Renewable-Colocated Green Hydrogen Production: Optimal Scheduling and Profitability

Abstract: We study the optimal green hydrogen production and energy market participation of a renewable-colocated hydrogen producer (RCHP) that utilizes onsite renewable generation for both hydrogen production and grid services. Under deterministic and stochastic profit-maximization frameworks, we analyze RCHP's multiple market participation models and derive closed-form optimal scheduling policies that dynamically allocate renewable energy to hydrogen production and electricity export to the wholesale market. Analytical characterizations of the RCHP's operating profit and the optimal sizing of renewable and electrolyzer capacities are obtained. We use real-time renewable production and electricity price data from three independent system operators to assess the impacts of hydrogen market prices, renewable generation, and electricity prices on RCHP's profitability.

• The paper derives a closed-form threshold policy that optimally allocates renewable energy between hydrogen production and grid participation.
• It shows a linear relationship between electrolyzer and renewable capacities, enabling simplified capacity planning within convex profitability regions.
• Empirical studies using US ISO data confirm that the flexible prosumer model consistently outperforms other market models under varying conditions.

This paper (2504.18368) investigates the optimal operation and profitability of a Renewable-Colocated Green Hydrogen Producer (RCHP). The RCHP utilizes onsite renewable generation (solar or wind) for both hydrogen production via electrolysis and participation in the wholesale electricity market. The core problem addressed is how an RCHP can maximize profit by dynamically allocating renewable energy between hydrogen production and electricity export/import, considering real-time electricity prices (LMPs) and hydrogen prices.

The paper defines four distinct market participation models for an RCHP:

• Standalone Hydrogen Producer (M0): Produces hydrogen only from colocated renewables, no grid connection.
• Renewable Producer (M1-p): Exports surplus renewable energy but cannot import power.
• Price-elastic Consumer (M1-c): Imports certified renewable energy to supplement onsite generation but cannot export power.
• Flexible Prosumer (M2): Can both export surplus renewable power and import certified renewable power.

The primary focus is on the flexible prosumer model (M2), which represents the most general case.

Optimal Production Scheduling

A key practical contribution is the derivation of a closed-form optimal scheduling policy for the RCHP under various market models, particularly M2. This policy dictates, for each time interval, how much power to send to the electrolyzer, how much to export to the grid, and how much to import from the grid (for M1-c and M2). The optimization problem, while initially non-convex, is solved analytically, resulting in a simple threshold policy.

The policy depends on comparing the real-time LMP and the level of renewable generation against pre-computed price and quantity thresholds. For the M2 model with positive LMPs and electrolyzer capacity ($Q_H$) less than renewable capacity ($Q_R$), the operational strategy falls into four regions (illustrated in Fig. 3a of the paper):

• Region R1 (Low LMP, Low Renewable): LMP is below a lower threshold ($\underline{\pi}_{\text{LMP}}$), and renewable generation ($n_t Q_R$) is below $Q_H$. The RCHP maximizes hydrogen production by importing power to meet $Q_H$.
• Region R2 (Moderate LMP, Low Renewable): LMP is between thresholds ($\underline{\pi}_{\text{LMP}}$ and $\bar{\pi}_{\text{LMP}}$), and renewable generation is below $Q_H$. The RCHP uses all available onsite renewable energy for hydrogen production, acting as a net-zero participant in the grid.
• Region R3 (High LMP): LMP is above an upper threshold ($\bar{\pi}_{\text{LMP}}$). The RCHP exports all renewable generation to the grid and produces no hydrogen, as selling electricity is more profitable.
• Region R4 (Moderate LMP, High Renewable): LMP is between thresholds, and renewable generation exceeds $Q_H$. The RCHP maximizes hydrogen production up to $Q_H$ using onsite power and exports the surplus renewable energy to the grid.

These thresholds ($\underline{\pi}_{\text{LMP}}$, $\bar{\pi}_{\text{LMP}}$) are functions of market parameters like hydrogen price, various production credits, and REC prices for imported/exported power. The existence of distinct thresholds for buying and selling RECs ($$c_{\text{REC}}^{\text{IM}} > c_{\text{REC}}^{\text{EX}}$$) creates the "net-zero" region (R2), where using self-generated power is optimal, avoiding both expensive imports and lower-value exports.

