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A Cournot-Nash Model for a Coupled Hydrogen and Electricity Market

Pavel Dvurechensky, Caroline Geiersbach, Michael Hintermüller, Aswin Kannan, Stefan Kater, Gregor Zöttl

Abstract

We present a novel model of a coupled hydrogen and electricity market on the intraday time scale, where hydrogen gas is used as a storage device for the electric grid. Electricity is produced by renewable energy sources or by extracting hydrogen from a pipeline that is shared by non-cooperative agents. The resulting model is a generalized Nash equilibrium problem. Under certain mild assumptions, we prove that an equilibrium exists. Perspectives for future work are presented.

A Cournot-Nash Model for a Coupled Hydrogen and Electricity Market

Abstract

We present a novel model of a coupled hydrogen and electricity market on the intraday time scale, where hydrogen gas is used as a storage device for the electric grid. Electricity is produced by renewable energy sources or by extracting hydrogen from a pipeline that is shared by non-cooperative agents. The resulting model is a generalized Nash equilibrium problem. Under certain mild assumptions, we prove that an equilibrium exists. Perspectives for future work are presented.

Paper Structure

This paper contains 20 sections, 5 theorems, 83 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Equilibrium model
  3. Network topology
  4. Agent's decisions and objective
  5. Decisions.
  6. Objective.
  7. Operational constraints
  8. Electricity network
  9. Gas network constraints
  10. The overall model
  11. Existence of an equilibrium
  12. Assumptions
  13. Existence of solutions to PDE
  14. Variational formulation.
  15. Recovery of classical solution.
  16. ...and 5 more sections

Key Result

Lemma 3.2

Suppose Assumption ass:PDE is satisfied. Then, for every $(\mathfrak{p},\mathfrak{q}) \in H^1(0,T)^{n_h}\times H^1(0,T)^{n_h}$ compatible with the initial condition $y_0 = (p_0,q_0)$, there exists a unique weak solution $y=(p,q) \in W(0,T;H,V)$ satisfying eq:gas-model-detailed-gas-1--eq:gas-model-de

Figures (2)

  • Figure 1: A coupled hydrogen and electricity network, where renewable energy sources are connected to the power grid for immediate use and some power can be used to power PtG stations, which are connected to the gas pipeline. GtP stations are depicted in the lower left and right, which uses hydrogen to produce power. In this system, hydrogen can be stored in the pipeline for later use. PtG and GtP stations are located at conversion nodes. The power lines are mathematically represented by edges $\mathcal{E}^E$ of the graph $\mathcal{G}^E$. The pipes in the gas pipeline are represented by edges $\mathcal{E}^H$ in the graph $\mathcal{G}^H.$
  • Figure 2: Representation of Figure \ref{['fig:networks']} into abstract components. PtG/GtP nodes connect the hydrogen network (in green) and electricity network (in blue). Sale and generation nodes are highlighted in yellow and red, respectively. Arrows represent direction of flow.

Theorems & Definitions (10)

  • Remark 2.1
  • Remark 2.2
  • Lemma 3.2
  • Lemma 3.3
  • proof
  • Lemma 3.4
  • proof
  • Theorem 3.5
  • proof
  • Theorem 3.6