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Long-Term Energy Management for Microgrid with Hybrid Hydrogen-Battery Energy Storage: A Prediction-Free Coordinated Optimization Framework

Ning Qi, Kaidi Huang, Zhiyuan Fan, Bolun Xu

arXiv:2407.21698v1math.OCcs.SYeess.SY

TL;DR

Long-term microgrid management with hybrid hydrogen-battery storage must contend with seasonal uncertainties and OCO's limited long-term view. The paper proposes a prediction-free coordinated framework with an adaptive OCO algorithm. It outperforms existing online optimization methods and achieves an acceptable gap relative to deterministic optimization with perfect foresight.

  • Problem

    OCO lacks a global view of long-term operations and adaptability to microgrid volatility, while existing algorithms may lack dynamic-regret guarantees or require prediction information.

    Source: §1.3 · p. 3, §1.2 · p. 3

  • Method

    The framework pairs an approximate semi-empirical hydrogen-storage model with two-stage coordination and adaptive virtual-queue OCO that tracks long-term patterns and experts for step-size updates.

    Source: §6 · p. 13

  • Results

    The proposed framework outperforms existing online optimization methods and achieves an acceptable gap compared to deterministic optimization with perfect foresight of uncertainties.

    Source: §6 · p. 13

  • Takeaways & Limitations

    Hydrogen-storage SoC references are critical to overall performance, making more reliable historical or AI-generated scenarios and sophisticated penalty-coefficient settings important.

    Source: §6 · p. 13

    The OCO algorithm's constraint violations remain a subject for future work, and the framework has yet to be extended to market-environment operations.

    Source: §6 · p. 13

Abstract

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This paper studies the long-term energy management of a microgrid coordinating hybrid hydrogen-battery energy storage. We develop an approximate semi-empirical hydrogen storage model to accurately capture the power-dependent efficiency of hydrogen storage. We introduce a prediction-free two-stage coordinated optimization framework, which generates the annual state-of-charge (SoC) reference for hydrogen storage offline. During online operation, it updates the SoC reference online using kernel regression and makes operation decisions based on the proposed adaptive virtual-queue-based online convex optimization (OCO) algorithm. We innovatively incorporate penalty terms for long-term pattern tracking and expert-tracking for step size updates. We provide theoretical proof to show that the proposed OCO algorithm achieves a sublinear bound of dynamic regret without using prediction information. Numerical studies based on the Elia and North China datasets show that the proposed framework significantly outperforms the existing online optimization approaches by reducing the operational costs and loss of load by around 30% and 80%, respectively. These benefits can be further enhanced with optimized settings for the penalty coefficient and step size of OCO, as well as more historical references.

1. Introduction

Long-term microgrid management must coordinate hydrogen and battery storage amid seasonal variation and uncertain renewable generation and load. The paper addresses gaps in hydrogen-storage modeling and prediction-free online optimization with a coordinated framework evaluated on Elia and North China data.

1.1. Background and motivation

  • Seasonal renewable variation and uncertain load motivate long-term coordination of batteries for short-term balancing and hydrogen storage for seasonal energy shifting.Microgrids can operate in grid-connected or island mode.Source: §1.1 · p. 2

1.2. Literature review

  • Prior work centers on short-term H-BES management, while long-term approaches face computational limits or retain forecasting dependence, and OCO lacks a long-term H-BES framework with dynamic-regret guarantees without predictions.The literature review also describes OCO's myopic behavior and the limitations of existing dynamic-regret bounds.Source: §1.2 · pp. 2–3

1.3. Research gap

  • The research gaps are nonlinear power-dependent hydrogen efficiency, reliance on unavailable or inaccurate prediction information, and OCO's limited long-term view and adaptability to volatile microgrids.Simplifying hydrogen efficiency can produce suboptimal or infeasible solutions.Source: §1.3 · p. 3

1.4. Contributions

  • The proposed semi-empirical model captures power-dependent hydrogen-storage efficiency and avoids overly optimistic or overly conservative strategies.Compared with the constant-efficiency model, it reduces practical yearly operational cost by 10% or 36% and yearly loss of load by 1.94 MWh or 3.85 MWh.Source: §1.4 · pp. 3–4
  • The framework combines offline hydrogen SoC-reference generation from historical and AI-generated data with kernel-regression updates and adaptive virtual-queue OCO for prediction-free decisions.Its OCO algorithm adds long-term pattern tracking and expert-tracking for step-size updates, and is proven to achieve a sublinear dynamic-regret bound.Source: §1.4 · p. 4
  • Across Elia and North China, references reduced operational costs 40%-57% and loss of load 60%-90%; versus prediction-dependent MPC, prediction-free OCO further reduced them 24%-29% and 73%-89%, respectively.The framework's benefits can be further enhanced through optimized OCO penalty and step-size settings and more historical references.Source: §1.4 · p. 4

2. Approximate

The paper models a hydrogen storage system using alkaline electrolysis, hydrogen storage, and PEMFC conversion, while excluding auxiliary equipment. Its equivalent storage model represents power-dependent charging and discharging behavior with tractable piecewise-linear functions.

