Optimized scheduling of integrated energy systems: a multi-dimensional electricity, hydrogen, ammonia, heat synergy approach using the LSDBO-WOA algorithm

Abstract

To enhance the accommodation capability and operational flexibility of renewable energy systems, address the insufficient architectural integration of existing ammonia-based energy systems, and overcome the limitations of current optimization algorithms in tackling complex nonlinear multi-objective problems, this paper proposes a synergistic integrated energy system with liquid ammonia as the central hub. The system integrates multi-energy flows encompassing electricity, hydrogen, ammonia, and heat, leveraging ammonia fuel cell power generation, ammonia cracking, and ammonia-blended gas turbines for both electricity and heat production. A bi-level optimization model is formulated, coupling upper-layer multi-objective capacity planning with lower-layer stochastic chance-constrained scheduling. To solve this model, a hybrid algorithm, designated as LSDBO-WOA, is developed by integrating an improved dung beetle optimizer (LSDBO) with the whale optimization algorithm (WOA). Case study results demonstrate that the proposed algorithm achieves markedly superior convergence performance compared to benchmark algorithms such as non-dominated sorting genetic algorithm II (NSGA-II), with an improvement of approximately 18.6% in comprehensive performance metrics. Furthermore, the proposed electricity–hydrogen–ammonia–heat system attains an overall energy efficiency exceeding 97.66% and reduces carbon emissions by 7.3% relative to the original system without ammonia integration.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-41136-8.

Introduction

Against the backdrop of a growing global energy crisis and environmental pollution, China has adopted the strategic targets of “carbon peak and carbon neutrality” to promote the transition toward clean and low-carbon energy. Renewable energy installations, especially wind and photovoltaic power, have grown rapidly. By 2023, China’s cumulative installed capacity of wind and photovoltaic (PV) power exceeded 1 billion kilowatts, accounting for over 30% of the national total installed capacity¹. However, renewable power generation is inherently intermittent and volatile, posing major challenges to the safe and stable operation of power grids. Achieving high-penetration integration of renewable energy has thus become a central issue in building a new power system².

The research framework of this paper is illustrated in Fig. 1.

Fig. 1.

A Comprehensive study on the optimization of a multi energy synergistic system utilizing the LSDBO-WOA algorithm.

Literature review

Integrated Energy Systems (IES) achieve complementary utilization by integrating multiple energy forms, including electricity and heat. They effectively mitigate fluctuations in renewable energy output and enhance energy utilization efficiency, serving as a key technological pathway for achieving the “Dual Carbon” goals. In recent years, the multi-dimensional synergistic IES encompassing electricity, hydrogen, ammonia, and heat has emerged as an advanced form of IES. Leveraging energy cascade utilization and chemical energy storage conversion technologies, it demonstrates significant potential in renewable energy integration, carbon emission reduction, and system flexibility enhancement. At the system architecture level, existing research has evolved from single-energy forms toward deep multi-energy coupling. Refs^3,4. validate the technical feasibility and emission reduction potential of hydrogen-ammonia blended fuels in end-use devices. Subsequently, the research scope has expanded to system integration: Ref⁵. explored the integration of ammonia as a hydrogen storage medium with fuel cells; Refs^6,7. focused on enhancing the wind and solar integration rate in ammonia-based systems; Ref⁸. discussed the role of ammonia in grid peak shaving. Particularly in multi-microgrid and park-level systems, hydrogen-ammonia synergy has been proven to deliver substantial low-carbon benefits⁹. Considering real-time energy pricing mechanisms, Ref¹⁰. proposed an optimal scheduling model for wind-solar hydrogen production and ammonia synthesis systems based on chance-constrained programming, achieving a high renewable energy integration rate and significant carbon emission reduction under uncertainty.