The closed-form solution (Theorem 1) provides explicit expressions for the optimal power dispatch variables ($P_H^*$, $P_{\text{EX}}^*$, $P_{\text{IM}}^*$) based on the real-time LMP and renewable capacity factor ($n_t$). This allows for easy implementation of the operational strategy without complex online optimization.

Profitability Analysis and Capacity Sizing

The paper develops a framework to analyze the expected operating profit of an RCHP over multiple periods, considering the randomness of renewable generation and LMPs. The expected operating profit ($J_{\text{OP}}$) is calculated as the expected gross profit under the optimal scheduling policy minus fixed operating costs for the renewable plant and electrolyzer (eq. 12, 13).

A significant finding (Theorem 2) is that the optimal matching of electrolyzer capacity ($Q_H^*$) to a given renewable capacity ($Q_R$) is linear, i.e., $Q_H^* = K Q_R$ for some constant $K$. The profitability landscape on the ($Q_R, Q_H$) plane is characterized by convex cones of profitable and deficit regions, separated by linear break-even lines (Fig. 2b). This structure simplifies capacity planning.

Furthermore, the paper addresses the joint optimization of $Q_R$ and $Q_H$ given a fixed budget for amortized fixed costs (Theorem 3). The necessary condition for optimality relates the expected profitability per unit capacity of renewable and electrolyzer to their respective fixed costs, allowing for efficient determination of the optimal capacity mix using a bisection search for the optimal capacity ratio $K$.

Empirical Studies and Practical Insights

The paper validates its analytical framework using historical LMP and renewable generation data from three US ISOs: NYISO, CAISO, and MISO. Key findings from the numerical studies provide practical insights:

• Market Model Impact: The flexible prosumer model (M2) consistently yields the highest operating profit across different regions and renewable types (Fig. 4, 6). The ability to dynamically import and export power based on market prices is crucial. At low hydrogen prices, M1-p (producer) performs closer to M2, while at high hydrogen prices, M1-c (consumer) performs closer to M2.
• Hydrogen Price Sensitivity: Higher hydrogen prices significantly increase profitability and expand the profitable region in the capacity plane (Fig. 4, 5). They also increase the optimal electrolyzer-to-renewable capacity ratio $K$, justifying investment in a larger electrolyzer to produce more hydrogen when its value is high.
• Renewable Profile Impact: The statistical characteristics of renewable generation (e.g., solar vs. wind capacity factors and correlation with LMPs) significantly impact profitability and the optimal capacity ratio (Table III, Fig. 6, 7). Concentrated solar peaks can lead to more curtailment or market sales than wind, affecting the balance between hydrogen production and electricity sales.
• Location Impact: Profitability varies across ISOs due to differences in average LMPs and renewable generation profiles (Fig. 6). Lower average electricity prices in NYISO, for example, can make importing power more cost-effective for M1-c and M2 models compared to CAISO, where prices are higher.
• Capacity Mismatch: Operating with suboptimal $Q_R$ and $Q_H$ (outside the optimal capacity line or the profitable region) leads to significant deficits, highlighting the importance of proper capacity sizing and matching (Fig. 5).

Implementation Considerations

• Real-time Control: The threshold policy (Theorem 1) is directly implementable in real-time control systems for the RCHP. It requires real-time data for LMP and onsite renewable generation, alongside pre-computed thresholds.
• Forecasting and Planning: Proposition 1 provides a computable framework for forecasting expected operating profit using historical data statistics. This is valuable for investment decisions and capacity planning. The analysis of optimal capacity ratio $K$ (Theorem 2, 3) provides guidance on designing RCHPs for maximum profitability given a budget.
• Data Requirements: Implementing the model requires access to historical and real-time LMP data, renewable generation profiles (capacity factors), hydrogen market prices, and system parameters (electrolyzer efficiency, fixed/variable costs, credit/REC prices).
• Model Limitations: The current model does not include hydrogen storage dynamics, fuel cells (for generating electricity from hydrogen), or hydrogen distribution costs. These would add complexity but are important for long-term profitability analysis and dispatchability. Incorporating piecewise linear electrolyzer models increases the number of thresholds but the fundamental structure remains threshold-based (Fig. 10).

In summary, the paper provides a rigorous, yet practically applicable, framework for optimizing the real-time operation and assessing the profitability of green hydrogen producers colocated with renewables. The derived closed-form solutions and capacity sizing guidelines offer concrete tools for developers and operators in this emerging field.