Paper: arXiv 2412.15959

Abstract

In this paper, we propose a complete modelling framework to value several batteries in the electricity intraday market at the trading session scale. The model consists of a stochastic model for the 24 mid-prices (one price per delivery hour) combined with a deterministic model for the liquidity costs (representing the cost of going deeper in the order book). A stochastic optimisation framework based on dynamic programming is used to calculate the value of the batteries. We carry out a back test for the years 2021, 2022 and 2023 for the German market and for the French market. We show that it is essential to take liquidity into account, especially when the number of batteries is large: it allows much higher profits and avoids high losses using our liquidity model. The use of our stochastic model for the mid-price also significantly improves the results (compared to a deterministic framework where the mid-price forecast is the spot price).

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical concepts such as stochastic optimization, dynamic programming, and multivariate models for price dynamics, but also demonstrates strong empirical rigor with a comprehensive backtest using three years of real market data from French and German intraday electricity markets, reconstructing order books and testing liquidity cost models.

Research Flowchart

  flowchart TD
  A["Research Goal: Value batteries in electricity intraday markets, accounting for liquidity costs"] --> B{"Data & Inputs"}
  B --> B1["German & French Market Data 2021-2023"]
  B --> B2["Order Book Data for Liquidity Costs"]
  
  B --> C{"Key Methodology"}
  C --> C1["Stochastic Model: 24 Mid-Prices"]
  C --> C2["Deterministic Model: Liquidity Costs"]
  
  C --> D["Computational Process: Dynamic Programming Optimization"]
  D --> E{"Backtesting & Analysis"}
  E --> F1["Liquidity Model: Higher profits & avoids losses"]
  E --> F2["Stochastic Price Model: Outperforms deterministic forecast"]
  
  F1 & F2 --> F["Key Findings: Liquidity & Stochastic modeling are essential for accurate valuation"]