Optimal scheduling of IES involves multiple decision variables, objectives, complex constraints, and uncertainties such as source–load mismatch. To date, many researchers have adopted NSGA-II and multi‑objective particle swarm optimization (MOPSO) to address these scheduling challenges^11,13, aiming to enhance computational efficiency. Ref¹⁴. employed the Beluga Whale Optimization (BWO) algorithm to solve capacity allocation for integrated power–hydrogen–heat cogeneration in energy systems. Ref¹⁵. investigates the systematic capacity optimization configuration of the Sparrow Search Algorithm (SSA). Various improved Dung Beetle Optimization (DBO) algorithms have shown superior performance in microgrid economic–environmental dispatch¹⁶ and parameter optimization^17,18. To coordinate long-term planning and short-term scheduling, the two-layer optimization framework has become a mainstream approach^10,19,20. To handle uncertainties in renewable energy and load within such two-layer problems, Ref¹⁰. and Ref¹³. adopt stochastic programming with chance constraints; Ref²¹. utilizes robust optimization to explore integration and diversified utilization of wind and solar resources; Ref²². employs distributionally robust optimization to address uncertainties in the coupled system. Ref²⁰. transforms the two-layer model into a single-layer problem using Karush-Kuhn-Tucker (KKT) conditions; Ref²¹. and Ref²³. apply column-and-constraint generation algorithms for solution. This research and recent relevant studies are summarized in Table 1.

Table 1.

Comparative evaluations between this study and other publications. Note: RE stands for Renewable Energy; ES stands for Energy System; HS stands for Hydrogen Energy System; AS stands for Ammonia Energy System; HFC and AFC denote Hydrogen Fuel Cell and Ammonia Fuel Cell, respectively.

Research gaps and contributions

In summary, existing research on integrated energy system architectures tends to be fragmented and limited to binary coupling. Most studies either focus separately on hydrogen or ammonia applications in specific devices, or remain confined to simple binary coupling modes such as “electricity–hydrogen” or “electricity–ammonia.” They fail to integrate hydrogen production, storage, transport, and utilization with ammonia synthesis, cracking, direct combustion, and fuel cell power generation into an organically synergistic circular system^2,6,20,24. Consequently, such system architectures are inherently limited and cannot achieve cascaded energy utilization and multidirectional conversion, which severely constrains overall system flexibility, efficiency, and carbon neutrality potential. When facing large-scale, nonlinear, multi-objective, and multi-constraint problems, traditional algorithms and some metaheuristic algorithms often suffer from slow convergence, susceptibility to local optima, and insufficient diversity in Pareto solution sets^7,25. Existing optimization approaches frequently fail to provide a wide range of high-quality trade-off solutions that balance competing objectives such as economy, environmental performance, efficiency, and energy utilization, resulting in inadequate decision support for intelligent system operation²⁶. Moreover, there is a lack of an integrated framework capable of deeply coupling multiple energy flows (electricity–hydrogen–ammonia–heat), incorporating efficient multi-objective optimization algorithms, achieving dynamic coordination between planning and scheduling, and quantifying uncertainties from both generation and load sides^27,31.

To address the aforementioned limitations, this paper constructs a multi-dimensional synergistic integrated energy system encompassing electricity, hydrogen, ammonia, and heat. The system utilizes the power grid, photovoltaic and wind power generation, and natural gas as primary energy inputs to meet electrical and thermal load demands. Key processes including ammonia synthesis, cracking, direct combustion, and fuel cell power generation are incorporated. A two-layer optimal scheduling study is conducted for this system.

The specific work is as follows:

(1) A multi-dimensional synergistic energy system integrating electricity, hydrogen, ammonia, and heat is established by combining electrolytic hydrogen production, ammonia synthesis, ammonia cracking, hydrogen/ammonia fuel cells, ammonia-blended gas turbines, and waste heat recovery. This system enables cascaded energy utilization and multi-energy complementarity. Liquid ammonia serves as a long-term energy storage medium, supporting three energy release pathways (power generation, cracking, and co-firing), which significantly enhances renewable energy integration while substantially reducing carbon emissions.

(2) By integrating WOA and LSDBO, a hybrid algorithm is proposed to solve the model, enabling enhanced solution of the multi-objective Pareto front.

(3) A two-layer optimal scheduling model with top–down coordination is established. The upper layer optimizes four objectives: minimized annualized cost, minimized carbon emissions, maximized system efficiency, and minimized energy curtailment rate. The lower layer employs stochastic chance constraints to convert source–load uncertainties into deterministic constraints, with the objective of minimizing expected operating costs.

