Exploring the Optimal Size of Grid-forming Energy Storage in an Off-grid Renewable P2H System under Multi-timescale Energy Management

Abstract: Utility-scale off-grid renewable power-to-hydrogen systems (OReP2HSs) typically include photovoltaic plants, wind turbines, electrolyzers (ELs), and energy storage systems. As an island system, OReP2HS requires at least one component, generally the battery energy storage system (BESS), that operates for grid-forming control to provide frequency and voltage references and regulate them through transient power support and short-term energy balance regulation. While larger BESS capacity increases this ability, it also raises investment costs. This paper proposes a framework of layered multi-timescale energy management system (EMS) and evaluates the most cost-effective size of the grid-forming BESS in the OReP2HS. The proposed EMS covers the timescales ranging from those for power system transient behaviors to intra-day scheduling, coordinating renewable power, BESS, and ELs. Then, an iterative search procedure based on high-fidelity simulation is employed to determine the size of the BESS with minimal levelized cost of hydrogen (LCOH). Simulations over a reference year, based on the data from a planned OReP2HS project in Inner Mongolia, China, show that with the proposed EMS, the base-case optimal LCOH is 33.212 CNY/kg (4.581 USD/kg). The capital expenditure of the BESS accounts for 17.83% of the total, and the optimal BESS size accounts for 13.6% of the rated hourly energy output of power sources. Sensitivity analysis reveals that by reducing the electrolytic load adjustment time step from 90 to 5 s and increasing its ramping limit from 1% to 10% rated power per second, the BESS size decreases by 53.57%, and the LCOH decreases to 25.458 CNY/kg (3.511 USD/kg). Considering the cost of designing and manufacturing utility-scale ELs with fast load regulation capability, a load adjustment time step of 5-10 s and a ramping limit of 4-6% rated power per second are recommended.

• The paper presents a hierarchical EMS that coordinates RS, LF, EH, and GFM layers to ensure frequency and voltage stability in off-grid systems.
• It employs high-fidelity electromagnetic transient and long-term energy simulations to determine an optimal BESS size of 6.8 MW/3.4 MWh and reduce LCOH.
• The study reveals that incorporating rapid EL load control and transient stability constraints prevents a 15-30% underestimation of required BESS capacity.

This paper (2409.05086) explores the optimal size of a grid-forming Battery Energy Storage System (BESS) in an off-grid Renewable Power-to-Hydrogen System (OReP2HS) under a proposed multi-timescale energy management system (EMS). The core challenge addressed is balancing the technical requirements for frequency and voltage stability in an islanded system with the economic imperative of minimizing the Levelized Cost of Hydrogen (LCOH).

Traditional approaches to sizing components in OReP2HS often rely on EMS with time resolutions of 5 minutes or more, neglecting the faster dynamics necessary for grid stability in off-grid operation. This oversight can lead to underestimating the required BESS capacity. The authors argue that grid-forming control, typically handled by the BESS, and fast load regulation capabilities of electrolyzers (ELs) are crucial for handling transient power imbalances that occur on millisecond to second timescales.

The paper proposes a hierarchical multi-timescale EMS designed to coordinate photovoltaic (PV) plants, wind turbines (WTs), BESS, and ELs across timescales ranging from power system transients (milliseconds) to intra-day scheduling (hours). The EMS consists of four main layers:

1. Rolling Scheduling (RS): Operating on a timescale of 5 minutes to 4 hours, this layer uses Mixed-Integer Linear Programming (MILP) to determine the optimal operational states (start-up, shut-down, standby) and baseline power consumption for each EL over a future horizon, based on renewable energy forecasts. The objective is to maximize hydrogen production revenue while considering EL state transition costs and penalties for renewable curtailment. Constraints include EL operating limits, BESS state of charge (SOC) limits, and overall power balance.
2. Load Following (LF): This module operates on a faster timescale (typically 5 seconds) and adjusts the load of individual ELs in real-time to track fluctuations in renewable power. This is analogous to Automatic Generation Control (AGC) in grid-connected systems. It uses fast forecasting of renewable power (via a moving average process) and a PI controller with SOC correction to generate real-time load adjustment commands for the ELs, reducing the burden on the BESS for second-level power balancing.
3. Emergency Handling (EH): Responding to critical events like WT, PV, or EL tripping (N-1 faults) within approximately 100 milliseconds, this strategy monitors system frequency and its rate of change (RoCoF). Based on predefined criteria (lookup table correlating frequency/RoCoF deviations to required power shedding/generation), it dispatches commands to renewable sources or ELs to quickly rebalance power, thereby reducing the transient energy support required from the grid-forming BESS.
4. Grid-forming Control (GFM): Integrated into the BESS controller, this operates at the fastest timescale (0.04 milliseconds). Using Voltage/Frequency (V/F) droop control, the BESS provides the fundamental frequency and voltage references for the entire OReP2HS, offering instantaneous transient power support to maintain stability.

