[Paper Review] Optimal Power Flow for DC Networks with Robust Feasibility and Stability Guarantees

Jianzhe Liu, Bai Cui+4 more|arXiv (Cornell University)|Feb 21, 2019

Optimal Power Flow Distribution51 references4 citations

TL;DR

This paper proposes a robust optimal power flow (OPF) framework for DC networks that ensures both feasibility and stability under uncertain renewable generation and load conditions. By reformulating a semi-infinite program into a tractable convex optimization problem using a tight convex inner approximation of the stability region, the method guarantees stable and feasible power flows across all uncertainty realizations, validated on IEEE test systems with significant uncertainty tolerance.

ABSTRACT

With high penetrations of renewable generation and variable loads, there is significant uncertainty associated with power flows in DC networks such that stability and operational constraint satisfaction are of concern. Most existing DC network optimal power flow (DN-OPF) formulations assume exact knowledge of loading conditions and do not provide stability guarantees. In contrast, this paper studies a DN-OPF formulation which considers both stability and operational constraint satisfaction under uncertainty. The need to account for a range of uncertainty realizations in this paper's robust optimization formulation results in a challenging semi-infinite program (SIP). The proposed solution algorithm reformulates this SIP into a computationally tractable problem by constructing a tight convex inner approximation of the stability set using sufficient conditions for the existence of a feasible and stable power flow solution. Optimal generator setpoints are obtained by optimizing over the proposed convex stability set. The validity and value of the proposed algorithm are demonstrated through various DC networks adapted from IEEE test cases.

Motivation & Objective

• Address the lack of stability and feasibility guarantees in existing DC network optimal power flow (DN-OPF) formulations under uncertain renewable generation and variable loads.
• Develop a robust optimization framework that ensures stable and feasible power flow across a range of uncertain loading and generation conditions.
• Overcome the computational intractability of semi-infinite programs arising from uncertainty by constructing a convex inner approximation of the stability set.
• Ensure that optimal generator setpoints are robust to uncertainty while maintaining system stability and operational constraints.
• Demonstrate the effectiveness and scalability of the proposed method on modified IEEE test systems with high renewable penetration.

Proposed method

• Formulate a robust DC network OPF as a semi-infinite program (SIP) to account for uncertainty in renewable generation and load across a bounded range of realizations.
• Derive sufficient conditions for the existence of a feasible and stable power flow solution, which are used to construct a convex inner approximation of the stability set.
• Replace the original SIP with a tractable convex optimization problem by replacing the infinite number of constraints with a finite set based on the convex stability region.
• Optimize generator setpoints over the convex stability set to ensure robust feasibility and stability under all uncertainty realizations.
• Use linear matrix inequality (LMI) conditions or similar convex constraints to represent the stability region, enabling efficient solution via standard conic optimization solvers.
• Validate the approximation quality by comparing the convex inner approximation to the true stability region through numerical case studies.

Experimental results

Research questions

• RQ1 How can a DC network OPF be formulated to guarantee stability and feasibility under uncertain renewable generation and load conditions?
• RQ2 What convex inner approximation of the stability set can be constructed using sufficient conditions for stable power flow?
• RQ3 How does the proposed robust OPF formulation compare in performance and computational tractability to traditional deterministic OPF methods?
• RQ4 To what extent does the convex inner approximation preserve the true stability region while remaining computationally efficient?
• RQ5 How well does the proposed method scale and perform on standard IEEE test systems with high uncertainty?

Key findings

• The proposed convex inner approximation of the stability set provides a tight and computationally tractable representation of feasible and stable power flow solutions under uncertainty.
• The robust OPF formulation ensures stability and feasibility across all uncertainty realizations, unlike conventional OPF methods that assume exact knowledge of system parameters.
• Numerical results on modified IEEE test systems demonstrate that the method maintains system stability even under high levels of renewable uncertainty.
• The solution approach transforms the inherently intractable semi-infinite program into a finite-dimensional convex optimization problem, enabling efficient computation.
• The method achieves robust performance with minimal conservatism, as validated by case studies showing high feasibility rates across diverse uncertainty scenarios.
• The framework is scalable and applicable to practical DC network configurations, including those with high renewable integration.