The subsequent chapters of this paper are organized as follows. Chapter 2 proposes an integrated energy system model featuring multi‑dimensional synergy among electricity, hydrogen, ammonia, and heat. Chapter 3 formulates a bi‑level optimal scheduling model for the proposed system. Chapter 4 describes the solution methodology based on the LSDBO‑WOA algorithm and analyzes the improvements incorporated into the algorithm. Chapter 5 validates the rationality and effectiveness of the proposed model and algorithm, and discusses their limitations. Finally, Chap. 6 concludes the paper.

Multi dimensional coordinated electricity hydrogen ammonia heat multi energy system model

System architecture

As shown in Fig. 2, the system achieves efficient and low-carbon energy supply through cascade utilization of energy and the integration of multiple technologies. It adopts a four-layer architecture from left to right: the energy supply layer, conversion and storage layer, energy transmission and distribution layer, and load layer. The energy supply layer is connected to the upstream power grid, PV panels, wind turbines, and the natural gas network. Serving as a hub, the conversion and storage layer utilizes electrolyzers to convert surplus renewable electricity into hydrogen. This hydrogen can either be directly supplied to fuel cells or synthesized with nitrogen produced by a PSA nitrogen generation unit into liquid ammonia for storage, thereby establishing a clean “electricity‑hydrogen‑ammonia” conversion chain. The energy consumption layer meets electrical and thermal demands through the distribution grid and district heating network, respectively. The core of the system lies in the synergistic hydrogen‑ammonia cycle. Liquid ammonia serves as an energy storage medium and can release energy via three pathways: (1) power generation through ammonia fuel cells, (2) hydrogen production via ammonia cracking with heat recovery, and (3) co‑firing with natural gas in gas turbines to reduce carbon emissions. The system further incorporates deep waste heat recovery: high‑temperature exhaust gases from gas turbines drive waste heat boilers for heating, while medium‑ and low‑temperature waste heat is recovered for power generation via an Organic Rankine Cycle (ORC), achieving cascade energy utilization.

Fig. 2.

Electricity hydrogen ammonia heat multi dimensional synergistic system architecture diagram. Note: Abbreviations of system components in the figure are elaborated in detail in Sect. 2.2 and 3.2.2.

Moreover, the system exhibits tight multi‑energy coupling characteristics: the power flow is primarily supplied directly by PV and wind, with surplus electricity used for hydrogen and ammonia production, while hydrogen/ammonia fuel cells and ammonia‑blended gas turbines cooperate to provide peak‑shaving support; the heat flow relies on a dual‑source system comprising waste heat boilers and gas boilers; and the gaseous energy flow adopts natural gas‑ammonia blending to enable low‑carbon combustion.

This design offers three key advantages: hydrogen/ammonia storage mitigates renewable energy fluctuations, zero‑carbon ammonia fuel reduces reliance on fossil fuels, and deep waste heat recovery enhances overall energy efficiency.

Modeling of typical system equipment units

(1) Electricity-to-Hydrogen Conversion.

1) Electrolytic Hydrogen Production.

The relationship¹³ between the power consumption of the electrolyzer (EL) and hydrogen production as:

1

where represents the newly produced hydrogen output at time t, represents the electrolytic hydrogen production efficiency, represents the power consumption of the EL at time t, and represents the lower heating value of hydrogen.

2) Hydrogen Fuel Cell (HFC).

The principle of HFCs is to convert the chemical energy of stored hydrogen into electrical and heat energy, serving as a key pathway for feeding hydrogen energy back into the grid. The relationship¹⁰ between the output power of a hydrogen fuel cell and hydrogen consumption as:

2

where represents the output power of the hydrogen fuel cell at time t, represents the hydrogen consumption for power generation at time t, and represents the power generation efficiency of the HFC.

During power generation, not all chemical energy in the fuel is converted into electrical energy; a significant portion is released as heat. This heat can be expressed as:

3

where represents the heat-electric conversion coefficient of the HFC.