2.1. Structure of hydrogen storage system

  • The modeled hydrogen storage system includes an alkaline electrolyzer, hydrogen tanks, and a PEMFC, while excluding compressors, cooling, and control systems.The electrolyzer converts electricity to hydrogen and oxygen; the PEMFC converts stored hydrogen back to electricity.Source: §2.1 · p. 4

2.2. Alkaline water electrolyzer model

  • Alkaline electrolyzer efficiency is nonlinear and power-dependent, peaking at around 20% of rated power.The model uses a piecewise-linear approximation for hydrogen production to facilitate dispatch optimization.Source: §2.2 · p. 5

2.3. PEMFC model

  • PEMFC hydrogen consumption and efficiency are nonlinear and power-dependent, with piecewise-linear hydrogen-consumption approximations.The illustrated PEMFC properties are modeled at 60°C and 10 bar.Source: §2.3 · p. 6, Figure 3 · p. 6

2.4. Equivalent hydrogen storage model

  • The equivalent hydrogen storage model links SoC to charge and discharge power, constrains SoC and power, and enforces a sustainable energy state over cycles.Piecewise-linear charging and discharging functions make the model tractable.Source: §2.4 · p. 6

3. Long-termenergymanagementofmicrogrid

The formulation considers an island-mode microgrid with renewable generation, diesel generators, hybrid hydrogen-battery storage, and local loads. Its dispatch objective minimizes system cost subject to generator, storage, load, renewable, and power-balance constraints.

3.1. Microgrid structure

  • The island-mode microgrid comprises wind and solar generators, diesel generators, H-BES, and local loads.The microgrid structure is illustrated in Figure 4.Source: §3.1 · p. 6, Figure 4 · p. 6

3.2. Problem formulation

  • The dispatch objective minimizes system cost, including diesel production costs, load-curtailment penalties, and H-BES operational costs.The formulation includes generator power and ramping bounds, storage and load constraints, renewable dispatch limits, and power balance; it relaxes complementary charge/discharge constraints and overlooks network power-flow constraints.Source: §3.2 · p. 6

4. Prediction-free

The framework addresses long-horizon microgrid dispatch without forecasts by pairing offline hydrogen SoC references with online reference tracking and adaptive OCO. Its theoretical analysis gives a dynamic-regret bound under stated assumptions and parameter settings.

4.1. Motivations

  • Long-term dispatch lacks reliable forecasts beyond several hours, while battery-first short-term dispatch can leave insufficient pre-stored hydrogen and cause load losses across seasonal changes.Piecewise linearization also introduces nonconvexity; a global hydrogen reference is proposed to help pre-determine efficiency.Source: §4.1 · p. 7

4.2. Two-stage

  • The two-stage framework generates hydrogen SoC references offline from historical RES and load data, then updates them by kernel regression as observations arrive before making online decisions.The references are intended to help avoid myopic decisions.Source: §4.2 · p. 7, Figure 5 · p. 8

4.3. Offline-stage optimization

  • Historical and seasonal scenarios, optionally augmented with GAN-generated extreme scenarios, feed a deterministic MILP that generates hydrogen-storage SoC references.For five years of historical data in a seasonal dispatch example, the text sets T to one season and N to 5×4.Source: §4.3 · p. 7

4.4. Online-stage optimization

  • Online reference tracking compares observed uncertainty histories with historical scenario sequences using Gaussian-kernel weights, updating the hydrogen SoC reference and selecting its efficiency segment.The real-time corrective dispatch minimizes instantaneous operational cost while penalizing deviation from the hydrogen SoC reference.Source: §4.4 · pp. 7–8
  • VQB-OCO uses virtual queues in place of unknown dual variables and past information to approximate current conditions, updating queues, decisions, and expert weights.Expert-tracking computes decisions in parallel across learning rates; the virtual queues rise when long-term constraints reach their bounds.Source: §4.4 · pp. 8–9

Stage1: Offline Optimization

  • The proposed OCO algorithm achieves O(T(1+P_x)) when κ=c=0.5, aligning with, which omits long-term constraints; achieves O(T^max{1−a−c,c}) dynamic regret using prediction data.Source: Stage1: Offline Optimization · p. 9

5. Case studies

The case studies evaluate the framework on Elia and North China data, from seasonal reference generation to online dispatch and sensitivity analysis. Results highlight the value of power-dependent hydrogen efficiency, reference tracking, and adaptive OCO decisions.

