⚡ electrical engineering

A state-of-charge based formulation for storage participation in electricity markets: Technical Reference

This paper proposes a novel electricity market design for storage devices that incorporates technical constraints like state-of-charge and round-trip efficiency by eliminating the need for continuous intra-horizon bidding while requiring a single end-of-horizon bid to manage deviations in the state-of-charge.

Original authors: Ross Baldick

Published 2026-06-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ross Baldick

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the electricity grid as a giant, bustling kitchen. In this kitchen, there are chefs (power plants) who cook meals (electricity) and customers who order them. For a long time, the kitchen only had two types of chefs: those who could cook instantly but needed expensive fuel (like gas or coal plants), and those who cooked for free but only when the sun was shining or the wind was blowing (solar and wind).

Recently, the kitchen got a new tool: a giant, magical pantry (energy storage). This pantry can take food (electricity) when it's cheap and abundant, store it, and serve it later when it's expensive and scarce.

The problem is that the current rules for how this pantry participates in the kitchen are confusing and inefficient. This paper, written by Ross Baldick, proposes a new, simpler set of rules to make the pantry work better.

Here is the breakdown of the paper's ideas using simple analogies:

1. The Old Way: The "Guessing Game"

Currently, the pantry owner has to act like a fortune teller. To decide when to fill the pantry and when to empty it, they have to submit a list of prices for every single hour of the next day.

The Flaw: They have to guess what the price of electricity will be at 2:00 PM, 3:00 PM, 4:00 PM, etc.
The Result: If they guess wrong, they make bad decisions. They might fill the pantry when they should have saved the space, or empty it when they should have waited. This leads to wasted money and a less efficient kitchen. It's like trying to play chess while blindfolded, guessing where your opponent will move.

2. The New Way: The "State of Charge" (SOC) Approach

The author proposes a system where the pantry owner doesn't have to guess the hourly prices. Instead, they just tell the kitchen manager (the market operator) one simple thing:

"I want my pantry to be X% full at the end of the day."

The kitchen manager then uses a super-computer to figure out the best way to fill and empty the pantry throughout the day to meet that goal while keeping the whole kitchen running efficiently.

3. The Key Features of the New System

The "Round-Trip" Tax (Efficiency)
The paper acknowledges that the pantry isn't perfect. If you put 100 apples in, you might only get 90 out later because some get squished or rot (this is called round-trip efficiency). The new math accounts for this loss automatically, so the kitchen manager knows exactly how much "food" is actually available.

The "End-of-Day" Bid
Instead of guessing every hour, the pantry owner only makes one bet: "I am willing to pay (or accept) $X to have my pantry end the day with a different amount of food than it started with."

If they think electricity will be very expensive tomorrow, they might bid to end the day with the pantry fuller.
If they think it will be cheap, they might bid to end the day with the pantry emptier.
This single bid replaces hundreds of hourly guesses.

The "Degradation" Cost
Just like a real pantry shelf wears out if you open and close it too much, the storage device wears out every time it charges and discharges. The new model includes a small "wear and tear" cost in the math, ensuring the pantry isn't overworked.

4. Why This Matters (The "Aha!" Moment)

The paper argues that the current system forces storage owners to play a game they aren't good at (predicting the future). The new system lets the storage owner focus on what they do know (how much energy they want to have at the end of the day) and lets the market operator handle the complex math of when to move that energy.

The Analogy of the Commuter:

Old Way: You have to tell your boss exactly what time you will leave your house and what time you will arrive at work for every single day of the next month, guessing traffic conditions. If you guess wrong, you get fired (or pay a penalty).
New Way: You just tell your boss, "I need to be at work by 9:00 AM." The boss (the market) then figures out the best route and departure time for you, considering traffic, road closures, and fuel costs. You just show up when you need to be there.

5. The "Side Effect": Helping Regular People

The paper also suggests that this same "pantry" logic could be applied to regular electricity users (like factories or even homes).

Imagine a factory that needs to use 1,000 units of energy a day but doesn't care when it uses them.
Under the new rules, the factory could act like a "storage device." They could say, "I need 1,000 units by the end of the day." The market would then automatically shift their usage to the cheapest times of the day, saving them money without them needing to be experts in electricity prices.

Summary

The paper proposes a smarter way to run the electricity market for storage. Instead of forcing storage owners to guess the future price of electricity every hour, it lets them simply state their goal for how much energy they want to have left at the end of the day. The market then does the heavy lifting to figure out the most efficient way to get there, saving money and making the grid more reliable.

Technical Summary: A State-of-Charge Based Formulation for Storage Participation in Electricity Markets

Problem Statement
The paper addresses the challenge of integrating high levels of energy storage systems (ESS) into electricity markets, particularly as renewable penetration increases and dispatchable thermal resources decrease. The author argues that current market designs in US organized markets (operated by ISOs/RTOs) inadequately represent ESS. The prevailing approach models storage as a paired generator and load, requiring the storage owner to submit interval-by-interval bids (for charging) and offers (for discharging) across the dispatch horizon.