(2) Hydrogen-Ammonia Conversion.

1) Pressure Swing Adsorption (PSA) Nitrogen Generation Equipment.

Nitrogen serves as an essential raw material for ammonia synthesis. PSA technology separates nitrogen from air. The relationship⁸ between nitrogen production and input power in PSA as:

4

where represents the input power of the PSA nitrogen generator at time t, represents the nitrogen production of the PSA at time t, and represents the mass-specific power of the PSA nitrogen generator.

2) Ammonia Synthesis Equipment (P2A).

The core of the P2A model involves the catalytic synthesis of liquid ammonia from hydrogen and nitrogen under high temperature and pressure. This process simultaneously consumes electrical energy and releases substantial reaction heat, achieving the coupling of electrical, chemical, and heat energy^2,8. The constraints for the P2A process are defined by Eq. (5).

5

where represents the power consumption of the P2A at time t, represents the mass flow rate of ammonia produced at time t, represents the electrical efficiency of the P2A process at time t, represents the heat power generated by the P2A process at time t, represents the release efficiency of the heat power generated by the P2A process at time t, and represents the heat power released per unit of synthesized ammonia, the mass ratio of ammonia, nitrogen, and hydrogen is 0.097:0.107:1, with a volume ratio of 2:1:3.

3) Ammonia Cracker (AC).

The AC reforms liquid ammonia back into hydrogen, serving as the key to reusing ammonia as hydrogen energy and closing the loop of the ammonia energy storage pathway²¹. The relationship between hydrogen production and ammonia consumption in the AC as:

6

where represents the cracking mass efficiency, represents the amount of ammonia consumed for cracking at time t, and represents the hydrogen production from cracking.

The ammonia cracking process generates significant heat, which can be expressed as:

7

where represents the specific heat capacity at constant pressure of the cracking products, and represent the temperatures of the gas at the cracker outlet and inlet, respectively, and represents the heat recovery efficiency of the heat exchanger.

(3) Ammonia/Hydrogen-Electricity/Heat Conversion Chain.

1) Ammonia Fuel Cell (AFC).

AFC directly consumes ammonia gas for power generation, representing one pathway for direct and efficient utilization of ammonia energy¹². The relationship between the output power of the AFC and the ammonia mass flow rate as:

8

where represents the power output of the AFC at time t, represents the mass flow rate of ammonia directly used for power generation in the AFC at time t, represents the lower heating value of ammonia, and represents the power generation efficiency of the AFC.

The heat output of the AFC as:

9

where represents the thermoelectric conversion coefficient of the AFC.

2) Ammonia-blended Gas Turbine (GT).

The GT generates electricity by combusting a mixture of natural gas and ammonia, serving as the core equipment for achieving low-carbon transformation of fossil energy within the system¹⁹. The total fuel mass flow rate of the GT as:

10

where represents the total fuel mass flow rate of the gas turbine, represents the natural gas mass flow rate, and represents the amount of ammonia directly used for combustion at time t.

11

12

where represents the GT power generation efficiency, represents the actual power output of the GT at time t, represents the ammonia blending ratio, represents the lower heating value of natural gas.

13

where represents the waste heat of the gas turbine at time t, represents the thermal-electric ratio.

3) Organic Rankine Cycle (ORC) Power Generation.

Recovering various low-to-medium temperature waste heat for power generation is a key technology for achieving cascaded energy utilization and enhancing overall system efficiency⁴. The relationship between input power and electrical output power for the ORC as:

14

where represents the ORC power generation at time t, represents the ORC heat input power at time t, and represents the waste heat conversion efficiency.

4) Gas Boiler (GB).

The GB generates heat by burning natural gas, serving as the primary and backup heating source for the system¹⁴.The heat output of the GB as:

15

where represents the heat generated by the gas boiler at time t, and represents the boiler efficiency.

5) Waste Heat Boiler (WHB).

Conventional boilers generate heat by burning fuel, whereas WHB recover residual heat from high-temperature flue gases emitted by GT and P2A²⁴ The actual heat output of WHB as:

16

where represents the heat exchange efficiency of the WHB.

