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Chance-Constrained Energy Storage Pricing for Social Welfare Maximization

Ning Qi, Ningkun Zheng, Bolun Xu

TL;DR

The paper tackles pricing energy storage under uncertainty by formulating a two-stage chance-constrained economic dispatch aimed at social welfare maximization. It derives deterministic reformulations and proves key properties: the storage opportunity price $\theta_t$ is convex in SoC and increases with net-load uncertainty, while being linearly coupled to energy and reserve prices and bounded to regulate market power. Theoretical results are complemented by an 8-zone ISO-NE case study showing substantial reductions in electricity payments and system costs when using the proposed pricing framework, relative to profit-maximizing benchmarks. The approach yields operator-ready default bids and a principled benchmark for monitoring storage market power, with strong scalability as renewables and storage capacity grow.

Abstract

This paper proposes a novel framework to price energy storage in economic dispatch with a social welfare maximization objective. This framework can be utilized by power system operators to generate default bids for storage or to benchmark market power in bids submitted by storage participants. We derive a theoretical framework based on a two-stage chance-constrained formulation which systematically incorporates system balance constraints and uncertainty considerations. We present tractable reformulations for the joint chance constraints. Analytical results show that the storage opportunity cost is convex and increases with greater net load uncertainty. We also show that the storage opportunity prices are bounded and are linearly coupled with future energy and reserve prices. We demonstrate the effectiveness of the proposed approach on an ISO-NE test system and compare it with a price-taker storage profit-maximizing bidding model. Simulation results show that the proposed market design reduces electricity payments by an average of 17.4% and system costs by 3.9% while reducing storage's profit margins, and these reductions scale up with the renewable and storage capacity.

Chance-Constrained Energy Storage Pricing for Social Welfare Maximization

TL;DR

The paper tackles pricing energy storage under uncertainty by formulating a two-stage chance-constrained economic dispatch aimed at social welfare maximization. It derives deterministic reformulations and proves key properties: the storage opportunity price is convex in SoC and increases with net-load uncertainty, while being linearly coupled to energy and reserve prices and bounded to regulate market power. Theoretical results are complemented by an 8-zone ISO-NE case study showing substantial reductions in electricity payments and system costs when using the proposed pricing framework, relative to profit-maximizing benchmarks. The approach yields operator-ready default bids and a principled benchmark for monitoring storage market power, with strong scalability as renewables and storage capacity grow.

Abstract

This paper proposes a novel framework to price energy storage in economic dispatch with a social welfare maximization objective. This framework can be utilized by power system operators to generate default bids for storage or to benchmark market power in bids submitted by storage participants. We derive a theoretical framework based on a two-stage chance-constrained formulation which systematically incorporates system balance constraints and uncertainty considerations. We present tractable reformulations for the joint chance constraints. Analytical results show that the storage opportunity cost is convex and increases with greater net load uncertainty. We also show that the storage opportunity prices are bounded and are linearly coupled with future energy and reserve prices. We demonstrate the effectiveness of the proposed approach on an ISO-NE test system and compare it with a price-taker storage profit-maximizing bidding model. Simulation results show that the proposed market design reduces electricity payments by an average of 17.4% and system costs by 3.9% while reducing storage's profit margins, and these reductions scale up with the renewable and storage capacity.
Paper Structure (24 sections, 8 theorems, 21 equations, 7 figures, 4 tables)

This paper contains 24 sections, 8 theorems, 21 equations, 7 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Market Design of Energy Storage
  4. Pricing Uncertainty in Stochastic Electricity Market
  5. Problem Formulation and Preliminaries
  6. Two-Stage Chance-Constrained Economic Dispatch
  7. Reformulation
  8. Robust Competitive Equilibrium
  9. Main Results
  10. SoC Monotonicity of Storage Opportunity Price
  11. Uncertainty Monotonicity of Storage Opportunity Price
  12. Regulated Market Power of Energy Storage
  13. Numerical Case Study
  14. Set-Up
  15. Prices versus Risk-Aversion and Uncertainty Realizations
  16. ...and 9 more sections

Key Result

Proposition 1

Given the relaxation of stnazir2021guaranteeing or the charge and discharge states, let $\{g_t^{*}\text{, }p_{t}^{*}\text{, }b_{t}^{*}\text{, }e_{t}^*\text{, }\varphi_{t}^{*}\text{, }\psi_{t}^{*}\}$ be an optimal solution of MCCED and $\{\lambda_t^{*}\text{, }\theta_t^{*}\text{, }\pi_t^{*}\}$ be dua

Figures (7)

  • Figure 1: Prices and costs under different risk aversions and different uncertainty realization: (a) energy price, (b) storage opportunity price, (c) reserve cost, and (d) system cost.
  • Figure 2: Cumulative cost curve of 76 conventional generators in the ISO-NE test system.
  • Figure 3: Opportunity prices under different initial SoC and uncertainty levels.
  • Figure 4: Expected opportunity prices under different cost functions and uncertainty levels.
  • Figure 5: Simulated and theoretical opportunity prices over four simulation days.
  • ...and 2 more figures

Theorems & Definitions (17)

  • Remark 1
  • Proposition 1
  • proof
  • Proposition 2
  • Corollary 1
  • proof
  • Proposition 3
  • proof
  • Proposition 4
  • proof
  • ...and 7 more