Solving Bilevel AC OPF Problems by Smoothing the Complementary Conditions -- Part I: Model Description and the Algorithm

TL;DR

This paper introduces a novel bilevel formulation for AC optimal power flow problems using smoothing techniques, enabling accurate modeling of market participants and solving the problem as a single-level optimization with convex quadratic AC OPF.

Contribution

It proposes a new smoothing-based bilevel model for AC OPF that accurately captures market dynamics and transforms into a solvable single-level problem using advanced convexification techniques.

Findings

Convex quadratic AC OPF achieves near nonlinear accuracy.

The smoothing technique effectively transforms bilevel problems.

The model facilitates strategic market participation analysis.

Abstract

The existing research on market price-affecting agents, i.e. price makers, neglects or simplifies the nature of AC power flows in the power system as it predominantly relies on DC power flows. This paper proposes a novel bilevel formulation based on the smoothing technique, where any price-affecting strategic player can be modelled in the upper level, while the market clearing problem in the lower level uses convex quadratic transmission AC optimal power flow (AC OPF), with the goal of achieving accuracy close to the one of the exact nonlinear formulations. Achieving convexity in the lower level is the foundation for bilevel modeling since traditional single-level reduction techniques do not hold for nonconvex models. The bilevel market participation problem with the AC OPF formulation in the lower level is transformed into a single-level problem and solved using multiple techniques such as the primal-dual counterpart, the strong duality theorem, the McCormick envelopes, the complementary slackness, the penalty factor, the interaction discretization as well as the proposed smoothing techniques. Due to an extensive amount of information and descriptions, the overall work is presented as a two-part paper. This first part provides a literature overview, positions the work and presents the model and the solution algorithm, while the solution techniques and case studies are provided in the accompanying paper.