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Optimal Operation and Valuation of Electricity Storages

Jean-Philippe Chancelier, Michel De Lara, François Pacaud, Teemu Pennanen, Ari-Pekka Perkkiö

TL;DR

The paper addresses optimal operation and valuation of electricity storages under price uncertainty. It develops a convex stochastic optimization framework and uses indifference pricing to value storage investments in incomplete markets. It employs stochastic dual dynamic programming (SDDP) to handle state constraints and provide market-consistent valuations, with a flexible model that accommodates various storage specs and price dynamics. Numerical experiments on a 30-day horizon illustrate how storage capacity, charging speed, and price views influence valuations, demonstrating practical relevance for expansion and pricing of storage assets.

Abstract

This paper applies computational techniques of convex stochastic optimization to optimal operation and valuation of electricity storages in the face of uncertain electricity prices. Our approach is applicable to various specifications of storages, and it allows for e.g.\ hard constraints on storage capacity and charging speed. Our valuations are based on the indifference pricing principle, which builds on optimal trading strategies and calibrates to the user's initial position, market views and risk preferences. We illustrate the effects of storage capacity and charging speed by numerically computing the valuations using stochastic dual dynamic programming.

Optimal Operation and Valuation of Electricity Storages

TL;DR

The paper addresses optimal operation and valuation of electricity storages under price uncertainty. It develops a convex stochastic optimization framework and uses indifference pricing to value storage investments in incomplete markets. It employs stochastic dual dynamic programming (SDDP) to handle state constraints and provide market-consistent valuations, with a flexible model that accommodates various storage specs and price dynamics. Numerical experiments on a 30-day horizon illustrate how storage capacity, charging speed, and price views influence valuations, demonstrating practical relevance for expansion and pricing of storage assets.

Abstract

This paper applies computational techniques of convex stochastic optimization to optimal operation and valuation of electricity storages in the face of uncertain electricity prices. Our approach is applicable to various specifications of storages, and it allows for e.g.\ hard constraints on storage capacity and charging speed. Our valuations are based on the indifference pricing principle, which builds on optimal trading strategies and calibrates to the user's initial position, market views and risk preferences. We illustrate the effects of storage capacity and charging speed by numerically computing the valuations using stochastic dual dynamic programming.

Paper Structure

This paper contains 15 sections, 4 theorems, 22 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. Optimal storage management and valuation
  3. Optimal storage management
  4. Indifference pricing
  5. Stochastic dual dynamic programming
  6. Stochastic dynamic programming
  7. Discretization of Markov processes
  8. Stochastic dual dynamic programming algorithm
  9. An example
  10. The optimization model
  11. A simple spot price model
  12. Computational results
  13. Data
  14. Convergence of the SDDP algorithm
  15. Sensitivity analysis

Key Result

Proposition 1

The optimum value $\varphi(x_0)$ of oc is convex as a function of $x_0$. If the function $\alpha\mapsto\varphi(x_0-\alpha p)$ is strictly decreasing, then the indifference price $\pi$ is the unique solution to the equation

Figures (10)

  • Figure 1: Annual, weekly and daily variations.
  • Figure 2: Left: logarithmic spot price, average and residuals. Right: histogram of the residual of the time series model.
  • Figure 3: AR-1 process and its discretization as a Markov chain with 3 quadrature points per period
  • Figure 4: Convergence of SDDP as we increase the number of quadrature points per period. The plot on the right is a zoomed version of the plot on the left.
  • Figure 5: Optimum value estimates for increasing number of quadrature points. The red and blue values are given by SDDP while the green values are obtained with out of sample simulation using the optimized Bellman functions.
  • ...and 5 more figures

Theorems & Definitions (4)

  • Proposition 1
  • Theorem 2: Optimality principle
  • Theorem 3: Existence of solutions
  • Theorem 4: Markovianity