# Utilizing the redundant constraints for the uplift payment elimination

## TL;DR

This paper proposes a method using redundant constraints and their Lagrangian relaxation to eliminate uplift payments in non-convex power markets without affecting market prices or duality gaps.

## Contribution

It introduces a novel approach to reduce uplift payments by exploiting redundant constraints that do not alter the centralized dispatch outcome.

## Key findings

- Redundant constraints can be constructed to eliminate uplift payments.
- Lagrangian relaxation of these constraints reduces uplift payments without changing the duality gap.
- The approach applies to markets with fixed load and can be extended to price-sensitive load scenarios.

## Abstract

A power market with non-convexities may not have an equilibrium price for power that provides economic stability of the centralized dispatch outcome. In this case, the market players are entitled to receive the uplift payments that compensate the economic profit lost when following the centralized dispatch. We consider a special class of the (possibly non-linear) redundant constraints that are redundant not only on the feasible set of the centralized dispatch optimization problem (and, therefore, do not change the centralized dispatch outcome) but also on the larger set obtained when the power balance constraint is relaxed. We show that the Lagrangian relaxation of these redundant constraints may reduce the uplift payments without changing the duality gap. For any given market price (or a pricing algorithm that sets the producer revenue as a function of its output volume) in a uninode multi-period power market with fixed load, we explicitly construct a family of the redundant constraints that do not change the maximum profit of the producer and result in zero uplift payment. We show that the introduction and subsequent Lagrangian relaxation of just one redundant constraint in the centralized dispatch problem suffice to eliminate the uplift payments for all the producers. In the case of the convex hull pricing method, the introduction of these redundant constraints affects neither the duality gap nor the market price for power. The results can be straightforwardly generalized to a power market with the price-sensitive load.

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Source: https://tomesphere.com/paper/1905.07966