). The transient temperature formulation provides additional grid flexibility and headroom benefits with minimal computational overhead.

Dynamic Line Ratings in AC Optimal Power Flow: Transient Temperature, Decomposition, and Large-scale Evaluation

TL;DR

The paper tackles grid congestion under rising renewables by embedding transient conductor-temperature dynamics into a multi-period ACOPF via Dynamic Line Rating (DLR). It develops a closed-form solution to the line heat equation and a finite reformulation, enabling a space-time decomposition solved with a provably convergent bi-level ADMM, scalable to a 2000-bus network. In large-scale ERCOT-like simulations, transient DLR achieves around 2% generation-cost reductions and 1–3% higher renewable output compared with static or ambient-based ratings, while offering localized headroom during rapid weather changes (5–20 minutes). The study also shows that transient DLR provides additional flexibility over steady-state DLR, particularly for short-lived, localized congestion, with convergence and computational costs comparable to steady-state approaches.

Abstract

As power grids experience increasing renewable penetration and rapid load growth from AI data centers and electrification, alleviating line congestion becomes critical to unlocking additional grid capacity. This work investigates Dynamic Line Rating (DLR), a congestion mitigation method that adjusts power line current limits in response to meteorological conditions. Unlike traditional approaches that impose predefined time-varying limits, we propose a novel optimization framework that embeds the transient-state heat equation governing conductor temperature dynamics, enabling direct constraints on conductor temperature rather than simplified steady-state approximations. We derive a closed-form solution to the heat equation, enabling a finite-dimensional reformulation of the dynamics. We then leverage a distributed decomposition method, a bi-level Alternating Direction Method of Multipliers (ADMM) algorithm with provable convergence, aided by regularity properties of the heat equation solution. These modeling and algorithmic innovations allow us to conduct the first large-scale evaluation of DLR using multi-period AC optimal power flow. Numerical experiments on the 2000-bus Texas grid demonstrate that DLR allows significant reduction in generation cost in congested systems over Static Line Rating (SLR) and Ambient Adjusted Ratings (AAR). The transient temperature formulation provides additional grid flexibility and headroom benefits with minimal computational overhead.

Paper Structure

This paper contains 24 sections, 9 theorems, 40 equations, 4 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Study of the Temperature Dynamics
  3. Single-period dynamics
  4. Multi-period Dynamics and Finite Reformulation
  5. Transient and steady-state temperature models
  6. Multi-period ACOPF with DLR and Ramping constraints
  7. Decomposition Strategy and Bi-level ADMM
  8. Decomposition strategy
  9. Bi-level ADMM Algorithm
  10. Convergence of the Algorithm
  11. Inner Convergence
  12. Global Convergence
  13. Computations
  14. Experimental Setup
  15. Data used
  16. ...and 9 more sections

Key Result

Theorem 5

Suppose that Assumptions ass:resistivity-ass:lin-conv hold. Then, for each line $ij$, the heat equation eq:heat_balance can be reformulated as: where $K_{0, ij} {=} K_{0 , ij}'{+} r_{ij}'\iota_{ij}$, $r'_{ij}{=} \frac{r_{ij}}{m_{ij}c_{p , ij}}$, $K_{1, ij} {=} \frac{k^c_{ij}}{m_{ij} c_{p , ij}}$, $K_{0 , ij}' {=} \frac{\pi D_{0 , ij} \epsilon \sigma T_{a , ij}^4 {+} q^s_{ij} {-} k^{c,0}_{ij}}{m_{

Figures (4)

  • Figure 1: Steady-state and transient temperature evolution on three time intervals.
  • Figure 2: Convergence behavior of the ADMM algorithm showing (a) inner iteration consensus and (b) primal feasibility gap. Colors denote outer iterations.
  • Figure 3: Line capacity (a), system cost (b), and (c) renewable output of all rating schemes over one summer day of operations.
  • Figure 4: Current difference (in %) between DLR-Trans and DLR-SS. The selected lines are those that are congested in DLR-SS and in which the current supplied is different in DLR-Trans.

Theorems & Definitions (22)

  • Remark 4
  • Theorem 5: Closed Form Solution
  • proof
  • Definition 6: Steady-state
  • Proposition 7
  • proof
  • Proposition 8
  • proof
  • Proposition 9
  • proof
  • ...and 12 more