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A Scenario-Spatial Decomposition Approach With a Performance Guarantee for the Combined Bidding of Cascaded Hydropower and Renewables

Luca Santosuosso, Simon Camal, Arthur Lett, Guillaume Bontron, Jalal Kazempour, Georges Kariniotakis

Abstract

This study develops a scalable co-optimization strategy for the joint bidding of cascaded hydropower, wind, and solar energy units, treated as a unified entity in the day-ahead market. Although hydropower flexibility can manage the stochasticity of renewable energy, the underlying bidding problem is complex due to intricate coupling constraints and nonlinear dynamics. A decomposition in both scenario and spatial dimensions is proposed, enabling the use of distributed optimization. The proposed distributed algorithm is eventually a heuristic due to non-convexities arising from the system's physical dynamics. To ensure a performance guarantee, trustworthy upper and lower bounds on the global optimum are derived, and a mathematical proof is provided to demonstrate their existence and validity. This approach reduces the average runtime by up to 35% compared to alternative distributed methods and by 57% compared to the centralized optimization. Moreover, it consistently delivers solutions, whereas both centralized and alternative distributed approaches fail as the size of the optimization problem grows.

A Scenario-Spatial Decomposition Approach With a Performance Guarantee for the Combined Bidding of Cascaded Hydropower and Renewables

Abstract

This study develops a scalable co-optimization strategy for the joint bidding of cascaded hydropower, wind, and solar energy units, treated as a unified entity in the day-ahead market. Although hydropower flexibility can manage the stochasticity of renewable energy, the underlying bidding problem is complex due to intricate coupling constraints and nonlinear dynamics. A decomposition in both scenario and spatial dimensions is proposed, enabling the use of distributed optimization. The proposed distributed algorithm is eventually a heuristic due to non-convexities arising from the system's physical dynamics. To ensure a performance guarantee, trustworthy upper and lower bounds on the global optimum are derived, and a mathematical proof is provided to demonstrate their existence and validity. This approach reduces the average runtime by up to 35% compared to alternative distributed methods and by 57% compared to the centralized optimization. Moreover, it consistently delivers solutions, whereas both centralized and alternative distributed approaches fail as the size of the optimization problem grows.

Paper Structure

This paper contains 14 sections, 1 theorem, 37 equations, 13 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Introduction
  3. Literature Review
  4. Motivation and Contributions
  5. Methodology
  6. Problem Statement
  7. Centralized Optimization Problem
  8. From Centralized to Distributed Optimization
  9. Distributed Optimization with Trustworthy Bounds
  10. Simulation Results and Discussion
  11. Out-of-Sample Validation
  12. Stylized Illustrative Example
  13. Full Scale Case Study
  14. Conclusion and Future Work

Key Result

Proposition 1

Let $\boldsymbol{\lambda} \coloneqq \left\{\boldsymbol{\lambda}_{n,\omega}\right\}_{n \in \boldsymbol{N}, \omega \in \boldsymbol{\Omega}}$ satisfy the following conditions (component-wise): Let and Then

Figures (13)

  • Figure 1: Diagram of the VPP under consideration, comprising CHPP and vRES.
  • Figure 2: Example of an operational curve from Compagnie Nationale du Rhône.
  • Figure 3: Visualization of the McCormick approximation in \ref{['eq:hydropower_output_McCormick']}, assuming a turbine efficiency of 95%.
  • Figure 4: Example of decomposed structure of problem \ref{['eq:cen_optim_problem']} when reformulated as the consensus problem \ref{['eq:decomposed_optim_problem']}. The edges in the bipartite graph represent the consistency constraint linking global variables with their local copies.
  • Figure 5: Illustration of the proposed CADMMB algorithm.
  • ...and 8 more figures

Theorems & Definitions (2)

  • Proposition 1
  • proof