📈 economics

Profit-Oriented Planning and Multi-Market Operation Model for Hybrid Energy Storage Systems

This paper proposes a bi-level optimization framework that jointly determines the optimal capacity sizing and multi-market bidding strategies for a price-maker hybrid energy storage system, enabling strategic allocation of heterogeneous storage components between energy arbitrage and reserve markets to maximize profitability.

Original authors: Lizhong Zhang, Junqi Liu, Jianxiao Wang, Lei Zhu

Published 2026-05-19

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Lizhong Zhang, Junqi Liu, Jianxiao Wang, Lei Zhu

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 electrical grid as a giant, bustling marketplace where electricity is bought and sold every second. In the past, this market was mostly run by big power plants (like gas generators) and a few predictable sources (like wind and solar). But as we add more wind and solar, the market becomes wilder and harder to predict, like a stormy sea. To keep the lights on, we need "shock absorbers" called Energy Storage Systems (ESS)—basically giant batteries that can store extra energy when it's cheap and release it when it's expensive.

This paper proposes a new, smarter way to run these batteries, specifically when an operator owns two different types of batteries working together as a team (a Hybrid Energy Storage System, or HESS).

Here is the breakdown of their idea using simple analogies:

1. The Problem: The "One-Size-Fits-All" Mistake

Most previous studies treated all batteries the same, or assumed they were just passive players who had to accept whatever price the market set (like a customer at a grocery store who can't negotiate).

However, in reality, a large battery operator is like a wholesale supplier. If they decide to sell a huge amount of energy at once, they can actually change the market price. They are a "price-maker," not a "price-taker."

Furthermore, not all batteries are built the same.

Battery A (The Marathon Runner): Has a huge tank (high energy) but a narrow pipe (low power). It's great for holding a lot of water but can't pour it out fast.
Battery B (The Sprinter): Has a small tank but a fire-hose pipe (high power). It can dump energy incredibly fast, but it runs out quickly.

The paper argues that you shouldn't treat these two as a single, blurry blob. You need a strategy that lets the "Marathon Runner" do long-distance tasks and the "Sprinter" do quick, high-speed tasks.

2. The Solution: A Two-Level Game Plan

The authors created a mathematical "game" with two levels to figure out the best strategy:

Level 1 (The Boss - Capacity Planning): The Boss decides how big the tanks should be for both the Marathon Runner and the Sprinter. They also decide how to bid in the market. The Boss wants to make the most money possible.
Level 2 (The Referee - Market Clearing): The Referee (the System Operator) looks at all the bids from the Boss, the wind farms, and the gas plants. The Referee's job is to balance the grid at the lowest possible cost. The Referee sets the final prices based on who offered what.

The Magic: The Boss plays first, but they are smart enough to predict exactly how the Referee will react to their bids. This allows the Boss to strategically place their bets to maximize profit.

3. The Strategy: Specialization and Teamwork

The results show that the best way to run this hybrid team is to specialize:

The Sprinter (High Power): This battery is used for Arbitrage. It charges up quickly when prices are low and dumps its energy out fast when prices spike. It also jumps into the "Real-Time" market (the emergency market) to fix sudden mistakes in the wind forecast.
The Marathon Runner (High Capacity): This battery is used for Reserves. It holds a steady amount of energy ready to be called upon to keep the grid stable. It doesn't need to move fast; it just needs to be there when needed.

The Secret Sauce: Internal Handoffs
The paper introduces a cool feature: Internal Power Transfer. Imagine the two batteries are in the same building. If the Sprinter is full but the Marathon Runner is empty, and the grid connection is clogged (like a traffic jam on the road to the city), the Sprinter can pass its extra energy directly to the Marathon Runner inside the building. This keeps the team flexible even when the outside world is blocked.

4. The Results: Who Makes the Money?

When they ran the numbers:

The Sprinter made the most money. Because it could move fast, it captured the biggest price spikes in the energy market.
The Marathon Runner made steady, reliable money by providing reserve services.
The Real-Time Market was tricky. Often, the prices in the emergency (real-time) market were lower than the planned (day-ahead) market. So, the batteries often ended up charging in the real-time market (buying cheap) rather than selling, which is the opposite of what you might expect.

5. Why This Matters

This paper proves that if you own a mix of different battery technologies, you shouldn't just lump them together. By treating them as distinct characters with different strengths and letting them "talk" to each other internally, you can make significantly more profit.

It's like running a delivery company: You don't use a slow, heavy truck to deliver a single urgent letter, and you don't use a fast, expensive motorcycle to move a ton of furniture. You use the right tool for the right job, and you let them coordinate their routes to avoid traffic jams. This paper provides the rulebook for how to do that with electricity.

