[Paper Review] Reinforcing Power Grid Transmission with FACTS Devices

Vladimir Frolov, Scott Backhaus+1 more|arXiv (Cornell University)|Jul 8, 2013

Optimal Power Flow Distribution17 references3 citations

TL;DR

This paper proposes a hybrid optimization framework that uses l1-norm minimization and sequential linear programming with cutting plane acceleration to strategically place and size FACTS devices for congestion relief in power grids. The method efficiently solves large-scale transmission network problems—demonstrating 40-second iterations on a 3299-line Polish grid model—while producing sparse, effective deployments that reduce thermal overloads without requiring all congested lines to be directly corrected.

ABSTRACT

We explore optimization methods for planning the placement, sizing and operations of Flexible Alternating Current Transmission System (FACTS) devices installed into the grid to relieve congestion created by load growth or fluctuations of intermittent renewable generation. We limit our selection of FACTS devices to those that can be represented by modification of the inductance of the transmission lines. Our master optimization problem minimizes the $l_1$ norm of the FACTS-associated inductance correction subject to constraints enforcing that no line of the system exceeds its thermal limit. We develop off-line heuristics that reduce this non-convex optimization to a succession of Linear Programs (LP) where at each step the constraints are linearized analytically around the current operating point. The algorithm is accelerated further with a version of the cutting plane method greatly reducing the number of active constraints during the optimization, while checking feasibility of the non-active constraints post-factum. This hybrid algorithm solves a typical single-contingency problem over the MathPower Polish Grid model (3299 lines and 2746 nodes) in 40 seconds per iteration on a standard laptop---a speed up that allows the sizing and placement of a family of FACTS devices to correct a large set of anticipated contingencies. From testing of multiple examples, we observe that our algorithm finds feasible solutions that are always sparse, i.e., FACTS devices are placed on only a few lines. The optimal FACTS are not always placed on the originally congested lines, however typically the correction(s) is made at line(s) positioned in a relative proximity of the overload line(s).

Motivation & Objective

• To address the challenge of optimal FACTS device placement and sizing in large transmission networks to relieve congestion caused by load growth or renewable fluctuations.
• To develop a computationally efficient method that avoids the curse of dimensionality in system-wide non-convex optimization.
• To enforce sparsity in FACTS deployment through l1-norm regularization, ensuring minimal device installation while maintaining system security.
• To enable real-time or near-real-time planning by accelerating convergence via cutting plane and linearization techniques.
• To validate the method on realistic large-scale systems, such as the MathPower Polish Grid, under single-contingency conditions.

Proposed method

• Formulates the FACTS placement and sizing problem as minimizing the l1-norm of inductance corrections, subject to thermal limit constraints on transmission lines.
• Uses sequential linear programming (SLP) with analytical linearization of constraints around the current operating point at each iteration.
• Applies a cutting plane method to reduce active constraints during optimization, checking feasibility of inactive constraints post-optimization.
• Models FACTS devices as adjustable line susceptances, enabling representation of their impact on power flows via modified line parameters.
• Employs a hybrid algorithm combining SLP and cutting plane techniques to handle non-convexity while maintaining computational tractability.
• Validates the approach on the 3299-line MathPower Polish Grid model, demonstrating scalability on standard hardware.

Experimental results

Research questions

• RQ1 Can a non-convex FACTS placement and sizing problem be efficiently solved at scale using a hybrid optimization approach?
• RQ2 Does enforcing l1-norm minimization on inductance corrections lead to sparse, practical FACTS deployments?
• RQ3 Can linearization and cutting plane methods maintain accuracy while drastically reducing computation time?
• RQ4 Where are optimal FACTS devices placed relative to the originally congested lines?
• RQ5 How does the method perform on large-scale real-world transmission systems under single-contingency conditions?

Key findings

• The proposed algorithm solves a single-contingency congestion problem on the 3299-line Polish grid model in approximately 40 seconds per iteration on a standard laptop.
• The method consistently produces sparse solutions, with FACTS devices installed on only a few transmission lines, even when the most heavily overloaded lines are not directly corrected.
• Optimal FACTS corrections are typically placed on lines in close proximity to the congested lines, not necessarily on the overloaded lines themselves.
• The algorithm’s linearization and cutting plane strategy significantly reduce the number of active constraints, accelerating convergence without sacrificing feasibility.
• The non-convex nature of the original problem is effectively managed through iterative linearization, with convergence demonstrated on both small and large-scale systems.
• Sensitivity analysis confirms that reducing a line’s own susceptance or adjusting neighboring line susceptances can effectively relieve flow overloads, depending on flow direction.