Comparison between row generation, column generation and column-and-row generation for computing convex hull prices in day-ahead electricity markets

Details

Supervisors

Papavasiliou, Anthony ; Madani, Mehdi

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée

Abstract

Due to the non-convexities in the day-ahead electricity markets, it can be shown that there are no uniform prices supporting the market equilibrium, i.e. there will be side payments for the participants to compensate their losses and missed opportunities. The pricing policy minimizing those side-payments aims to computing the Convex Hull Prices (CHP). To compute such prices, one requires the convex hull of the feasibility constraints describing each individual generator involved in the electricity market. The convex hull is modelled through an extended formulation introducing more variables and constraints than the initial mixed-integer optimization program modelling the market. Therefore the extended formulation is a large linear optimization program. Instead of simply solving this optimization program, different improved methods are investigated: row generation, column generation, and column-and-row generation. These methods are used to provide CHP and improve the initial time performances of the extended formulation. The purpose of this master thesis is to compare those improved methods. Each of the methods is separately described to demonstrate its basic principles and its time performances on one real-world example. The performance of each method was compared based on four data sets with different inputs. The most efficient method was then selected and described in greater detail.