Technical Summary: Profit-Oriented Planning and Multi-Market Operation Model for Hybrid Energy Storage Systems

Problem Statement
The increasing penetration of variable renewable energy sources necessitates enhanced power system flexibility, driving the deployment of independent energy storage operators (ESOs). While existing literature extensively addresses capacity sizing for price-taker storage systems or the operational coordination of aggregated distributed resources, there is a gap in the joint optimization of capacity planning and multi-market bidding for a price-maker ESO managing a Hybrid Energy Storage System (HESS). Current models often fail to preserve the technological heterogeneity of integrated components, frequently aggregating diverse storage technologies into a single bidding entity, which masks individual operational advantages. Furthermore, existing optimization models typically assume energy transfers occur solely between storage units and the main grid, overlooking the operational flexibility provided by internal energy routing between co-located heterogeneous systems.

Methodology
The authors propose a bi-level optimization framework to jointly optimize profit-oriented decisions regarding capacity planning and multi-market operation for an ESO managing two heterogeneous storage systems ( $s_1$ and $s_2$ ).

Upper-Level Problem (ULP): The ESO acts as a price-maker, maximizing total profit by determining the optimal rated capacities ( $E_s$ ) and submitting price-quantity offers across the day-ahead joint energy-reserve market and the real-time balancing market. The ULP explicitly models the internal power transfer mechanism between the two storage systems, allowing for coordinated energy management when grid access is constrained. The objective function includes revenue from energy arbitrage, reserve provision, and real-time balancing, minus marginal operational costs and amortized investment costs.
Lower-Level Problems (LLP): These represent the System Operator's (SO) market clearing processes.
- LLP 1 (Day-Ahead): A cost-minimization problem that co-optimizes energy and up/down-reserve capacities based on submitted offers from the ESO, wind generators, and gas generators. It determines clearing prices ( $\lambda$ ) and schedules.
- LLP 2 (Real-Time): A cost-minimization problem that clears the balancing market to restore system equilibrium following wind forecast deviations. It utilizes previously procured day-ahead reserves and new real-time offers, with deployment strictly constrained by day-ahead commitments.
Solution Technique: The bi-level model is reformulated as a single-level Mathematical Program with Equilibrium Constraints (MPEC). To handle the non-convexities and bilinear terms (products of endogenous prices and quantities), the authors employ a Big-M reformulation and McCormick envelopes to linearize the problem into a Mixed-Integer Linear Program (MILP). Due to the large scale of the resulting MILP, a Benders' decomposition algorithm is utilized. This approach separates long-term investment variables (capacities) from short-term operational decisions, generating distinct optimality cuts for each typical day to preserve information and accelerate convergence.

Key Contributions

Bi-level Framework for Price-Maker HESS: The paper proposes a novel framework that co-optimizes capacity planning for two heterogeneous storage systems and their participation in both day-ahead and real-time markets, explicitly modeling the ESO as a price-maker whose bids influence market clearing prices.
System-Differentiated Bidding Strategies: Unlike models that aggregate storage, this framework allows the ESO to submit independent price-quantity offers for each technology per market. This exploits the complementary characteristics of diversified storage (e.g., high energy density vs. high power density) to tailor market participation.
Explicit Internal Power Transmission Modeling: The model formulates the power transfer mechanism between heterogeneous storage systems. This enables coordinated internal energy management, providing a critical buffer to sustain market participation and profitability when grid exchange capacities are restricted.

Results
Numerical experiments using data from the Australian National Electricity Market (day-ahead) and Canadian AESO (wind) demonstrate the following:

Optimal Capacity Allocation: The model determines a mixed investment portfolio where the system with a high power-to-capacity ratio ( $s_2$ ) is sized to capture arbitrage profits through rapid, high-volume transfers in volatile pricing windows. Conversely, the system with a low power-to-capacity ratio ( $s_1$ ) is optimized to specialize in providing baseline reserve margins in the day-ahead market.
Market Impact: As a price-maker, the ESO strategically shifts market equilibrium. During discharge, it inserts capacity into the merit order to capture market share from marginal gas generators without triggering lower price tiers. During charge, it strategically bids to exhaust the capacity of cheaper generators, avoiding the activation of more expensive units that would raise the marginal clearing price.
Profit Distribution: The day-ahead market serves as the primary revenue stream. The high-power system ( $s_2$ ) generates the majority of the joint operational profit, particularly in energy arbitrage, while the low-power system ( $s_1$ ) contributes significantly to reserve revenue. Real-time market profits are generally negative, as the ESO tends to charge in real-time to balance wind forecast deviations when real-time prices are lower than day-ahead prices.
Internal Transmission Value: Under scenarios with limited grid access (congestion), internal power transmission is activated. This mechanism allows the operator to reallocate power within the hybrid system, mitigating grid constraints and influencing optimal capacity planning decisions.

Significance
The paper claims that its framework provides differentiated bidding strategies and market participation flexibility for HESS, enhancing overall profitability. By preserving technological heterogeneity and modeling internal coordination, the study demonstrates that treating storage systems as a unified, price-making entity allows for more effective strategic planning than aggregating them or treating them as price-takers. The results validate the necessity of independent decision variables for heterogeneous systems and highlight the value of internal coordination in sustaining market participation under physical grid constraints. The authors note that future work will investigate the impact of renewable generation and load forecast uncertainties, as well as detailed degradation models and multi-operator market equilibrium.