To evaluate the optimal BESS size under this EMS, the authors develop comprehensive simulation models: a refined electromagnetic transient model capturing detailed switching dynamics of converters and transient behaviors for millisecond-scale analysis (GFM and EH tests), and a simplified switching-function model for efficient long-term (8760 hours) energy balance simulations.

The optimal BESS size is determined using a high-fidelity simulation-based iterative search procedure. The objective is to minimize LCOH, calculated by annualizing capital costs (including BESS replacement based on degradation), fixed and variable O&M costs, and dividing by the annual hydrogen yield. The search iteratively adjusts BESS capacity and charging/discharging rate, testing against three key constraints using the appropriate simulation models:

• Maintaining frequency and voltage within predefined limits (indicating successful grid-forming ability and transient stability).
• Ensuring continuous operation and stability during simulated N-1 fault scenarios (emergency handling effectiveness).
• Maintaining long-term energy balance with BESS SOC within operational limits over a full year.

The case study is based on a planned OReP2HS project in Inner Mongolia, China, featuring three 6.25 MW WTs, one 6.25 MWp PV plant, and four 5 MW alkaline ELs. Using local meteorological data, the iterative search determined the base-case optimal grid-forming BESS size to be 6.8 MW / 3.4 MWh. This battery capacity is equivalent to 13.6% of the rated hourly energy output of the renewable sources. The capital expenditure of the BESS accounts for 17.83% of the total project capital expenditure. The base-case optimal LCOH was evaluated at 33.212 CNY/kg (approximately 4.581 USD/kg). The annual battery degradation rate was estimated at 4.87%.

Simulation results demonstrated the EMS effectiveness: the LF strategy successfully made ELs track renewable power fluctuations, reducing BESS regulation needs. The BESS handled remaining fast fluctuations to maintain frequency and voltage stability, with its SOC managed within limits by the SOC correction and RS layers. The EH strategy was shown to enable faster frequency recovery and reduce BESS SOC depletion during simulated WT tripping events compared to operation without EH.

The study found a significant positive correlation between BESS SOC and renewable power output, suggesting potential for predictive control strategies to optimize BESS management and mitigate degradation based on renewable forecasts.

Comparing their method (considering stability constraints) with typical literature approaches (5-minute resolution, neglecting transient stability), the authors showed that neglecting transient stability constraints leads to a significant underestimation (15-30%) of the required BESS capacity. Furthermore, the proposed multi-timescale EMS resulted in a smaller optimal BESS size and lower LCOH compared to implementing rule-based or MILP-only EMS (from literature) while still satisfying the stability constraints, highlighting the value of coordinating control across multiple timescales.

Sensitivity analysis on the impact of EL load flexibility parameters ($\Delta t_\mathrm{LF}$ and ramping limit) showed that both parameters significantly affect the optimal BESS size and LCOH. Decreasing $\Delta t_\mathrm{LF}$ or increasing the EL ramping limit reduces the required BESS size and LCOH because ELs can take on more of the balancing burden. Reducing $\Delta t_\mathrm{LF}$ was found to have a more significant impact than increasing the ramping limit. The minimal LCOH (25.458 CNY/kg) was achieved with a 5-s LF time step and a 0.5 MW/s ramping limit (10% of rated power). However, considering technological feasibility and cost for utility-scale ELs, the authors recommend a ramp limit of 4-6% of rated power per second and a LF time step of 5-10 seconds as a practical balance, achieving competitive LCOH values (ranging from 25.458 to 26.246 CNY/kg).

In conclusion, the paper demonstrates that a multi-timescale EMS and high-fidelity simulation are essential for accurately sizing the grid-forming BESS in OReP2HS, ensuring stability and minimizing LCOH. The flexibility of ELs, particularly their ramping capability and the frequency of their adjustments, plays a critical role in reducing BESS requirements. Future work includes refining the EMS with probabilistic forecasts, developing more efficient optimization methods for multi-component sizing, and expanding the EMS to integrate downstream hydrogen infrastructure and consumers.