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Unlocking Transmission Flexibility under Uncertainty: Getting Dynamic Line Ratings into Electricity Markets

Zhiyi Zhou, Christoph Graf, Yury Dvorkin

TL;DR

This paper develops a transient dynamic line rating (DLR) framework that models conductor temperature as a stock-like inter-temporal state, enabling inter-temporal transmission flexibility while ensuring thermal security. It integrates the transient DLR model into a multi-period, chance-constrained DC-OPF, accounting for correlated weather and renewable uncertainty via affine approximations and SOC reformulations, and derives locational marginal prices (LMP) and reserve prices (LMRP) that support market equilibrium. The authors demonstrate significant congestion relief and cost reductions, along with emissions reductions, across 11-zone and 1814-node NYISO representations, while highlighting how zonal versus nodal formulations influence price signals and participant revenues. The results underscore the practical potential and challenges of deploying DLR-enabled markets, including the need for thermal reserves and robust uncertainty management to maintain reliability and economic efficiency.

Abstract

Static transmission line ratings may lead to underutilization of line capacity due to overly conservative assumptions. Grid-enhancing technologies (GETs) such as dynamic line ratings (DLRs), which adjust line capacity based on real-time conditions, are a techno-economically viable alternative to increase the utilization of existing power lines. Nonetheless, their adoption has been slow, partly due to the absence of operational tools that effectively account for simultaneous impacts on dispatch and pricing. In this paper, we represent transmission capacity with DLRs as a stock-like resource with time-variant interdependency, which is modeled via an approximation of line temperature evolution process, decoupling the impacts of ambient weather conditions and power flow on transmission line temperature and thus capacity. We integrate DLRs into a multi-period DC optimal power flow problem, with chance constrains addressing correlated uncertainty in DLRs and renewable generation. This yields non-convex problems that we transform into a tractable convex form by linearization. We derive locational marginal energy and ancillary services prices consistent with a competitive equilibrium. Numerical experiments on the 11-zone and 1814-node NYISO systems demonstrate its performance, including impacts on dispatch, pricing, and marginal carbon emissions.

Unlocking Transmission Flexibility under Uncertainty: Getting Dynamic Line Ratings into Electricity Markets

TL;DR

This paper develops a transient dynamic line rating (DLR) framework that models conductor temperature as a stock-like inter-temporal state, enabling inter-temporal transmission flexibility while ensuring thermal security. It integrates the transient DLR model into a multi-period, chance-constrained DC-OPF, accounting for correlated weather and renewable uncertainty via affine approximations and SOC reformulations, and derives locational marginal prices (LMP) and reserve prices (LMRP) that support market equilibrium. The authors demonstrate significant congestion relief and cost reductions, along with emissions reductions, across 11-zone and 1814-node NYISO representations, while highlighting how zonal versus nodal formulations influence price signals and participant revenues. The results underscore the practical potential and challenges of deploying DLR-enabled markets, including the need for thermal reserves and robust uncertainty management to maintain reliability and economic efficiency.

Abstract

Static transmission line ratings may lead to underutilization of line capacity due to overly conservative assumptions. Grid-enhancing technologies (GETs) such as dynamic line ratings (DLRs), which adjust line capacity based on real-time conditions, are a techno-economically viable alternative to increase the utilization of existing power lines. Nonetheless, their adoption has been slow, partly due to the absence of operational tools that effectively account for simultaneous impacts on dispatch and pricing. In this paper, we represent transmission capacity with DLRs as a stock-like resource with time-variant interdependency, which is modeled via an approximation of line temperature evolution process, decoupling the impacts of ambient weather conditions and power flow on transmission line temperature and thus capacity. We integrate DLRs into a multi-period DC optimal power flow problem, with chance constrains addressing correlated uncertainty in DLRs and renewable generation. This yields non-convex problems that we transform into a tractable convex form by linearization. We derive locational marginal energy and ancillary services prices consistent with a competitive equilibrium. Numerical experiments on the 11-zone and 1814-node NYISO systems demonstrate its performance, including impacts on dispatch, pricing, and marginal carbon emissions.

Paper Structure

This paper contains 23 sections, 3 theorems, 101 equations, 16 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Conceptual Framework
  3. Uncertainty-Aware Transmission Flexibility
  4. DLRs and transmission flexibility
  5. Correlated weather-dependent renewable generation and DLR uncertainty
  6. Approximation of non-convex chance constraints
  7. Pricing with DLRs
  8. Singe-period formulation
  9. Multi-period formulation
  10. Comparison of LMP and LMRP under different line ratings
  11. Numerical Experiments
  12. Approximation of line temperature evolution
  13. Illustrative example
  14. 11-zone NYISO system
  15. Single-day analysis
  16. ...and 8 more sections

Key Result

Theorem 1

Consider the model in (trans). Let the current ambient conditions (e.g., wind speed, wind direction, ambient temperature, and solar radiation) and conductor parameters (e.g., diameter, resistor) satisfy: where $\Delta r$ is a small term associated with $q_r$, which depends on $T_c$ and ambient conditions $W$; $\Delta s$ is a small term related to $q_s$; $F_1(\Delta r, \Delta s)$ quantifies the re

Figures (16)

  • Figure 1: Illustrative cases for transient DLRs: both the power flow trajectories $\{P_{1,0},P_{1,1}\}$ and $\{P_{2,0},P_{2,1}\}$ are valid realizations of the transient DLR over the two time periods, since both cases reach the thermal limit at time $t_2$
  • Figure 2: Summary of three line rating models with the main assumptions.
  • Figure 3: Flowchart for the proposed transient DLR model
  • Figure 4: Line temperature evolution under three seasonal scenarios using the benchmark model (red) and proposed model (blue) in \ref{['DLR:transient']}
  • Figure 5: Illustrative three-node system.
  • ...and 11 more figures

Theorems & Definitions (3)

  • Theorem 1: Conservative temperature evolution based on transient heating balance
  • Theorem 2: Market equilibrium for single-period OPF
  • Theorem 3: Market equilibrium for multi-period OPF