Multi dimensional synergistic integrated energy system dual layer optimal scheduling model

Model framework

To achieve synergistic coordination across electricity, hydrogen, ammonia, and heat, and to realize a complementary multi-energy integrated energy scenario, this paper constructs a dual-layer optimal scheduling model for a multi-dimensional synergistic integrated energy system. The model framework is shown in Fig. 3.

Fig. 3.

Two-layer optimization model framework.

In Fig. 3, the upper-layer model is a multi-objective capacity planning model. It aims to minimize total annualized costs, minimize carbon emission, minimize energy curtailment rate, and maximize system efficiency, thereby optimizing the capacity allocation and strategy parameters of all units within the system. The lower-layer model is the operational scheduling optimization model. For the capacity plan transmitted from the upper level, it aims to minimize expected operating cost under scenarios with uncertainties in wind and solar power generation and load, achieving optimal decision-making for equipment output within the scheduling cycle.

Synthesizing the above framework, the bi‑level optimal scheduling problem for the proposed electricity–hydrogen–ammonia–heat system is formulated as follows:

17

where represents the upper-level decision variables, represents the lower-level decision variables, represents the four-objective vector of the upper-level model, corresponding to total annualized cost, carbon emissions, system negative efficiency (to unify the minimization direction), and renewable curtailment rate (see Sect. 3.2.1), represents the objective function of the lower-level model, i.e., the expected operating cost (see Sect. 3.3.2), represents all constraints of the upper-level model, including capacity, matching, and other relevant constraints (see Sect. 3.2.2), represents all constraints of the lower-level model, encompassing power balance, operational limits, stochastic chance constraints, etc. (see Sect. 3.3.3), and represents the optimal solution of the lower-level optimization problem for a given upper-level decision .

Upper layer multi objective capacity planning model

Objective function

(1) Minimize total annualized cost.

Economically, the system aims to minimize its total annualized costs, encompassing the annual investment costs of equipment, energy procurement costs during operation, operational maintenance and curtailment penalty costs, hydrogen-ammonia system process costs, and carbon emission costs.

1) Annual Investment Costs of Equipment

18

where d represents the fixed-cost equipment type, D represents the fixed-cost equipment set, represents the investment cost coefficient for equipment d, and represents the installed capacity of equipment d.

2) Energy Procurement Costs

19

where represents the fixed operation and maintenance cost coefficient for equipment d, represents the natural gas unit price, and represent the grid electricity purchase and sale prices at time t, respectively, and represent the grid electricity purchase and sale power at time t, respectively.

3) Operational Maintenance and Curtailment Penalty Costs

20

where k represents the operational costs by equipment type, K represents the operational costs by equipment set, represents the variable maintenance coefficient for equipment k, represents the operating volume of equipment k at time t, and represent the unit costs for wind and solar curtailment penalties, respectively, and represent the curtailed wind and solar power at time t, respectively.

4) Hydrogen-ammonia System Process Costs

21

where represents the electricity cost coefficient for electrolytic hydrogen production, represents the unit cost of nitrogen preparation, represents the operating cost coefficient for P2A, represents the unit cost of ammonia cracking, and represents the unit cost of ammonia combustion.

5) Carbon Emission Costs

22

where represents the carbon trading price, , , , and represent the carbon emission factors per unit of electricity generation for grid power, natural gas, HFC, and AFC, respectively, represents the ammonia blending ratio, and represents the carbon reduction factor for ammonia combustion.

Therefore, the minimization of the system’s total annualized costs can be expressed as:

23

(2) Minimizing Carbon Emission.

Environmentally, the system aims to minimize the total carbon emissions over its lifecycle:

24

(3) Maximizing System Efficiency.

In energy utilization, the system aims to maximize system efficiency, that is, maximizing the ratio of useful energy output to primary energy input in the system.

25

where and represent the user’s electricity and heat loads satisfied at time t, represents the lower heating value of ammonia, and represents the combustion heat utilization coefficient(after deducting boiler heat loss).

(4) Minimizing Energy Curtailment Rate.

