Cost Optimized Scheduling in Modular Electrolysis Plants (2402.05148v1)

Abstract: In response to the global shift towards renewable energy resources, the production of green hydrogen through electrolysis is emerging as a promising solution. Modular electrolysis plants, designed for flexibility and scalability, offer a dynamic response to the increasing demand for hydrogen while accommodating the fluctuations inherent in renewable energy sources. However, optimizing their operation is challenging, especially when a large number of electrolysis modules needs to be coordinated, each with potentially different characteristics. To address these challenges, this paper presents a decentralized scheduling model to optimize the operation of modular electrolysis plants using the Alternating Direction Method of Multipliers. The model aims to balance hydrogen production with fluctuating demand, to minimize the marginal Levelized Cost of Hydrogen (mLCOH), and to ensure adaptability to operational disturbances. A case study validates the accuracy of the model in calculating mLCOH values under nominal load conditions and demonstrates its responsiveness to dynamic changes, such as electrolyzer module malfunctions and scale-up scenarios.

• The paper presents a decentralized ADMM-based scheduling model within a Multi-Agent System to optimize modular electrolysis plant operations.
• The paper demonstrates high accuracy and scalability through simulations with AEM electrolyzers, achieving close production-demand matching and rapid rescheduling during malfunctions.
• The paper effectively minimizes marginal LCOH by integrating CapEx, OpEx, and start-up costs, ensuring robust performance under dynamic operating conditions.

Decarbonization efforts highlight green hydrogen production via electrolysis as a crucial technology, especially when powered by volatile renewable energy sources. Modular electrolysis plants, composed of individual Process Equipment Assemblies (PEAs), offer flexibility and scalability but pose challenges in coordinating many modules, particularly when they have heterogeneous characteristics and operating conditions fluctuate. Traditional centralized control methods struggle with this complexity and lack scalability.

This paper proposes a decentralized scheduling model based on the Alternating Direction Method of Multipliers (ADMM) implemented within a Multi-Agent System (MAS) to optimize the operation of modular electrolysis plants. The goal is to balance hydrogen production with fluctuating demand, minimize the marginal Levelized Cost of Hydrogen (mLCOH), and ensure adaptability to operational disturbances like module malfunctions.

The architecture builds upon a refinement of the Process Orchestration Layer (POL) for modular plants, incorporating a Demand Side Management (DSM) component that sets overall hydrogen production targets and a PEA-Scheduling component. Each electrolysis-PEA is represented by a dedicated software agent, a PEA-agent. This MAS structure allows for scalable expansion by adding PEAs and their agents. The PEA-Scheduling component uses the MAS to allocate the plant operating point (hydrogen demand) among the individual electrolysis-PEAs in a cost-optimal way, aggregating their availability to inform the DSM.

The cost optimization relies on minimizing the mLCOH for each electrolyzer. mLCOH accounts for Capital Expenditures (CapEx), Operational Expenditures (OpEx), Operation & Maintenance (O&M), efficiency, and critically, start-up costs to mitigate degradation from frequent cycling. The cost function for a PEA-agent is formulated as:

$f(x) = \text{O%%%%0%%%%M}_{t} + \frac{\text{CapEx}_{t} + \text{OpEx}_{t}(x) + C^{SU}\cdot Y_t}{\text{mH2}_{t}(x) + \delta}$

where $x$ represents the local decision variables (e.g., operating point), $C^{SU}$ are start-up costs, $Y_t$ is a binary variable for start-up, mH2$_t$ is the hydrogen production rate, and $\delta$ is a small value to prevent division by zero. OpEx are calculated based on the operating point, capacity, electricity cost, and scheduling interval, only when the electrolyzer is operational. CapEx and O&M are annualized based on initial investment, utilization time, load factor, and discount rate.