This traditional approach forces ESS owners to forecast electricity prices within the dispatch horizon to make optimal charging and discharging decisions. The paper contends that such forecasts are inherently subject to uncertainty regarding random events (e.g., renewable output) and system conditions. Consequently, forecast errors lead to sub-optimal dispatch, increased operational costs, and reduced market efficiency. Furthermore, as ESS penetration grows, the endogeneity of price forecasts (where one ESS's forecast depends on others' actions) exacerbates these inefficiencies. The paper posits that current models fail to capture the fundamental physical characteristics of storage: inter-temporal linkages via State-of-Charge (SOC) and round-trip efficiency, without fuel costs.

Methodology
The paper proposes a market design where the Independent System Operator (ISO) centrally optimizes the ESS's State-of-Charge (SOC) trajectory, explicitly modeling technical characteristics such as round-trip efficiency and SOC limits.

Formulation: The dispatch horizon is divided into intervals $t = 1, \dots, T$ . The ISO defines variables for charging power ( $p_t$ ), discharging power ( $g_t$ ), and SOC ( $s_t$ ).
SOC Dynamics: The SOC evolves according to a linear equation incorporating charging efficiency ( $\alpha$ ), discharging efficiency ( $\beta$ ), and self-discharge ( $\gamma$ ). Crucially, the model enforces that charging and discharging cannot occur simultaneously.
Cost Structure: The model includes degradation costs proportional to charge and discharge rates.
Bid/Offer Mechanism: Instead of interval-by-interval bids, the storage owner submits:
1. Technical parameters (capacity, efficiency, degradation coefficients).
2. A single end-of-horizon bid/offer. This is a willingness-to-pay function, $w(\Delta s_T)$ , representing the value of deviating the final SOC ( $s_T$ ) from the "no-participation" SOC ( $\bar{s}_T$ , the SOC if the ESS did nothing).
Optimization: The ISO solves a welfare-maximization problem (minimizing total system cost including degradation and subtracting bid benefits) subject to power balance, transmission constraints, and SOC dynamics. Locational Marginal Prices (LMPs) are derived from the Lagrange multipliers of the system constraints.
Settlement: Settlement is based on energy charged and discharged at LMPs, plus the bid benefit for the final SOC deviation. There is no direct payment for SOC itself.

Key Contributions

Elimination of In-Horizon Price Forecasting: The primary contribution is a market design that removes the requirement for ESS owners to forecast prices within the dispatch horizon. The ISO handles the inter-temporal optimization, while the ESS only needs to assess the value of energy after the horizon ends.
Faithful Technical Representation: The model explicitly incorporates round-trip efficiency and SOC constraints into the central dispatch optimization, aligning with the requirements of FERC Order 841 to recognize the unique characteristics of electric storage resources.
Efficiency and Scalability: By decoupling the ESS from the need to predict volatile intra-horizon prices, the design aims to reduce dispatch sub-optimality caused by forecast errors. The paper cites recent work indicating that solving this formulation for over 100 ESS units in large-scale systems (e.g., MISO) is computationally feasible within day-ahead market timeframes.
Extension to Demand-Side Resources: The paper demonstrates that the SOC model can be specialized to represent price-responsive demand (e.g., industrial loads with daily energy requirements) by setting charging capacity to zero and treating the load as an energy-limited resource.

Results
The paper illustrates the proposed design through a stylized day-ahead market example with 6 intervals, featuring thermal generation, renewable generation, and a single ESS.

Base Case: With moderate future price forecasts, the ISO optimally charges the ESS during low-price/renewable-rich intervals and discharges during high-demand intervals. The ESS achieves a positive surplus without needing to predict specific interval prices.
High Willingness-to-Pay: When the ESS forecasts higher future prices, the ISO adjusts the dispatch to retain more energy (higher end-of-horizon SOC), altering the marginal pricing in later intervals.
Comparison to Current Designs: The paper argues that if interval-by-interval bids were used instead, achieving the same welfare-optimal dispatch would require the ESS to submit bids that perfectly match the clearing prices. If the ESS uses fixed prices or imperfect forecasts, it would likely result in negative surplus or sub-optimal dispatch. The proposed model guarantees positive surplus (arbitrage profit) without requiring intra-horizon price prediction.

Significance and Claims
The paper claims that its proposed formulation offers a more robust and efficient mechanism for storage participation, particularly as storage penetration increases. It argues that the current reliance on ESS owners forecasting intra-horizon prices is a structural flaw that leads to operational challenges analogous to those caused by inaccurate transmission or unit commitment models.

The author emphasizes that the design is compatible with the philosophy of US organized markets, which have historically evolved to explicitly represent technical characteristics (e.g., transmission constraints, unit commitment costs) to improve welfare. By treating SOC and round-trip efficiency as central to the optimization rather than as constraints on user-submitted bids, the design adheres to FERC Order 841's mandate to remove barriers to storage participation. The paper concludes that while the model requires significant changes to existing market structures and leaves ancillary services for future work, it provides a necessary foundation for scaling storage integration in high-renewable grids.