Extended Load Flexibility of Utility-Scale P2H Plants: Optimal Production Scheduling Considering Dynamic Thermal and HTO Impurity Effects (2301.12242v1)

Abstract: In the conversion toward a clear and sustainable energy system, the flexibility of power-to-hydrogen (P2H) production enables the admittance of volatile renewable energies on a utility scale and provides the connected electrical power system with ancillary services. To extend the load flexibility and thus improve the profitability of green hydrogen production, this paper presents an optimal production scheduling approach for utility-scale P2H plants composed of multiple alkaline electrolyzers. Unlike existing works, this work discards the conservative constant steady-state constraints and first leverages the dynamic thermal and hydrogen-to-oxygen (HTO) impurity crossover processes of electrolyzers. Doing this optimizes their effects on the loading range and energy conversion efficiency, therefore improving the load flexibility of P2H production. The proposed multiphysics-aware scheduling model is formulated as mixed-integer linear programming (MILP). It coordinates the electrolyzers' operation state transitions and load allocation subject to comprehensive thermodynamic and mass transfer constraints. A decomposition-based solution method, SDM-GS-ALM, is followingly adopted to address the scalability issue for scheduling large-scale P2H plants composed of tens of electrolyzers. With an experiment-verified dynamic electrolyzer model, case studies up to 22 electrolyzers show that the proposed method remarkably improves the hydrogen output and profit of P2H production powered by either solar or wind energy compared to the existing scheduling approach.

• The paper introduces a multiphysics-aware MILP model that incorporates dynamic thermal and HTO impurity effects in alkaline electrolyzers.
• It employs a decomposition-based SDM-GS-ALM algorithm to efficiently scale scheduling for utility-scale plants while addressing operational transitions.
• Case studies demonstrate up to 7.74% increased hydrogen production and 8.72% profit improvement, highlighting enhanced load flexibility and renewable integration.

This paper (2301.12242) addresses the challenge of optimally scheduling utility-scale Power-to-Hydrogen (P2H) plants composed of multiple alkaline electrolyzers to enhance their load flexibility and profitability when integrated with volatile renewable energy sources. Traditional scheduling methods often rely on simplified, steady-state models of electrolyzers, which impose fixed operating constraints like minimum load limits and constant efficiency. This conservative approach limits the potential to fully utilize renewable energy and provide grid services.

The core contribution of this work is the development and application of an optimal production scheduling approach that explicitly incorporates the dynamic thermal and hydrogen-to-oxygen (HTO) impurity crossover effects of alkaline electrolyzers. These dynamics significantly influence the electrolyzer's loading range, ramping capability, and energy conversion efficiency under varying operating conditions. By modeling these effects dynamically, the scheduling can exploit the fact that an electrolyzer might be able to operate below its steady-state minimum load or ramp faster for short periods without violating critical safety or operational limits.

The paper presents a comprehensive multiphysics-aware scheduling model formulated as a mixed-integer linear programming (MILP) problem. This model coordinates the operational state transitions (Production, Standby, Idle) and load allocation among multiple electrolyzers. The key components of the model include:

1. Electrolyzer State Transition Model: Based on binary variables representing the operational state (Production, Standby, Idle) and transitions (Startup), similar to unit commitment problems in power systems. Minimal gap constraints between shutdown and startup are included.
2. Hydrogen Production and Power Consumption Model: Relates electrical power consumption to hydrogen production flow. Unlike linear models used in many previous works, this model uses a nonlinear, concave production function approximated by a polyhedron, capturing the dependency on temperature and voltage. Ramping limits on hydrogen production are also considered.
3. Temperature Dynamic Model: A first-order model capturing how the electrolyzer's temperature changes based on electrolytic heat generation, natural dissipation, active cooling, and auxiliary heating. This model includes constraints related to maximum operating temperature and temperature-dependent cell voltage limits, which impact the feasible load range and ramping capability.
4. HTO Impurity Dynamic Model: Models the accumulation and discharge of hydrogen impurities in the oxygen product stream. This is crucial because HTO impurity concentration increasing above a safety limit (e.g., 2%) requires shutdown. The model captures that impurity accumulation is faster at low loads but takes time, allowing for temporary operation below the steady-state minimum load.