For renewable energy integration, the system aims to minimize curtailed wind power, curtailed solar power, curtailed hydrogen, and curtailed ammonia.

26

where and represent curtailed wind and solar power, respectively, represents the system’s total load, and represent curtailed hydrogen and ammonia, respectively.

Constraints

(1) Conventional Unit Capacity Constraints

27

where represents the actual power output of wind power at time t, represents the rated installed capacity of the wind turbine (WT), represents the actual power output of photovoltaic power at time t, represents the rated installed capacity of the photovoltaic (PV), represents the rated electrical power capacity of the EL, represents the HST inventory at time t, represents the maximum capacity of the hydrogen storage tank (HST), represents the rated electrical power capacity of the GT, represents the rated electrical power capacity of the P2A, represents the rated power of the PSA nitrogen generator, represents the ammonia inventory at time t, represents the maximum capacity of the ammonia storage tank (AST), represents the rated processing capacity of the AC, represents the rated electrical power capacity, represents the heat storage capacity at time t, represents the rated thermal storage capacity of the thermal energy storage (TES), represents the rated capacity of the WHB, and represent the upper capacity limits for hydrogen and ammonia fuel cells, respectively.

(2) Ammonia Blending Ratio Constraint

28

(3) Equipment Capacity Matching Constraints

29

30

In Eqs. (29)-(30), represents the EL capacity matching coefficient, and represents the P2A matching coefficient.

Lower layer operational scheduling model

Source load uncertainty model

Source-load uncertainty primarily stems from deviations in wind and solar power generation forecasts and load forecasts, whose randomness is expressed as:

31

32

33

In the above equations, , , and represent the actual wind and solar power generation, actual electricity load, and actual heat load at time t, , , and represent the predicted wind and solar power generation, predicted electricity load, and predicted heat load at time t, respectively, and represents the fluctuation range.

To unify dimensions, the relative deviation quantity is defined to standardize the uncertainty parameter:

34

where ,, and represent the normalized relative deviation of wind and solar power output, normalized relative deviation of electricity load, and normalized relative deviation of heat load, respectively.

The construction of the stochastic opportunity constraint is as follows:

35

where and represent the total system power supply and heating power at time t, respectively, and represents the confidence level.

Deterministic equivalence transformation is the core mathematical technique for handling stochastic opportunity constraint¹⁰. Its essence lies in converting probabilistic constraints into deterministic linear constraints. This paper adopts the normal distribution assumption and quantile transformation method.

Assume load fluctuations follow a normal distribution:

36

where represents the random load.

Through the inverse function of the standard normal distribution, equates the probability constraints to:

37

where . This implies using standard deviations as the safety margin to cover fluctuation scenarios with a probability of .

Objective function

The objective of stochastic opportunity-constrained scheduling is to analyze the impact of source-load uncertainty on operational costs for a given capacity configuration, employing a probability distribution-based stochastic optimization method. By minimizing expected operational cost, it achieves both economic efficiency and stability. Scheduling decisions must strictly satisfy power/heat load balancing and equipment safety constraints at the confidence level . The underlying optimization goal is to minimize the total operational cost’s expected value under the probability distribution, described by the following mathematical model:

38

where X represents the input parameter, i.e., the equipment capacity configuration specified in the upper-level model, Y represents the lower-layer operational control decision vector, represents the source-load uncertainty random variable, following a normal distribution, represents the operational cost function, formally equivalent to the operational component within the upper-layer economic objective, encompassing the cumulative values of energy procurement cost, operational maintenance cost, carbon emission cost, and curtailment penalties over the scheduling cycle.

Stochastic opportunity constraint optimization achieves long-term economic optimality by minimizing . Based on the confidence level , it generates a security margin to ensure probabilistic satisfaction of supply-demand balance.

Constraints

(1) Power Balance Constraints.

1) Electrical Power Balance

39

2) Heat Power Balance

40

where and represent the charging and discharging heat power at time t, respectively.

3) Hydrogen Power Constraint

41

(2) Ammonia Synthesis Unit Constraint.

Due to the limited flexibility of the ammonia synthesis process, this study sets the upper and lower limits for the ramping rate of the P2A unit at 10% and 19% of its maximum capacity, respectively.

