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Multi-Interval Energy-Reserve Co-Optimization with SoC-Dependent Bids from Battery Storage

Cong Chen, Siying Li, Lang Tong

TL;DR

This work tackles co-optimized energy-reserve market clearing with SoC-dependent bids from battery storage, where conventional nonconvex formulations hinder large-scale deployment. It introduces a robust optimization framework to handle uncertain regulation trajectories and proves that, when bids satisfy the Equal Decremental-Cost Ratio (EDCR) condition, the clearing problem becomes a standard convex piecewise-linear program. The authors also provide a method to generate EDCR bids and prove that, under reasonable assumptions, EDCR bids yield higher storage profitability than SoC-independent bids, with numerical experiments showing 28%–150% gains and modest system-cost reductions. The results demonstrate a computationally tractable path to align storage costs (degradation and opportunity costs) with market dispatch, enabling broader integration of battery storage in wholesale markets and improved reliability with reserves.

Abstract

We consider the problem of co-optimized energy-reserve market clearing with state-of-charge (SoC) dependent bids from battery storage participants. While SoC-dependent bids capture storage's degradation and opportunity costs, such bids result in a non-convex optimization in the market clearing process. More challenging is the regulation reserve capacity clearing, where the SoC-dependent cost is uncertain as it depends on the unknown regulation trajectories ex-post of the market clearing. Addressing the nonconvexity and uncertainty in a multi-interval co-optimized real-time energy-reserve market, we introduce a simple restriction on the SoC-dependent bids along with a robust optimization formulation, transforming the non-convex market clearing under uncertainty into a standard convex piece-wise linear program and making it possible for large-scale storage integration. Under reasonable assumptions, we show that SoC-dependent bids yield higher profit for storage participants than that from SoC-independent bids. Numerical simulations demonstrate a 28%-150% profit increase of the proposed SoC-dependent bids compared with the SoC-independent counterpart.

Multi-Interval Energy-Reserve Co-Optimization with SoC-Dependent Bids from Battery Storage

TL;DR

This work tackles co-optimized energy-reserve market clearing with SoC-dependent bids from battery storage, where conventional nonconvex formulations hinder large-scale deployment. It introduces a robust optimization framework to handle uncertain regulation trajectories and proves that, when bids satisfy the Equal Decremental-Cost Ratio (EDCR) condition, the clearing problem becomes a standard convex piecewise-linear program. The authors also provide a method to generate EDCR bids and prove that, under reasonable assumptions, EDCR bids yield higher storage profitability than SoC-independent bids, with numerical experiments showing 28%–150% gains and modest system-cost reductions. The results demonstrate a computationally tractable path to align storage costs (degradation and opportunity costs) with market dispatch, enabling broader integration of battery storage in wholesale markets and improved reliability with reserves.

Abstract

We consider the problem of co-optimized energy-reserve market clearing with state-of-charge (SoC) dependent bids from battery storage participants. While SoC-dependent bids capture storage's degradation and opportunity costs, such bids result in a non-convex optimization in the market clearing process. More challenging is the regulation reserve capacity clearing, where the SoC-dependent cost is uncertain as it depends on the unknown regulation trajectories ex-post of the market clearing. Addressing the nonconvexity and uncertainty in a multi-interval co-optimized real-time energy-reserve market, we introduce a simple restriction on the SoC-dependent bids along with a robust optimization formulation, transforming the non-convex market clearing under uncertainty into a standard convex piece-wise linear program and making it possible for large-scale storage integration. Under reasonable assumptions, we show that SoC-dependent bids yield higher profit for storage participants than that from SoC-independent bids. Numerical simulations demonstrate a 28%-150% profit increase of the proposed SoC-dependent bids compared with the SoC-independent counterpart.
Paper Structure (31 sections, 8 theorems, 58 equations, 8 figures, 1 table)

This paper contains 31 sections, 8 theorems, 58 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Summary of contribution
  3. Related work
  4. Paper organization and notations
  5. Co-Optimized Energy-Reserve Market Clearing with SoC-Dependent Bids
  6. Storage operation model in energy-reserve co-optimization
  7. SoC-dependent bids
  8. Bid-in cost of co-optimized storage operation
  9. Energy-reserve co-optimization as a robust optimization
  10. Convexification of SoC-Dependent Energy-Reserve Market Clearing
  11. EDCR bids and convexification
  12. Pricing and profit in SoC-dependent market
  13. Profitability of EDCR Bid
  14. EDCR Bid Generation Approach
  15. Profitability of EDCR bid
  16. ...and 16 more sections

Key Result

Theorem 1

The energy-reserve co-optimization (eq:NONCVX) becomes a linear program, if all SoC-dependent bids are EDCR bids and eq:Simul_CD can be relaxed. In particular, the single-stage bid-in cost $f^*$ of the energy-reserve co-optimization of (eq:ROmileage) is given by The multi-stage storage operation cost $F^*$ in (eq:robustcost) has the following explicit convex piecewise linear form with $\alpha_j(

Figures (8)

  • Figure 1: Left: The SoC-dependent bid and offer format when $K=3$. Right: Cost of charging the storage by $(p^c_{t}+m^d_{j,t})\delta$ from $\hat{e}_{j,t}$ to $\hat{e}_{j+1,t}$.
  • Figure 2: Storage bids and simulation results of the toy example, including market clearing prices, bid-in profitof storage, and true profit of storage.
  • Figure 3: One-shot dispatch results. (Top left: system operation cost; top right: storage throughput; bottom left: storage bid-in profit; bottom right: storage true profit).
  • Figure 4: Rolling-window dispatch results. (Top left: system operation cost; top right: storage throughput; bottom: storage bid-in profit).
  • Figure 5: Energy demand in the simulation.
  • ...and 3 more figures

Theorems & Definitions (10)

  • Definition 1: Monotonic SoC-Dependent Bids
  • Definition 2: EDCR Condition
  • Theorem 1: Convexification of Energy-Reserve Co-Optimization
  • Proposition 1
  • Theorem 2: Profitability of the EDCR Bid
  • Lemma 1
  • Proposition 2
  • Lemma 2
  • Lemma 3
  • Lemma 4