Approximation of supply curves

ArXiv ID: 2311.10738 “View on arXiv”

Authors: Unknown

Abstract

In this note, we illustrate the computation of the approximation of the supply curves using a one-step basis. We derive the expression for the L2 approximation and propose a procedure for the selection of nodes of the approximation. We illustrate the use of this approach with three large sets of bid curves from European electricity markets.

Keywords: Supply curves, L2 approximation, Bid curves, Electricity markets, Commodities (Electricity)

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper presents a rigorous mathematical derivation of the L2 approximation for supply curves using specific basis functions and provides explicit solutions, indicating high mathematical complexity. It also includes empirical validation on real European electricity market data with detailed procedures for node selection and performance evaluation, demonstrating significant data and implementation focus.

  flowchart TD
    A["Research Goal: Approximate Supply Curves<br>using a One-Step Basis"] --> B{"Data: 3 Sets of European<br>Electricity Market Bid Curves"}
    
    B --> C["Methodology: Derive L2<br>Approximation Expression"]
    
    C --> D["Computational Process: Selection<br>of Approximation Nodes"]
    
    D --> E{"Computation: Apply<br>L2 Approximation"}
    
    E --> F["Key Outcomes"]
    
    F --> G["Explicit Expression<br>for L2 Approximation"]
    F --> H["Procedure for<br>Node Selection"]
    F --> I["Validated with<br>Real Market Data"]