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Storage Participation in Electricity Markets: Arbitrage and Ancillary Services

Dirk Lauinger, Luc Coté, Andy Sun

TL;DR

The paper tackles how storage operators should bid for both intertemporal arbitrage and frequency regulation in electricity markets under functional uncertainty. It develops an exact finite-dimensional reformulation that replaces infinite continuous-time constraints with a finite set of linear constraints, yielding a mixed-integer bilinear program; tractable relaxations and restrictions allow fast solution, including near real-time performance. The approach is validated with a four-year European market backtest, showing that joint participation in FCR and arbitrage can more than double profits and substantially reduce energy throughput versus arbitrage-only strategies, with intraday trading further boosting profitability and ensuring SOC feasibility in many cases. The results indicate clear practical value for high-penetration storage, offering a scalable, fast, and robust method to exploit multimarket opportunities while preserving system reliability. Overall, the work advances robust multimarket storage optimization by bridging continuous-time SOC dynamics with discrete-time market decisions and providing actionable, computationally efficient techniques.

Abstract

Electricity storage is used for intertemporal price arbitrage and for ancillary services that balance unforeseen supply and demand fluctuations via frequency regulation. We present an optimization model that computes bids for both arbitrage and frequency regulation and ensures that storage operators can honor their market commitments at all times for all fluctuation signals in an uncertainty set inspired by market rules. This requirement, initially expressed by an infinite number of nonconvex functional constraints, is shown to be equivalent to a finite number of deterministic constraints. The resulting formulation is a mixed-integer bilinear program that admits mixed-integer linear relaxations and restrictions. Empirical tests on European electricity markets show a negligible optimality gap between the relaxation and the restriction. The model can account for intraday trading and, with a solution time of under 5 seconds, may serve as a building block for more complex trading strategies. Such strategies become necessary as battery capacity exceeds the demand for ancillary services. In a backtest from 1 July 2020 through 30 June 2024 joint market participation more than doubles profits and almost halves energy storage output compared to arbitrage alone.

Storage Participation in Electricity Markets: Arbitrage and Ancillary Services

TL;DR

The paper tackles how storage operators should bid for both intertemporal arbitrage and frequency regulation in electricity markets under functional uncertainty. It develops an exact finite-dimensional reformulation that replaces infinite continuous-time constraints with a finite set of linear constraints, yielding a mixed-integer bilinear program; tractable relaxations and restrictions allow fast solution, including near real-time performance. The approach is validated with a four-year European market backtest, showing that joint participation in FCR and arbitrage can more than double profits and substantially reduce energy throughput versus arbitrage-only strategies, with intraday trading further boosting profitability and ensuring SOC feasibility in many cases. The results indicate clear practical value for high-penetration storage, offering a scalable, fast, and robust method to exploit multimarket opportunities while preserving system reliability. Overall, the work advances robust multimarket storage optimization by bridging continuous-time SOC dynamics with discrete-time market decisions and providing actionable, computationally efficient techniques.

Abstract

Electricity storage is used for intertemporal price arbitrage and for ancillary services that balance unforeseen supply and demand fluctuations via frequency regulation. We present an optimization model that computes bids for both arbitrage and frequency regulation and ensures that storage operators can honor their market commitments at all times for all fluctuation signals in an uncertainty set inspired by market rules. This requirement, initially expressed by an infinite number of nonconvex functional constraints, is shown to be equivalent to a finite number of deterministic constraints. The resulting formulation is a mixed-integer bilinear program that admits mixed-integer linear relaxations and restrictions. Empirical tests on European electricity markets show a negligible optimality gap between the relaxation and the restriction. The model can account for intraday trading and, with a solution time of under 5 seconds, may serve as a building block for more complex trading strategies. Such strategies become necessary as battery capacity exceeds the demand for ancillary services. In a backtest from 1 July 2020 through 30 June 2024 joint market participation more than doubles profits and almost halves energy storage output compared to arbitrage alone.

Paper Structure

This paper contains 49 sections, 12 theorems, 59 equations, 10 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background: Storage deployment in electricity markets
  3. Research Question and Prior Work
  4. Contributions
  5. Structure
  6. Notation.
  7. Problem Description
  8. Power output and SOC
  9. Functional uncertainty set for regulation signals
  10. Robust storage optimization model and challenges of discretization
  11. Robust storage optimization model and challenges of discretization
  12. Finite-Dimensional Reformulation
  13. Intuition behind the Upper Bound on the SOC
  14. Evaluating Feasibility of Candidate Decisions
  15. Optimizing over Candidate Decisions
  16. ...and 34 more sections

Key Result

Proposition 1

The power output function $x$ is affine increasing in $x^0(t)$, affine nondecreasing in $x^\uparrow(t)$, affine nonincreasing in $x^\downarrow(t)$, and either convex or concave piecewise linear, nondecreasing in $\xi(t)$ for any $t \in \mathcal{T}$.

Figures (10)

  • Figure 1: Specific loss and power to storage vs power output.
  • Figure 2: Risks of time discretization.
  • Figure 3: Applying the lifting and adjoint operators to a regulation signal.
  • Figure 4: The optimal value function $\varphi(x^0_l, x^\downarrow_l, \bar{\lambda}_k)$ for fixed $x^0_l$ and $x^\downarrow_l$.
  • Figure 5: The optimal value function $\varphi(x^0_l, x^\downarrow_l, \bar{\lambda}_k)$ for fixed $\bar{\lambda}_k$. Contour lines are in brown, iso-$x^0_l$ lines are in blue, iso-$x^\downarrow_l$ lines are in black, the boundary between charging and discharging is in green.
  • ...and 5 more figures

Theorems & Definitions (30)

  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Remark 1: Coupling between market bids
  • Remark 2
  • Example 1: Risks of time discretization
  • Proposition 4
  • Proposition 5: Bounds on power output
  • Proposition 6: Lower bound on SOC
  • Proposition 7: Upper bound on SOC
  • ...and 20 more