Optimal hydrogen-battery energy storage system operation in microgrid with zero-carbon emission

0 Introduction

The increasing integration of renewable energy sources (RESs) into microgrids plays a crucial role in addressing the prevailing issues of energy scarcity and environmental degradation [1].Nonetheless,this integration introduces a myriad of technical complexities in the energy management of microgrids,primarily because of the stochastic and intermittent characteristics of RESs [2].Energy utilization efficiency is a critical aspect that requires close scrutiny in this context.

To address rapid power fluctuations within microgrids,the integration of various flexible energy resources,including energy storage systems and adaptable loads,has been proposed [3].Many previous studies pay significant attention to the operational strategies of microgrids.A twostage robust optimization approach is introduced in [4] to address the economic dispatch problem in microgrids and derive practical optimal schedules for diesel engines and energy storage systems.A multi-interval economic dispatch strategy is presented in [5] for distributed energy resources,including fuel generators,to enhance the capability of a microgrid to efficiently harness renewable power.An optimal energy management strategy for a standalone microgrid incorporating diesel generators,resulting in a～ 68% reduction in greenhouse gas emissions,is discussed in [6].However,the strategies mentioned above involve the use of fossil-fuel-powered generators,which contributes to increased greenhouse gas emissions.To realize a zerocarbon-emission microgrid,the adoption of emissionfree flexibility solutions,such as hydrogen energy storage systems,become imperative.

Hydrogen energy storage (HES) systems serve as a viable emission-free flexibility option for microgrids [7].A robust operational strategy for a hybrid hydrogen-battery energy storage system is proposed in [8] to minimize the operational costs in microgrids.The decentralized energy management strategy applied to the Photovoltaic (PV)/hydrogen/battery system in [9] enhances the voltage stability of the microgrid across various operational modes.In [10],hydrogen storage,battery storage,and responsive demand are leveraged as flexible resources to mitigate the uncertainties associated with renewable energy sources (RESs).The dispatch decisions for hydrogen and battery storage are governed by a model predictive control algorithm in [11],which maximizes the output from the distributed power supplies.A robust optimization approach is employed in [12] for scheduling microgrid operations,incorporating heat power and hydrogen storage.However,in these studies,the operational constraints of fuel cells (FC) and electrolysis devices (ED) often overlook the minimum start-up and shutdown durations,on the assumption that they are capable of rapid activation and deactivation.This assumption deviates from practical scenarios in which frequent start-ups and shutdowns of FCs and EDs are avoided to ensure efficient and sustainable operation.Although the aforementioned studies optimize HES systems as integral storage units,they do not adequately address the charge/discharge limits of the hydrogen storage tank in coordination with the dispatch characteristics of FCs and EDs.The dispatch capability of hydrogen storage is constrained by the limitations of chemical reactions,which hinders its ability to respond swiftly to power imbalances and track uncertainties on a short timescale [13].By contrast,battery storage exhibits a robust capability for rapid response and is often utilized in real-time operations.

Battery energy storage (BES) systems are renowned for their rapid response capabilities,which play pivotal roles in absorbing excess power from renewable energy sources (RESs) and supplying electricity during peak demand periods,thereby significantly enhancing microgrid energy management efficiency.In [14],a convex model predictive control strategy is proposed to accelerate the computation of dynamic optimal power flows while simultaneously improving the charging and discharging efficiencies.A probabilistic constraint is introduced in [15] to represent the uncertainties in energy storage spinning reserve capacities and strike a balance between reliability and economic efficiency in microgrid operations.A novel decisionmaking strategy that accounts for uncertainties in renewable energy and load demands is proposed in [16] to reduce the operational costs of microgrids.However,upper and lower state-of-charge (SoC) bounds are presumed to remain constant within each time interval.While such SoC dispatch decisions based on short-term predictions may be suitable for immediate timeframes,they may not be efficient over an entire day given the capacity constraints of the BES.This can potentially lead to suboptimal SoC scheduling in subsequent time slots,resulting in increased operational costs and potential constraints [17].Therefore,optimizing the SoC bounds from a daily perspective is imperative to ensure a more pragmatic SoC scheduling based on uncertainties.

