A Framework for Eliminating Paradoxical Orders in European Day-Ahead Electricity Markets through Mixed-Integer Linear Programming Strong Duality

TL;DR

This paper introduces a novel pricing mechanism for European day-ahead electricity markets using Augmented Lagrangian Duality, ensuring incentive compatibility, eliminating paradoxical orders, and maintaining revenue adequacy with computational efficiency.

Contribution

It proposes an ALD-based pricing framework that guarantees incentive compatibility and removes paradoxical orders in MILP-based electricity markets, with a modified SAVLR algorithm for practical computation.

Findings

ALD pricing mechanism is incentive-compatible and eliminates paradoxical orders.

The modified SAVLR algorithm efficiently computes optimal multipliers.

Numerical experiments confirm the economic and computational advantages.

Abstract

The presence of integer variables in the European day-ahead electricity market renders the social welfare maximization problem non-convex and non-differentiable, making classical marginal pricing theoretically inconsistent. Existing pricing mechanisms often struggle to balance revenue adequacy with incentive compatibility, typically relying on discriminatory uplift payments or suffering from weak duality. Leveraging the Augmented Lagrangian Duality (ALD) framework, which establishes strong duality for Mixed-Integer Linear Programming (MILP), this paper proposes a novel ALD pricing mechanism. We analytically prove that this mechanism is inherently incentive-compatible, aligning centralized dispatch with individual incentives without requiring side payments. Notably, we demonstrate that the ALD price signals intrinsically eliminate Paradoxically Rejected Orders (PROs) and Paradoxically Accepted Orders (PAOs) for supply orders. For the demand side, a sufficient condition is introduced to further guarantee revenue adequacy, resulting in a transparent and financially consistent settlement system. To ensure computational tractability, we modify the Surrogate Absolute-Value Lagrangian Relaxation (SAVLR) method to efficiently compute the exact penalty coefficients and optimal Lagrangian multipliers. Numerical experiments on illustrative examples and the Nordic 12-area electricity market model confirm the superior economic properties of the ALD pricing mechanism and the tractability of the modified SAVLR algorithm.