42

(3) AST Constraints

43

44

where represents the total ammonia consumption at time t.

(4) Hydrogen-Ammonia Synergistic Coupling Constraints.

1) EL Capacity and Ramp Power Constraints

45

46

where represents the renewable energy absorption matching coefficient, set to in this study to ensure full renewable energy absorption potential, and represent the maximum allowable upper and lower ramping powers for EL, respectively.

2) Ammonia Storage-Cracking Capacity Ratio Constraint

47

3) Ammonia Blending Energy Supply Constraint

48

4) Fuel Supply Capacity Matching Constraint

49

(5) TES Dynamics and Logic Constraints

50

51

52

where and represent the charging and discharging states of the TES at time t, respectively, both being binary variables, and represent the rated charging and discharging power of the TES, respectively.

Solution methodology for the two layer model based on the LSDBO-WOA algorithm

LSDBO-WOA algorithm

Compared to LSDBO, the LSDBO-WOA algorithm incorporates improvements in population initialization, population stratification, and exploration strategy. The dynamic execution process of the algorithm is illustrated in Fig. 4.

Fig. 4.

Dynamic process of algorithm execution.

During the population initialization stage, the optimization algorithm first employs the Cubic chaotic map to generate initial individuals. As illustrated in Fig. 5, this type of map exhibits typical chaotic characteristics when the number of iterations is sufficiently high, including sensitive dependence on initial conditions, topological transitivity, and the mixing property¹⁵.

Fig. 5.

Characteristics of the cubic chaotic map.

Furthermore, an opposition-based learning strategy is employed to generate opposition solutions, further expanding the exploration scope of the solution space based on the uniformly distributed population yielded by the chaotic map, thereby increasing the probability of identifying the global optimum. In addition, the LSDBO-WOA algorithm introduces a dynamic population stratification mechanism, in which the population is divided into three subpopulations according to fitness, each assigned a distinct search strategy. Figure 6-(a) and (b) illustrate the enhanced WOA encircling mechanism employed in the algorithm, which integrates the spiral search behavior of WOA with the long-range jumping characteristics of Lévy flights.

Fig. 6.

Schematic diagram of the enhanced encircling mechanism in WOA.

The enhanced T‑distribution perturbation generates substantial disturbances leveraging the heavy-tailed nature of the T‑distribution, thereby increasing solution diversity. This mechanism is further coupled with a memory‑guided strategy that leverages historical high‑quality solution information to steer the search direction.

Two layer model solution strategy with LSDBO-WOA

The upper-layer model is characterized by multi-objective, nonlinear, and large-scale properties, presenting significant challenges for conventional optimization methods. While the LSDBO is applicable to large-scale integrated energy system optimization, it exhibits limitations such as weak local exploitation capability and insufficient diversity in the solution set. To address these shortcomings, this paper proposes a hybrid LSDBO-WOA algorithm that integrates the mechanisms of LSDBO and the WOA. Concurrently, considering the single-objective, nonlinear, and relatively smaller-scale nature of the lower-layer model, the stochastic chance constraints are transformed into deterministic equivalent constraints with safety margins through chance-constrained programming and the assumption of a normal distribution. Consequently, the lower-layer model is formulated as a deterministic Mixed-Integer Linear Programming (MILP) problem. Professional solvers such as Gurobi are then invoked to minimize the expected operating cost, outputting key metrics including optimal dispatch schedules. The overarching solution process for the dual-layer model is illustrated in Fig. 7. The two layers exhibit dynamic synergy and tight coupling: planning results from the upper layer serve as parameter inputs to the lower layer, while operational evaluation results from the lower layer can be fed back into the fitness calculation of the upper layer. This forms a closed-loop system of integrated iterative optimization for “planning-operation,” aimed at achieving a balance among the four objectives.

Fig. 7.

Two-layer model solution process.