Furthermore,the unpredictability and fluctuations in the outputs of renewable energy sources (RESs) and loads present significant challenges for energy management.Numerous studies adopt stochastic optimization (SO) [18] and robust optimization (RO) [19] to address these issues.SO methods involve generating a vast array of scenarios to represent the potential realization of uncertainty based on the precise probability distribution of RESs and load outputs,necessitating the resolution of the problem for each scenario.However,obtaining an accurate probability distribution is seldom feasible in practical settings,and this approach is computationally intensive [20].However,RO methods seek to optimize the objectives under the worstcase scenario within a defined uncertainty interval [21],facilitating rapid and robust optimization.

This study introduces an adaptive RO framework tailored for the operation of a microgrid incorporating a hybrid hydrogen battery storage system,with a focus on addressing uncertainties.Instead of utilizing fossil fuel-powered generators,which are notorious for their greenhouse gas emissions,this study integrates a hydrogen storage tank,ED,and FC to establish an emission-free microgrid.Previous methodologies pertaining to battery storage dispatch,which employ a single-stage management approach without imposing SoC interval constraints,fall short in terms of efficiency owing to the large charge and discharge powers.In contrast,this study proposes a twostage management strategy for a hybrid hydrogen battery storage system to enhance SoC dispatch while mitigating uncertainties,ultimately reducing microgrid operational costs and achieving emission-free operation.Furthermore,a two-stage adaptive RO model is formulated to encapsulate the management of a hybrid hydrogen battery storage system-integrated microgrid.To solve this two-stage optimization problem,which includes integer recourse variables in the second stage,a novel outer-inner columnand-constraint generation algorithm (outer-inner-CCG) is introduced.The key contributions of this study are summarized as follows.

(1) This study introduces a management framework for a microgrid that integrates hybrid hydrogen battery storage to realize operation with zero-carbon-emissions.

(2) A two-stage operational model is proposed for a hybrid hydrogen battery storage system that integrates SoC management for BESs.This strategy aims to optimize the daily operational costs of a microgrid by establishing interval constraints in the day-ahead stage.

(3) To address the uncertainties inherent in microgrid operations,the framework is formulated as an adaptive RO model that includes integer recourse variables.Subsequently,an outer-inner-CCG algorithm is employed to solve this optimization problem.

The remainder of this paper is organized as follows.A hybrid hydrogen battery storage system integrated microgrid operational model is presented in Section 1.An adaptive RO model is introduced in Section 2,and the procedure of the corresponding outer-inner-CCG algorithm is presented in Section 3.Numerical case studies are presented in Section 4.Finally,Section 5 presents the conclusions.

1 Hydrogen-battery energy storage system integrated microgrid

1.1 Structure of a hydrogen-battery energy storage system integrated microgrid

The microgrid under consideration (Fig.1) comprises a hybrid hydrogen battery energy storage system (HBESS) and various RESs.An HBESS comprises both energyconversion and energy-storage components.The storage components include a hydrogen storage tank (HST) and BES system,whereas the conversion components consist of an FC and an ED [22].The RESs integrated into the microgrid are PV and wind turbines (WTs),both of these sources and electricity demand exhibit uncertainties.This necessitates a more efficient operational strategy for optimizing the functioning of microgrids.For achieving zero-carbon emissions,our microgrid framework design manages the HBESS to fulfill the power needs of the load demands.This approach facilitates decarbonization by eliminating the need for diesel-powered engines and generators.Consequently,the framework not only reduces reliance on fossil fuels,but also significantly contributes to the reduction of greenhouse gas emissions,aligning with the global sustainability goals.

