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Pooling Probabilistic Forecasts for Cooperative Wind Power Offering

Honglin Wen, Pierre Pinson

TL;DR

This paper tackles the problem of forecast incoherence among wind power producers forming coalitions for market participation. It introduces a reconcile-then-optimize framework where heterogeneous probabilistic forecasts are first reconciled into a coherent joint view using a nonparametric neural reconciler that acts as a universal approximator. Using the reconciled forecasts, a two-stage stochastic program determines the aggregate day-ahead offer and scenario-based dual values, from which a core, budget-balanced allocation is constructed and ex-post adjustments are made based on realized outcomes. Empirical evaluation on NYISO data shows that the proposed approach improves probabilistic forecast quality (lower Energy Score and better calibration) and yields higher realized profits for the cooperative strategy compared to independent offering and baseline reconciliation methods. The results demonstrate practical viability and theoretical soundness, while also highlighting ongoing challenges such as remaining under-dispersion and potential extensions to distributed, privacy-aware reconciliation.

Abstract

Wind power producers can benefit from forming coalitions to participate cooperatively in electricity markets. To support such collaboration, various profit allocation rules rooted in cooperative game theory have been proposed. However, existing approaches overlook the lack of coherence among producers regarding forecast information, which may lead to ambiguity in offering and allocations. In this paper, we introduce a ``reconcile-then-optimize'' framework for cooperative market offerings. This framework first aligns the individual forecasts into a coherent joint forecast before determining market offers. With such forecasts, we formulate and solve a two-stage stochastic programming problem to derive both the aggregate offer and the corresponding scenario-based dual values for each trading hour. Based on these dual values, we construct a profit allocation rule that is budget-balanced and stable. Finally, we validate the proposed method through empirical case studies, demonstrating its practical effectiveness and theoretical soundness.

Pooling Probabilistic Forecasts for Cooperative Wind Power Offering

TL;DR

This paper tackles the problem of forecast incoherence among wind power producers forming coalitions for market participation. It introduces a reconcile-then-optimize framework where heterogeneous probabilistic forecasts are first reconciled into a coherent joint view using a nonparametric neural reconciler that acts as a universal approximator. Using the reconciled forecasts, a two-stage stochastic program determines the aggregate day-ahead offer and scenario-based dual values, from which a core, budget-balanced allocation is constructed and ex-post adjustments are made based on realized outcomes. Empirical evaluation on NYISO data shows that the proposed approach improves probabilistic forecast quality (lower Energy Score and better calibration) and yields higher realized profits for the cooperative strategy compared to independent offering and baseline reconciliation methods. The results demonstrate practical viability and theoretical soundness, while also highlighting ongoing challenges such as remaining under-dispersion and potential extensions to distributed, privacy-aware reconciliation.

Abstract

Wind power producers can benefit from forming coalitions to participate cooperatively in electricity markets. To support such collaboration, various profit allocation rules rooted in cooperative game theory have been proposed. However, existing approaches overlook the lack of coherence among producers regarding forecast information, which may lead to ambiguity in offering and allocations. In this paper, we introduce a ``reconcile-then-optimize'' framework for cooperative market offerings. This framework first aligns the individual forecasts into a coherent joint forecast before determining market offers. With such forecasts, we formulate and solve a two-stage stochastic programming problem to derive both the aggregate offer and the corresponding scenario-based dual values for each trading hour. Based on these dual values, we construct a profit allocation rule that is budget-balanced and stable. Finally, we validate the proposed method through empirical case studies, demonstrating its practical effectiveness and theoretical soundness.
Paper Structure (20 sections, 4 theorems, 29 equations, 2 figures, 4 tables)

This paper contains 20 sections, 4 theorems, 29 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Probabilistic Forecast Reconciliation
  3. Learning-based Reconciliation Model
  4. Parameter Estimation
  5. Trading Strategy and Allocation Mechanism
  6. Trading Strategy of Single WPP
  7. Cooperative Wind Power Offering
  8. Case study
  9. Setups and Benchmarks
  10. Independent offering
  11. Bottom-up reconciliation
  12. Projection-based reconciliation jeon2019probabilisticpanagiotelis2023probabilistictsiourvas2024learning
  13. Evaluation Metrics
  14. Energy Score
  15. Calibration
  16. ...and 5 more sections

Key Result

Lemma 1

Let $(X,Y)$ be a random pair taking values in $\mathcal{X}\times \mathcal{Y}$ with joint distribution $F_{X,Y}$, where $\mathcal{Y}$ is assumed to be a standard Borel space. Then, there exits a random vector $\eta\sim \mathcal{N}(\mathbf{0},\mathbf{I}_d)$ where $d$ is the dimension of $Y$, and a Bor almost surely.

Figures (2)

  • Figure 1: The proposed "reconcile-then-optimize" framework.
  • Figure 2: Multivariate rank histograms for different methods (consistency bars were obtained through simulation of perfectly calibrated forecasts brocker2007increasing).

Theorems & Definitions (9)

  • Definition 1: Coherence
  • Lemma 1: Normalizing flow
  • proof
  • Proposition 1: Universal approximator
  • proof
  • Proposition 2: Core allocation
  • proof
  • Proposition 3: Ex-post allocation
  • proof