[Paper Review] Methodology for Multi-stage, Operations- and Uncertainty-Aware Placement and Sizing of FACTS Devices in a Large Power Transmission System

Vladimir Frolov, Michael Chertkov|arXiv (Cornell University)|Jul 7, 2017

Power System Optimization and Stability24 references3 citations

TL;DR

This paper proposes a multi-stage, uncertainty-aware optimization framework for strategically placing and sizing FACTS devices (series and shunt) in large power systems to defer costly transmission line expansions. Using a hybrid heuristic of alternating AC power flow solutions and mixed-integer linear/quadratic programs, the method minimizes total cost—combining investment and operational expenses—across multiple load growth scenarios and time frames, achieving scalable, operationally feasible, and sparse FACTS deployment on the 2736-bus Polish system.

ABSTRACT

We develop new optimization methodology for planning installation of Flexible Alternating Current Transmission System (FACTS) devices of the parallel and shunt types into large power transmission systems, which allows to delay or avoid installations of generally much more expensive power lines. Methodology takes as an input projected economic development, expressed through a paced growth of the system loads, as well as uncertainties, expressed through multiple scenarios of the growth. We price new devices according to their capacities. Installation cost contributes to the optimization objective in combination with the cost of operations integrated over time and averaged over the scenarios. The multi-stage (-time-frame) optimization aims to achieve a gradual distribution of new resources in space and time. Constraints on the investment budget, or equivalently constraint on building capacity, is introduced at each time frame. Our approach adjusts operationally not only newly installed FACTS devices but also other already existing flexible degrees of freedom. This complex optimization problem is stated using the most general AC Power Flows. Non-linear, non-convex, multiple-scenario and multi-time-frame optimization is resolved via efficient heuristics, consisting of a sequence of alternating Linear Programmings or Quadratic Programmings (depending on the generation cost) and AC-PF solution steps designed to maintain operational feasibility for all scenarios. Computational scalability and application of the newly developed approach is illustrated on the example of the 2736-nodes large Polish system. One most important advantage of the framework is that the optimal capacity of FACTS is build up gradually at each time frame in a limited number of locations, thus allowing to prepare the system better for possible congestion due to future economic and other uncertainties.

Motivation & Objective

• To develop a computationally scalable methodology for optimal placement and sizing of FACTS devices in large transmission networks.
• To address the challenge of long-term transmission expansion planning under uncertain load growth and economic development.
• To minimize total cost—combining investment and operational expenses—across multiple time frames and load scenarios.
• To ensure operational feasibility across all scenarios by maintaining voltage and line flow limits through coordinated device control.
• To enable gradual, sparse, and strategically timed deployment of FACTS devices to defer costly transmission line expansions.

Proposed method

• The framework uses a multi-stage, multi-scenario optimization model with time frames representing planning horizons and scenarios representing load growth uncertainty.
• It formulates a non-convex, non-linear AC optimal power flow problem with mixed-integer variables for FACTS device investment decisions.
• A heuristic alternates between solving linear or quadratic programs (for operational cost minimization) and full AC power flow solutions to maintain feasibility across all scenarios.
• Scenario generation involves piecewise-constant load profiles derived from a base load growth curve, with stochastic perturbations using zero-mean Gaussian noise.
• The method enforces budget constraints per time frame and ensures that all operational limits (voltage, line flows) are satisfied in every scenario.
• Initial generation profiles are derived via ACOPF with thermal limits relaxed, followed by proportional load-generation scaling to match base-case loading.

Experimental results

Research questions

• RQ1 How can FACTS devices be optimally placed and sized in large power systems to defer costly transmission line investments under uncertain load growth?
• RQ2 What is the impact of multi-stage, scenario-based planning on the cost-effectiveness and operational feasibility of FACTS deployment?
• RQ3 How can non-convex, multi-scenario, multi-time-frame AC optimal power flow problems be efficiently solved at scale?
• RQ4 To what extent can FACTS deployment reduce congestion and extend system loadability without violating operational constraints?
• RQ5 How does the proposed method compare to traditional line expansion or heuristic-based FACTS placement in terms of cost and scalability?

Key findings

• The proposed methodology successfully reduced total cost by deferring transmission line investments through optimal, gradual FACTS deployment across the 2736-bus Polish system.
• The framework achieved operational feasibility across all 6 scenarios per time frame, with congestion prices reduced in high-load conditions.
• The method enabled a sparse, location-specific deployment of FACTS devices—only a limited number of buses and lines were equipped—demonstrating practical scalability.
• The use of alternating LP/QP and AC-PF steps maintained feasibility while achieving convergence in reasonable time for large-scale systems.
• The approach extended the system's operational domain under stressed conditions, allowing the system to remain feasible beyond the base-case infeasibility threshold.
• The scenario sampling scheme, using Gaussian perturbations on re-scaled base loads, effectively modeled load distribution uncertainty while preserving ACOPF feasibility.