Fig.1 Structure of a HBESS integrated microgrid

1.2 Two-stage operational strategy

This study introduces a two-stage operational strategy for storage systems to minimize the operational costs of the microgrid while achieving a zero-carbon emission footprint.In the day-ahead phase,the ED utilizes power to charge the hydrogen storage system during periods of low electricity prices.When the electricity prices peak,the FC is deployed to generate electricity and deplete the hydrogen storage system.In the subsequent intraday phase,the battery storage system is actively managed,and it undergoes charging and discharging cycles to maintain the power balance in response to the realized uncertainties.The SoC scheduling for battery storage during this intraday phase adheres to the interval set in the day-ahead stage,ensuring cost-effectiveness from a daily operational standpoint.The optimization processes for both the dayahead and intraday stages are synchronized with the solutions derived under the worst-case scenario of power injection from RESs.

1.3 Operation models of devices 1.3.1 ED

An ED uses electrical energy to generate hydrogen,and this is governed by the following equation.

where is the hydrogen produced by the ED,and is the power consumed by the ED.

1.3.2 FC

The fuel cell converts hydrogen into electricity,a process that can be described by the following formulation.

where is the hydrogen consumed by the FC and is the power produced by the FC.

1.3.3 HST

The operational scheduling of HST is formulated as follows.

Constraint (3) delineates the capacity limitations of hydrogen storage.Constraint (4) defines the lower and upper bounds of the SoC for the HST.Equations (5) and (6) specify the minimum and maximum power consumption and production capacity of the ED and FC,respectively.Equation (7) ensures mutual exclusivity in the operations of the FC and ED,preventing their simultaneous operation.

1.3.4 BES SoC scheduling

The operational scheduling of BES is formulated as follows.

Constraint (8) provides a formulation for updating the capacity of a BES.Constraints (9) and (10) define the SoC interval demarcated by the upper and lower limits,respectively,which are confined by the minimum and maximum SoC thresholds,respectively.Constraint (11) states that the disparity between these upper and lower bounds is subject to the limitations imposed by interval width coefficients.Constraint (12) defines the minimum and maximum SoC parameters for the BES.Equations (13) and (14) specify the minimum and maximum capacities of the charging and discharging power of the BES,respectively.Equation (15) ensures that the BES cannot be in both charging and discharging states concurrently.

2 Formulation for an adaptive RO model

2.1 Day-ahead operation model

The objective function encompasses the cost of electricity procured from the main grid and operational expenses associated with the FC,ED,PV,WT,and BES,and all these are encapsulated in the following formulations.

Here,γ ∈{,}FC ED .When γ is the FC,(24)–(29) are the FC constraints.When γ is the ED,(24)–(29) are the ED constraints.Lon and Loff are the initial startup and shutdown times,respectively.Equations (24) and (25) formulate the relationship between the startup/shutdown operation and on/off states of γ at time t.In practical scenarios,both the FC and ED are subject to constraints regarding the startup and shutdown durations.These constraints are essential for mitigating frequent activation and deactivation and thereby enhancing the operational efficiency and extending the service life of these devices.Hence,(26) represents the minimum start-time constraint,and (27) shows the minimum shutdown-time constraint.Equation (28) denotes the power-balance constraint,and (29) limits the microgrid tie-line power.

2.2 Intraday operation model

The objective and constraints in the intraday stage are as follows.

2.3 Uncertainty modeling of PV and WT

Deviations (prediction errors) from the expected values and actual observed values of the PV,WT,and load demands are inevitable owing to various factors such as forecasting models and sudden changes in weather conditions.To address this,uncertainty sets are formulated to encompass both the variability of nominal values and range of potential prediction errors of the outputs from the PV,WT,and load demands,as detailed in the following formulation.

Here, are the output power realizations of the PV,WT,and load,respectively,at time are the nominal output power values from the PV,WT,and load,respectively,at time t. denote the deviations from the nominal power output values at time t. control the uncertainty range.An expansion in the uncertainty range leads to a corresponding increase in the uncertainty,which in turn,enhances the robustness of the solution in the face of uncertainty,while simultaneously rendering the objective more conservative.

The worst-case scenario is assumed to materialize at the boundary values of the uncertainty set.Consequently,(31)–(33) can be considered equivalent to (34)–(36).

