Battery Bidding under Price Uncertainty in Wholesale Electricity Markets

Technical Summary: Battery Bidding under Price Uncertainty in Wholesale Electricity Markets

Problem Statement
Grid-scale batteries are increasingly critical for integrating variable renewable energy and ensuring grid reliability. However, observed bidding patterns in wholesale electricity markets—specifically, systematic gaps between submitted bids and realized day-ahead market (DAM) prices—often resemble "withholding" behavior (e.g., unusually high sell bids or low buy bids). While such patterns raise concerns about market power and strategic manipulation, existing market power mitigation measures have shown limited impact on battery dispatch. The central question addressed by this paper is whether these bid patterns can arise from rational, competitive operations under price uncertainty and risk management, rather than from the exercise of market power.

Methodology
The authors develop an asset-level, price-taking model of a battery operator participating in the day-ahead market. The model is designed to optimize stepwise bid curves (quantity–price pairs) rather than just dispatch quantities, aligning with actual market participation mechanics.

1. Model Formulation:

   • Objective: The battery maximizes a mean–Conditional Value-at-Risk (CVaR) objective, trading off expected revenue against downside risk.
   • Uncertainty: Market prices are represented by a finite set of hourly price scenarios.
   • Constraints: The model incorporates physical constraints (power limits, storage capacity, charge/discharge efficiency) and market constraints (no simultaneous charge/discharge, enforced via a deadband between buy and sell prices).
   • State-of-Charge (SoC): Inventory dynamics are modeled through expected SoC evolution across scenarios, ensuring the battery does not charge when full or discharge when empty in expectation.

2. Exact Linear Programming (LP) Reformulation:

   • A natural formulation of this problem is a Mixed-Integer Linear Program (MILP) due to the binary nature of market clearing (whether a bid clears depends on if the realized price crosses the bid price).
   • The authors prove that for a finite set of sampled price scenarios, the optimal bid prices can be restricted to the set of sampled prices without loss of optimality.
   • This observation allows the clearing indicators to be precomputed as fixed coefficients, transforming the MILP into an exact Linear Programming (LP) reformulation.
   • Significance: This reformulation reduces solution times from hours (for the MILP) to less than a second, making empirical analysis computationally tractable. It also exposes economically meaningful dual variables, such as the shadow price of the SoC constraint, which represents the battery's intertemporal opportunity cost.

3. Empirical Analysis:

   • The model is tested using 2024 Day-Ahead Market (DAM) price data from the California ISO (CAISO).
   • Price uncertainty is modeled using a Gaussian process calibrated to historical residuals, with a scalar parameter controlling the level of uncertainty.
   • Three simulations are conducted:
     1. Risk-neutral evening discharging with varying initial SoC.
     2. Risk-neutral midday charging and evening discharging (full intraday cycle).
     3. Risk-averse operations (varying the mean-CVaR weight) under the full intraday cycle.

Key Contributions and Results

1. Rational Withholding without Market Power:
   The paper demonstrates that "withholding" behavior (submitting bids that avoid clearing in the day-ahead market) can arise naturally from competitive, price-taking behavior. When stored energy is scarce, the opportunity cost of using that energy now versus saving it for a potentially higher-priced future hour increases. This rational valuation leads to higher sell bids, even without market power.

2. State-of-Charge (SoC) Dependence of Uncertainty:
   The effect of price uncertainty on bidding is non-monotonic and depends heavily on the battery's initial inventory:

   • Scarce Inventory: Greater uncertainty increases the value of holding energy for future high-price opportunities, raising sell bid prices.
   • Abundant Inventory: When the battery has ample energy to cover peak hours, greater uncertainty can actually lower sell bid prices. The operator becomes more willing to liquidate excess inventory over a broader range of scenarios to avoid being left with unsold energy at the end of the horizon.

3. Layered Bid Structures from Risk Management:
   Introducing risk aversion (via the CVaR term) reshapes bid curves into "layered" structures.

   • To secure a revenue floor, the battery lowers a portion of its sell bids to ensure execution across a broad set of scenarios.
   • Simultaneously, it retains a portion of its capacity at very high (withholding-looking) prices to preserve exposure to rare but valuable price spikes.
   • This results in a bid curve that balances core execution stability with upside potential, rather than a simple shift in the entire curve.

Significance and Claims
The paper claims that observed battery bid patterns in wholesale markets, often interpreted as evidence of market manipulation, can be fully explained by legitimate economic operations under uncertainty. The authors argue that:

• Interpretive Shift: Market monitoring frameworks must distinguish between strategic withholding (market power) and risk-adjusted, price-taking behavior. The latter is a rational response to the intertemporal nature of battery storage and price volatility.
• Methodological Utility: The exact LP reformulation provides a practical tool for empirical analysis, allowing researchers to solve complex bidding problems efficiently and extract dual variables that offer economic insights into opportunity costs.
• Policy Implication: The findings suggest that current market power mitigation tools may be misaligned with the actual drivers of battery behavior, which are often rooted in risk management and inventory scarcity rather than strategic manipulation.

The paper concludes by noting that while the model isolates energy arbitrage, future work should extend this framework to include co-optimization with ancillary services and resource adequacy obligations, which would further influence bid formation through additional opportunity costs.