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Value-oriented forecast reconciliation for renewables in electricity markets

Honglin Wen, Pierre Pinson

TL;DR

This paper tackles forecast coherence in a two-level wind energy trading setting with heterogeneous loss functions by introducing a value-oriented forecast reconciliation powered by a Nash bargaining framework. It models reconciliation as a learnable function conditioned on base forecasts and context, coupled with a weighted proportional allocation that distributes balancing costs fairly. A primal-dual empirical risk minimization algorithm estimates reconciliation parameters under equilibrium constraints, and the approach is validated through simulations and a real-world Danish case study. Results show that value-oriented reconciliation can consistently increase profits for all participating wind power producers, highlighting the importance of forecast value and fair information sharing in multi-agent decision tasks.

Abstract

Forecast reconciliation is considered an effective method to achieve coherence (within a forecast hierarchy) and to improve forecast quality. However, the value of reconciled forecasts in downstream decision-making tasks has been mostly overlooked. In a multi-agent setup with heterogeneous loss functions, this oversight may lead to unfair outcomes, hence resulting in conflicts during the reconciliation process. To address this, we propose a value-oriented forecast reconciliation approach that focuses on the forecast value for all individual agents. Fairness is ensured through the use of a Nash bargaining framework. Specifically, we model this problem as a cooperative bargaining game, where each agent aims to optimize their own gain while contributing to the overall reconciliation process. We then present a primal-dual algorithm for parameter estimation based on empirical risk minimization. From an application perspective, we consider an aggregated wind energy trading problem, where profits are distributed using a weighted allocation rule. We demonstrate the effectiveness of our approach through several numerical experiments, showing that it consistently results in increased profits for all agents involved.

Value-oriented forecast reconciliation for renewables in electricity markets

TL;DR

This paper tackles forecast coherence in a two-level wind energy trading setting with heterogeneous loss functions by introducing a value-oriented forecast reconciliation powered by a Nash bargaining framework. It models reconciliation as a learnable function conditioned on base forecasts and context, coupled with a weighted proportional allocation that distributes balancing costs fairly. A primal-dual empirical risk minimization algorithm estimates reconciliation parameters under equilibrium constraints, and the approach is validated through simulations and a real-world Danish case study. Results show that value-oriented reconciliation can consistently increase profits for all participating wind power producers, highlighting the importance of forecast value and fair information sharing in multi-agent decision tasks.

Abstract

Forecast reconciliation is considered an effective method to achieve coherence (within a forecast hierarchy) and to improve forecast quality. However, the value of reconciled forecasts in downstream decision-making tasks has been mostly overlooked. In a multi-agent setup with heterogeneous loss functions, this oversight may lead to unfair outcomes, hence resulting in conflicts during the reconciliation process. To address this, we propose a value-oriented forecast reconciliation approach that focuses on the forecast value for all individual agents. Fairness is ensured through the use of a Nash bargaining framework. Specifically, we model this problem as a cooperative bargaining game, where each agent aims to optimize their own gain while contributing to the overall reconciliation process. We then present a primal-dual algorithm for parameter estimation based on empirical risk minimization. From an application perspective, we consider an aggregated wind energy trading problem, where profits are distributed using a weighted allocation rule. We demonstrate the effectiveness of our approach through several numerical experiments, showing that it consistently results in increased profits for all agents involved.

Paper Structure

This paper contains 17 sections, 6 theorems, 47 equations, 5 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Value-oriented Forecasting and Decision Making
  4. Aggregated Wind Energy Trading
  5. Methodology
  6. Problem Formulation
  7. Value-oriented Forecast Reconciliation
  8. Nash Bargaining based Reconciliation
  9. Weighted Proportional Allocation Mechanism
  10. Profit Allocation within the Aggregation
  11. Model Training via Empirical Risk Minimization
  12. Simulations
  13. Experimental Setups
  14. Case 1
  15. Case 2
  16. ...and 2 more sections

Key Result

Theorem 2.1

[eppen1979notehartman2000cores] In a multi-location newsvendor system, the total optimal expected cost of the centralized system is lower than that of the decentralized system.

Figures (5)

  • Figure 1: wind energy trading as an aggregation.
  • Figure 2: Average profit change over independent offers for each wind power producer across different models in Case 1
  • Figure 3: Average profit change over independent offers for each wind power producer under learning-based and linear reconciliation in Case 1
  • Figure 4: Average profit change over independent offers for each wind power producer across different models in Case 2
  • Figure 5: Average profits for each wind power producer in cases where base forecasts are either mean or quantile forecasts

Theorems & Definitions (13)

  • Theorem 2.1
  • Definition 3.1: Coherent forecast
  • Proposition 3.1
  • proof
  • Corollary 3.1
  • Proposition 3.2
  • proof
  • Proposition 3.3
  • Corollary 3.2
  • Definition 3.2: Extra profit
  • ...and 3 more