The resulting MILP problem, which includes nonlinear terms that are linearized using standard big-M methods, becomes large and computationally intensive, especially for plants with many electrolyzers. To address this scalability issue for utility-scale plants (tens of electrolyzers), the paper adopts a decomposition-based solution method called SDM-GS-ALM (Simplicial Decomposition Method with Block Gauss-Seidel and Augmented Lagrangian Method) [36]. This algorithm leverages the separable structure of the problem, where the constraints for each electrolyzer are largely independent, coupled only by the total power consumption constraint. The method decomposes the large problem into smaller subproblems for each electrolyzer and a coupling problem, solved iteratively. This significantly reduces computation time compared to solving the full MILP directly.

The dynamic temperature and HTO impurity models used in the scheduling are experimentally validated on a small-scale alkaline electrolyzer, showing a decent fit between simulation and experimental data, confirming their ability to capture the relevant dynamics.

Case studies are presented for plants with 4 and 22 electrolyzers, using real-world solar and wind power profiles. The results demonstrate that the proposed multiphysics-aware scheduling method effectively utilizes the dynamic flexibility of the electrolyzers. Specifically:

• Temperature dynamics are exploited to allow gradual load increase during startup as the electrolyzer heats up.
• HTO impurity dynamics are considered to permit temporary operation below the steady-state minimum load, utilizing more low-power renewable energy than traditional methods.
• Compared to traditional scheduling (without dynamic multiphysics), the proposed method shows significant improvements:
  • For a 4-electrolyzer plant under a PV profile, hydrogen output increased by 0.825%, and profit increased by 1.83%.
  • Under various wind and PV scenarios, the average profit improvement was 1.438% for wind and 0.982% for PV.
  • For a large-scale plant with 22 electrolyzers, hydrogen production increased by 7.74%, and profit by 8.72% compared to the traditional method.

The scalability analysis confirms that the proposed decomposition-based solution method scales approximately linearly with the number of electrolyzers, making it feasible for scheduling plants with dozens of units, whereas direct MILP solving becomes computationally intractable.

Practical Implementation:

Implementing this research involves:

1. Detailed Electrolyzer Modeling: Obtaining or estimating the parameters for the dynamic temperature and HTO impurity models (heat capacity, thermal resistances, impurity flow rates, discharge constants, voltage curve coefficients) for the specific alkaline electrolyzers used in the plant. This may require experimental data collection.
2. MILP Formulation: Translating the dynamic models and state transitions into a set of linear equations and inequalities, potentially using big-M formulation for products of binary and continuous variables or for piecewise linear functions.
3. Decomposition Implementation: Implementing the SDM-GS-ALM algorithm. This requires setting up the structure to solve the electrolyzer subproblems (RSP, CHUP) and the coupling problem (CP) iteratively. The CHUP involves solving a possibly non-convex problem for each electrolyzer to find a new vertex for the feasible region approximation.
4. Integration with Forecasts: The method relies on forecasts of renewable energy availability. For real-world operation, this would be implemented in a receding horizon control framework, where the optimization is run periodically based on updated forecasts and plant status.
5. Computational Infrastructure: Requires optimization solvers capable of handling MILPs (like Gurobi, CPLEX) for the subproblems and an orchestration layer to manage the decomposition algorithm, potentially running subproblems in parallel. The scalability allows for solving larger problems on standard computing infrastructure.

Limitations and Future Work:

The paper acknowledges the reliance on accurate renewable energy forecasts. Future work should incorporate handling uncertainty, potentially through stochastic optimization or robust control methods. Integrating the P2H plant scheduling within a broader Power-to-X framework, considering dynamic constraints of coupled chemical processes like ammonia or methanol synthesis, is also identified as a direction for future research.