[Paper Review] Risk-Based Distributionally Robust Optimal Power Flow With Dynamic Line Rating

Cheng Wang, Rui Gao+3 more|arXiv (Cornell University)|Dec 21, 2017

Thermal Analysis in Power Transmission31 references3 citations

TL;DR

This paper proposes a risk-based distributionally robust optimal power flow (DROPF) framework that integrates dynamic line rating (DLR) to enhance transmission capacity utilization under wind power uncertainty. By modeling uncertainties via a Wasserstein ambiguity set with moment constraints, the approach ensures robustness to data perturbations and correlations between wind generation and line ratings, reformulating the problem as a tractable conic program that outperforms sample average approximation in out-of-sample performance.

ABSTRACT

In this paper, we propose a risk-based data-driven approach to optimal power flow (DROPF) with dynamic line rating. The risk terms, including penalties for load shedding, wind generation curtailment and line overload, are embedded into the objective function. To hedge against the uncertainties on wind generation data and line rating data, we consider a distributionally robust approach. The ambiguity set is based on second-order moment and Wasserstein distance, which captures the correlations between wind generation outputs and line ratings, and is robust to data perturbation. We show that the proposed DROPF model can be reformulated as a conic program. Considering the relatively large number of constraints involved, an approximation of the proposed DROPF model is suggested, which significantly reduces the computational costs. A Wasserstein distance constrained DROPF and its tractable reformulation are also provided for practical large-scale test systems. Simulation results on the 5-bus, the IEEE 118-bus and the Polish 2736-bus test systems validate the effectiveness of the proposed models.

Motivation & Objective

• To address the challenge of underutilized transmission capacity due to conservative static line ratings (SLR) in power systems with high wind penetration.
• To incorporate dynamic line rating (DLR), which adapts line capacity based on real-time environmental conditions, to improve transmission utilization.
• To model uncertainties in wind generation and DLR data robustly, while accounting for correlations and data perturbations.
• To develop a computationally tractable optimization framework that ensures operational reliability and economic efficiency under risk-sensitive objectives.
• To validate the proposed DROPF model on test systems of varying scale, demonstrating superior out-of-sample performance compared to traditional SAA approaches.

Proposed method

• The framework embeds risk penalties for load shedding, wind curtailment, and line overload directly into the objective function to reflect operational costs.
• A distributionally robust optimization (DRO) approach is employed using a Wasserstein ambiguity set defined by second-order moment information and Wasserstein distance to model uncertainty in wind and DLR data.
• The ambiguity set captures dependencies between wind generation outputs and line ratings, enhancing robustness to data perturbations and model misspecification.
• The original DROPF model is reformulated as a second-order cone program (SOCP) via strong duality, enabling efficient solution via standard solvers.
• For large-scale systems, a Wasserstein-distance-constrained variant (W-DROPF) is proposed, which is computationally efficient and maintains strong out-of-sample performance.
• An approximation technique is introduced to reduce computational burden while preserving the model's robustness and performance.

Experimental results

Research questions

• RQ1 How can dynamic line rating be effectively integrated into optimal power flow to improve transmission utilization under wind power uncertainty?
• RQ2 What is the impact of modeling wind and DLR uncertainties using a distributionally robust framework with Wasserstein distance and moment constraints?
• RQ3 How does the proposed DROPF model compare to the sample average approximation (SAA) in terms of out-of-sample performance and robustness?
• RQ4 Can the proposed DROPF model be efficiently reformulated into a tractable conic program for practical power system applications?
• RQ5 What is the trade-off between computational complexity and performance when using moment-constrained versus Wasserstein-only ambiguity sets in large-scale systems?

Key findings

• The proposed DROPF model significantly outperforms the sample average approximation (SAA) in out-of-sample performance, even when using an approximation, due to better handling of distributional uncertainty.
• The W-DROPF variant, which uses only Wasserstein distance constraints, achieves superior out-of-sample performance compared to SAA on the large-scale Polish 2736-bus system, despite reduced computational complexity.
• The moment-constrained DROPF (M-DROPF) and W&M-DROPF models, while more accurate, are computationally prohibitive for large systems due to semi-definite programming (SDP) reformulations.
• The reformulation of the DROPF model as a second-order cone program (SOCP) enables efficient solution using standard solvers like MOSEK, ensuring practical applicability.
• Simulation results on the 5-bus, IEEE 118-bus, and Polish 2736-bus systems confirm the model’s robustness, scalability, and effectiveness in reducing operational risks and curtailment.
• The framework effectively captures correlations between wind generation and DLR, leading to more accurate and reliable security-constrained dispatch decisions.