Considering the uncertainties associated with the PV and WT outputs,the problem manifests itself as a nonconvex and nonlinear optimization challenge.This is formulated as an adaptive two-stage RO problem.

Constraint (37b) involves only the binary variables related to the states of FC and ED including the original Constraints (7) and (24)–(27).Constraints (5),(6),(9),(10),and (13)–(15) comprise the binary variables representing the charging/discharging states of BES.Continuous variables are grouped into (37c).Constraints (1)–(4),(8),(11),and (12),and (29) involve only the continuous variables are written into (37d).Constraint (28) includes the uncertain variable u forming (37e).w and z are the vectors denoting the first stage binary and continuous variables,respectively.wu is the vector of the second-stage integer variables,and zu is the vector of the second-stage integer control variables.Other bold letters denote the vectors and matrices of parameters.

3 Solution algorithm

The adaptive RO problem,represented by (37a)–(37e),can be decomposed into a master problem and subproblem,as explained in the subsequent section.Constraint (37c) specifies that the control variables for the charge/discharge states of the BES system are incorporated within the sub-problem,with the binary variables treated as integer recourse variables.To address this adaptive robust optimization challenge,we introduce the outer-inner-CCG algorithm.This approach distinguishes itself from the traditional CCG algorithm [23],which is limited to solving adaptive robust problems by applying linear programming (LP) to the sub-problem.By contrast,our proposed outerinner-CCG algorithm employs a dual-stage CCG iteration,enabling it to accommodate mixed-integer recourses [24].

3.1 Outer CCG:Master problem

The master problem is formulated as follows.

Here,η is a slack variable denoting the objective value of the sub-problem.Kout is the maximum number of the iteration in master problem.The superscript k denotes the kth outer iteration.uk∗is the worst-case scenarios found in the kth iteration.By solving the master problem,the low bound LBout can be obtained as the objective value of the origin problem.The upper bound can be calculated using the objective of the sub-problem.The iteration process is shown in Algorithm 1.

Algorithm 1:Outer-CCG

3.2 Inner CCG:Sub-problem

The sub-problem is encapsulated by subsequent equations incorporating binary variables,continuous variables,and uncertain parameters.Given the maximum minute nature of this problem,it is not agreeable to transform it into a maximization problem through its dual.Consequently,the inner-CCG method detailed in Algorithm 2 is employed for its resolution.

Algorithm 2:Inner-CCG

Here,Kin is the maximum number of iterations in the sub-problem,and w* is the optimal solution to the master problem.

In Algorithm 1,(41a) is maximized under a given x*; u* denoting the worst-case scenario of the RESs and load outputs is obtained.The objective of the sub-problem is to optimize θ∗,which aims to update the upper bound of the master problem.Within (41b),the presence of bilinear terms resulting from the multiplication of a binary variable by a continuous variable necessitates linearization.Linearization is performed using the big-M method,as detailed in [25].The corresponding linearization procedure is presented in the Appendix.The proposed adaptive optimization model is characterized with the outer-inner-CCG algorithm.The optimization framework is shown in Fig.2.

Fig.2 Outer-inner-CCG algorithm framework

4 Case study

4.1 Parameter setting

The cost coefficients,FC,ED,and hybrid energy-storage parameters of electricity and hydrogen are listed in Table 1 [26].The nominal output curves of the PV,WT,and load are shown in Fig.3(a) [27].The rated powers of the PV and WT plants are 600 and 300 kW,respectively.The nominal maximum load over 24 h is 1200 kW,and the minimum load is 500 kW.The parameter configuration is predicated on the anticipated scenarios involving elevated storage system capacities driven by the augmented penetration of RESs,variability in load demand,and critical requirement for improved grid reliability.Future energy policies and electricity market frameworks are expected to facilitate the integration of storage capacity for the provision of ancillary services.Additionally,the selected FC conversion efficiency corresponds to the maximum values observed in recent experimental and prototype studies [28].The dayahead market electricity price follows the curve shown in Fig.3(b) [29].The power outputs from the PV,WT,and load are presumed to fluctuate within a ±20% range around their nominal values.To avoid overly conservative results,the budgets of their total deviations (ΓPV,ΓWT,and ΓL) are established at 20.The simulations are conducted using Python/Gurobi on a computer equipped with an Intel(R) Core i5-7600 CPU (3.5 GHz processor) and 16 GB of RAM,with an acceptable solution gap set at 0.004%.