The optimization problem for the overall system is distributed among the PEA-agents and solved using ADMM. The primary constraint is meeting the total hydrogen demand $D_t$ in each period $t$. Each PEA-agent $n$ needs to ensure its production mH2$_{n,t}$ combined with the production of other agents $\sum_{j \neq n} \text{mH2}_{j,t}$ meets the demand:

$$g(z) = \sum \limits_{j \in \mathcal{N}\setminus n} \text{mH2}_{j,t} + \text{mH2}_{n,t}(z) - \text{D}_t$$

where $z$ represents the global decision variables, and $\mathcal{N}$ is the set of all PEA-agents. The hydrogen production rate mH2$_t$ is modeled as a quadratic function of the operating point Op$_t$, multiplied by a binary variable indicating operation state. Operating points must be within defined minimum and maximum limits (Op$_{min}$, Op$_{max}$). Electrolyzers can be in idle or production states, with transitions involving a holding time.

ADMM iteratively solves the problem. In each iteration $k$:

1. Each PEA-agent minimizes the augmented Lagrangian $\mathcal{L}_\rho$ locally with respect to its local variables $x$, considering its mLCOH function and the current global state and Lagrange multiplier.

   $$x^{k+1} = \argmin_x \; \mathcal{L}_\rho (x,z^k,y^k )$$

2. The PEA-agents collectively minimize $\mathcal{L}_\rho$ with respect to the global variables $z$ (effectively, ensuring the sum of local production meets the demand based on the updated $x$).

   $$z^{k+1} = \argmin_z \; \mathcal{L}_\rho(x^{k+1}, z, y^k )$$

3. The Lagrange multiplier $\lambda_t$ (represented by $y$) is updated based on the current discrepancy between the local ($x$) and global ($z$) states. This dual update incorporates the demand deviation and the gradient of the mLCOH function, allowing agents with smaller cost gradients to adjust their operating points more readily to meet demand.

   $y^{k+1} = y^k+p(Ax^{k+1}+Bz^{k+1}-c)$

These steps repeat until the changes in $x$, $z$, and $y$ are below a specified tolerance $\varepsilon$.

The implementation uses the Java Agent Development Framework (JADE). An activity diagram illustrates the PEA-agent workflow: receiving demand targets from DSM, initializing variables, iteratively performing ADMM steps (local optimization, communicating production, receiving production from others, checking demand, global optimization via $z$ update, dual update), checking convergence, storing results, and progressing through scheduling periods. Results from the previous period are used for initialization in the next to ensure smooth transitions.

A case paper validated the model using simulation models and financial parameters of three Anion Exchange Membrane (AEM) electrolyzers (Enapter EL 4). Practical considerations:

• Modeling Accuracy: The quadratic approximation of the production curve showed good alignment with simulation data ($\mathrm{R}^{2}$ of 0.9943), enabling accurate modeling of heterogeneous electrolyzers.
• Cost Calculation: The ADMM model accurately reproduced LCOH values compared to published data for nominal load, confirming mLCOH as a suitable metric for single-period optimization.
• Dynamic Scheduling: Under varying demand, the aggregated production from the optimized schedule closely matched simulation results (nRMSE of 3.3%), although the approximation led to higher deviations at lower loads (30-60%).
• Scalability (R2): The model was successfully scaled from 3 to 10 electrolyzers without requiring manual configuration changes. New PEA-agents were simply instantiated and joined the cooperative scheduling process, demonstrating the low-effort adaptability crucial for modular plants compliant with standards like MTP.
• Robustness to Malfunctions (R3): Simulating a module malfunction showed that the remaining operational agents could quickly recognize the failure (due to production quantity exchange) and redistribute the load to meet the demand. This rescheduling took approximately 4 iterations, translating to less than 40ms on the test hardware, demonstrating the model's inherent robustness without separate disturbance management routines.
• Monitoring and Control (R6): The implementation integrated monitoring and control functionalities by communicating optimized setpoints to the simulation via a standardized MTP interface, allowing real-time operational status tracking.
• Convergence: Analysis of the Lagrange multiplier $\lambda_t$ showed its role in driving convergence, with larger increases occurring during larger demand deviations, preventing oscillations and ensuring stability.

Compared to related work, the decentralized ADMM-MAS approach fills a gap by providing a method suitable for the distributed nature of modular electrolysis plants that explicitly considers costs, handles heterogeneous units, is scalable, and is inherently robust to resource failures, integrating monitoring and control capabilities often missing in optimization-focused studies.

Future work includes validating the model in real-world operation at the P2O-Lab and investigating the computational effort required for significantly larger and more heterogeneous electrolysis plants.