5.1. Set-up

  • The test microgrid used 200 kW of renewables split equally between solar and wind; battery and hydrogen storage capacities were each half the load capacity, with durations of 2 and 400 hours, respectively.The case studies used 15-minute Elia data from 2014–2023 and hourly North China wind and load data from 1981–2020.Source: §5.1 · p. 9, Table 2 · p. 10

5.2. Offline-stage optimization

  • Elia’s monthly average wind, solar, and load show seasonal patterns: wind is abundant in spring and winter, solar peaks in summer, and load peaks in winter.Net load peaks in winter and is lowest in summer, indicating a role for hydrogen storage in seasonal balancing.Source: §5.2 · p. 10, Figure 6 · p. 10
  • Constant-efficiency models raised total system cost by 10% or 36% versus E1, while the highest-efficiency model added 1.94 MWh of loss-of-load cost.The highest constant-efficiency case had the lowest operational cost ($97,188), while the lowest-efficiency case had the highest ($132,933); constant efficiency could also cause infeasible operation.Source: §5.2 · p. 10, Figure 7 · p. 10

5.3. Online-stage optimization

  • The proposed kernel-regression references R2–R6 tracked seasonal RES and load patterns better than the averaged R7 reference, with lower RMSE in Elia.Additional generated scenarios could improve tracking, but excessive generated data in R6 led to overfitting and reduced accuracy.Source: §5.3 · p. 11, Table 4 · p. 11, Figure 8 · p. 11
  • In Elia, M1 outperformed the other online strategies on cost-effectiveness, with lower loss of load and reference RMSE than the alternatives and a reported 27% optimality gap versus M0.M1 and M2 also performed better economically than M3 and M4, which made myopic hydrogen-discharge decisions.Source: §5.3 · p. 11, Table 5
  • North China tests show that reference-based optimization outperformed methods without references and OCO-based methods outperformed MPC-based methods, though cost and reliability were worse than in Elia.North China’s wind-only renewable supply resulted in insufficient generation and greater load curtailment.Source: §5.3 · p. 12

5.4. Sensitivity analysis

  • Increasing the reference-tracking penalty reduced RMSE monotonically, but operational cost reached a minimum at φ = 90000 before rising.The result shows that better tracking did not always coincide with lower cost.Source: §5.4 · p. 12, Figure 11 · p. 12
  • Updated references reduced operational cost by 1.09%–1.70% and loss of load by 5.68%–8.52% versus fixed references; expert-tracking step sizes reduced these metrics by 0.67%–1.29% and 0.06%–3.16%, respectively.M1 reached an acceptable reliability level with twice the renewable capacity, while M2 needed at least four times the capacity.Source: §5.4 · p. 13, Table 6 · p. 13, Figure 12 · p. 13

6. Conclusion

The paper presents a prediction-free framework for long-term microgrid energy management with hybrid hydrogen-battery storage, using a power-dependent hydrogen model and coordinated offline references and online decisions. Case studies support its performance against constant-efficiency models and existing online methods, while identifying reference quality and OCO constraint violations as concerns.

6. Conclusion

  • The proposed approximate semi-empirical hydrogen-storage model uses piecewise-linear relaxation to represent power-dependent efficiency and, compared with the constant-efficiency model, avoids both overly optimistic and overly conservative strategies.Source: §6 · p. 13
  • The framework outperforms existing online optimization methods and maintains an acceptable gap to deterministic optimization with perfect foresight.Its offline hydrogen SoC references use historical and AI-generated scenarios with kernel regression, while online decisions use feedback and newly observed data.Source: §6 · p. 13
  • Hydrogen SoC references are critical to overall performance, making reliable historical or AI-generated scenarios and careful penalty-coefficient settings important.Source: §6 · p. 13
  • The OCO algorithm’s limited global view and sensitivity to step size motivate long-term pattern-tracking penalties and expert-tracking step-size updates.Source: §6 · p. 13
  • Further work will address constraint violations in OCO and extend the framework to market-environment operations.Source: §6 · p. 13

A. Proof of storage priority

The proof compares battery-only discharge with mixed battery-hydrogen discharge and concludes that hydrogen storage is used only after the battery is fully discharged or charged.

A. Proof of storage priority

B. Proof of bounded dynamic regret

The supplied proof steps use convexity, relaxation, and cited lemmas before combining intermediate inequalities to complete the argument.

B. Proof of bounded dynamic regret

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