Table 1 Parameters

Fig.3 (a) Nominal outputs of the PV,WT,and load.(b) Day-head market electricity price

Fig.4 Power of a tie-line

4.2 Day-ahead operational stage

Figure 4 illustrates the scheduling of power across the tie line for transactions with the main grid.This illustrates the strategy of the microgrid for procuring electricity when the prices are low and selling it back during peak price periods.This approach is adopted to maximize income,thereby contributing to a reduction in operational costs.

Figure 5 (a) illustrates the power dynamics involving the ED and FC,where a black curve denotes the electrical power consumed by the ED predominantly during periods of low electricity prices,and a red curve represents the power generated by the FC during intervals of elevated electricity prices.These operational strategies are meticulously adopted to reduce overall operational expenditures.The corresponding state of charge of the HST (SoH) under the worst-case scenario is shown in Fig.5(b).Throughout the daily cycle,the SoH experiences an increase proportional to the increases in the PV and WT power outputs,and decreases to meet peak load demands.Subsequently,it undergoes replenishment during midnight hours,when the electricity prices are at their lowest.The results of this experiment validate the capability of hydrogen storage to adjust to the price fluctuations and mitigate uncertainties,through the implementation of the adaptive RO method.

Fig.5 HST optimization results:(a) power consumed by the ED and produced by the FC and (b) SoH states in the worst case

Fig.6 BES optimization results:(a) Charge/Discharge power and (b) SoC states in the worst case

The charging and discharging power profiles of the BES are shown in Fig.5(a).The upper and lower bounds of the SoC along with the optimized SoC states under the worst-case scenario are shown in Fig.5(b).The maximum operating power of electrochemical energy storage is configured to significantly exceed that of the ED and FC.This design choice enhances the capacity of the MG to manage energy flows more flexibly.This arrangement is advantageous during peak demand periods,and it ensures the availability of energy,particularly during instances of diminished renewable energy generation.These figures collectively demonstrate the role of the BES system in absorbing the surplus power during morning hours and discharging energy in the evening to accommodate the peak load demands and mitigate the financial implications of elevated electricity market prices.Subsequently,the SoC is gradually restored to its initial state,ensuring compliance with the daily operational requirements.

4.3 Intraday operational stage

4.3.1 Feasibility check and comparison with other methods

To assess the efficacy and resilience of the proposed model,a set of 10,000 scenarios,adhering to a uniform probability distribution within the predefined lower and upper bounds,is generated using Monte Carlo sampling.Each scenario represents a distinct case for the realization of uncertainty.In the intraday dispatch phase,the variables determined during the first stage are held constant,and the operations for the remainder of the day are optimized.To underscore the superior robustness of the proposed adaptive robust model,a comparative analysis is conducted against two foundational baseline models.

(I) Model A (intraday simulation only)

A traditional microgrid operation model,characterized by a single-stage approach,directly incorporates realized values as parameters in its formulation.

(II) Model B (intraday simulation only)

A rolling horizon-based approach is employed to orchestrate the BES system,omitting SoC scheduling and confining SoC decisions to the intraday dispatch phase.This model is selected owing to its enhanced accuracy in shortterm uncertainty forecasting.In this second model,only the BES SoC scheduling decisions for the initial hour are executed,with subsequent decisions deferred until the next three-hour rolling horizon is initiated.

The comparison results of the feasibility check for different models are listed in Table 2.The average operational costs and feasibility rates of each model are calculated and tabulated.Model A exhibits the lowest feasibility rate,owing to its lack of recourse mechanisms to accommodate the rapid fluctuations inherent to RESs.Model B,employing a rolling horizon-based methodology,shows a significant improvement in feasibility by enhancing optimization in adjacent hours,albeit at a higher average operational cost compared to the proposed model.The proposed model stands out because it achieves complete feasibility and substantially lower operating costs,thereby underscoring its robustness and efficiency.

Table 2 Feasibility check results

4.3.2 Sensitivity analysis

To investigate the impact of the uncertainty range on the total operational cost and infeasibility rate,three levels of uncertainty are set as listed in Table 3.The uncertainty budgets incrementally increased from Case A to Case C.The corresponding cost and infeasibility rate data for these scenarios,compiled in Table 4,reveal a trend in which both the average costs and feasibility rates increase in tandem with heightened uncertainty budgets.Notably,Case C encompasses the entire spectrum of uncertainty,illustrating that the operational costs incurred in this scenario are poised to offer maximum robustness.

Table 3 Uncertain budget setting

Table 4 Sensibility analysis with different uncertainty budgets

4.4 Performance of the SoC planning model

To investigate the effectiveness of the SoC planning model of the battery storage system in the proposed model,a comparative analysis is conducted with a model that does not incorporate the dispatch of battery storage systems from a whole-day perspective.Cases A–D (Table 5),characterized by varying levels of uncertainty,are employed as the basis for this evaluation.Except for the SoC planning model,the other parameters are the same in all cases.The outcomes detailed in Table 5 indicate that implementing SoC planning results in average microgrid operational cost reductions of 2.64,2.35,1.89,and 1.69% in the respective case studies.This indicates the significance of incorporating SoC planning into the battery storage system model,as it enables a more efficient scheduling of charging and discharging operations over an entire day,thereby significantly decreasing the operational costs of the microgrid.

Table 5 Results with and without SoC planning

4.5 Convergence analysis

To investigate the convergence performance of the proposed outer-inner-CCG algorithm in solving the hybrid electricity-hydrogen energy storage system management problem,the convergence curves of the inner-and outer-CCG algorithms are shown in Fig.7.The initial values of UBin,LBin,UBout,and |U B in-LBin |are set to 8000,-8000,8000,and -8000,respectively.A logarithmic scale with a base of 10 is set on the y-axis.As depicted in Fig.7,the parameters |U Bi n-LBin |and |U B o ut - LBout | can converge to a threshold below 10e-8 within only four iterations,indicating that the outer-inner-CCG algorithm efficiently achieves a robust solution.This rapid convergence highlights the capability of the algorithm to provide reliable and effective solutions for complex energy storage system management and underscores its practical applicability in various scenarios.

Fig.7 Convergence curves of the outer-inner-CCG algorithm

5 Conclusion

This study proposes an adaptive robust HBESSintegrated microgrid operation model with SoC management to minimize operating costs.In this model,the day-ahead stage utilizes robust optimization to establish the upper and lower bounds of the battery storage SoC,while the intraday stage focuses on dispatching battery storage within the defined SoC interval,considering the uncertainty realization from a holistic daily perspective and achieving operation cost reduction.To hedge against uncertainties,an adaptive RO method is proposed to adapt the proposed HBESSintegrated microgrid operation model with integer recourse variables,which are then solved by the proposed outerinner-CCG algorithm.The results of the simulations confirm the exceptional performance,efficiency,and resilience of the proposed adaptive RO model.

Appendix

As shown in Algorithm 2,the dual problem in the inner-CCG is formulated as

The item uTυ is a bilinear term.Hence,u,which denotes the uncertainty variable,is first formulated in the following format according to (34)–(36):

Here,u+ and u- are the binary variables representing the uncertainty degree.By utilizing the big-M method,the uTυ is linearized via the following equations,where two auxiliary continuous variables are introduced: and .M is the value of big-M.

Nomenclature

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant No.72331008,and No.72271211,and PolyU research project 1-YXBL.

Declaration of Competing Interest

We declare no conflicts of interests.