Case studies

All model development and numerical solutions in this study were performed on a LAPTOP-O3M6STIA (with Windows 11 Home Chinese Edition, AMD Ryzen 7 8845Hw processor). The simulation environment utilized MATLAB R2023b (including YALMIP version 20230312) and called Gurobi 10.0.3 as the MILP solver. Results from a typical winter day in a certain region were selected for the collaborative analysis of the four energy flows: electricity, hydrogen, ammonia, and heat. The system equipment is shown in Fig. 2. The forecasted outputs of wind and solar power at different time periods, as well as the electricity and heat load forecasts, are available online in Supplementary Figure S4; the parameters of each device are available online in Supplementary Table S1; the system calculation parameters are available online in Supplementary Table S2; and the real-time electricity prices are available online in Supplementary Table S3.

Algorithm results analysis

Analysis of algorithm comparison results

In solving the comprehensive energy system optimization problem, this paper further compares the distribution of the Pareto solution set between LSDBO-WOA and the other three algorithms. The results are shown in Figs. 8 and 9.

Fig. 8.

Distribution of pareto solution sets for four objective functions calculated by four algorithms.

Fig. 9.

Two-dimensional projection of the distribution of the Pareto solution set for the four objective functions computed by the four algorithms.

Figure 9-(a) clearly reveals a significant trade-off between economic and environmental objectives. Compared to the other three algorithms, the solution set obtained by the LSDBO-WOA algorithm is significantly concentrated in the lower-left region, forming a tight solution cluster that closely approaches the ideal boundary. This indicates that the algorithm can systematically identify optimization solutions achieving lower emissions at a reduced cost level. Similar performance differences can be observed in Fig. 9-(b). The LSDBO-WOA solution set again exhibits a superior Pareto frontier near the low-cost, low-waste-energy-rate region. While traditional algorithms like MOPSO and NSGA-II show some solution distribution, they are generally disadvantaged in terms of dominance relationships—meaning most of their solutions underperform the corresponding hybrid algorithm solutions in either cost or reliability objectives. Figure 9-(c) reveals that LSDBO-WOA solutions concentrate more in the region of high curtailment rates and lower carbon emissions within this plane. Compared to other algorithms, LSDBO-WOA achieves relatively lower carbon emissions at the same curtailment rate.

Additionally, this paper employs four multi-objective evaluation metrics to assess the algorithm’s performance. The Inverted Generational Distance (IGD) measures the comprehensive convergence and distribution of the Pareto front obtained by the algorithm relative to the true Pareto front. A smaller IGD value indicates that the solution set is closer to the true front and more uniformly distributed. It can be calculated using the following mathematical model.

53

where represents the set of reference points on the true Pareto front, P represents the set of non-dominated solutions obtained by the algorithm, and represents the minimum Euclidean distance from a reference point v to the solution set P.

Generational Distance (GD) measures the average distance from the Pareto solution set obtained by the algorithm to the true Pareto front, reflecting the convergence of the solution set. A smaller GD value indicates that the solution set is closer to the true front. Its calculation model is as follows:

54

where represents the minimum Euclidean distance from a solution x to the true front.

Spacing measures the distribution uniformity of adjacent solutions in the Pareto solution set, reflecting the diversity/distribution of the solution set. A smaller Spacing value indicates a more uniform distribution of solutions in the objective space. Its calculation model is as follows:

55

where n represents the number of non-dominated solutions, represents the distance from the i-th solution to its nearest neighbor in the objective space, and represents the mean of all .

IGD simultaneously measures convergence (whether the solution set is close to the true front) and diversity (whether the solution set covers the entire true front). It is a core indicator for comprehensively evaluating algorithm performance. GD focuses solely on convergence, i.e., how close the individuals in the solution set are to the true front. A smaller GD indicates that the algorithm can effectively approximate the true optimal boundary. Spacing evaluates the uniformity of the solution set’s distribution in the objective space, helping to determine whether the algorithm tends to cluster in certain regions while neglecting others. A smaller Spacing implies that decision-makers have a more diverse set of trade-off options to choose from. The computational time required for an algorithm to complete one optimization run reflects its computational efficiency. In this paper, the running time is taken as the average value over five runs. The test results of the four algorithms in the integrated energy system considered in this study are presented in Table 2.

Table 2.

Comparison of multi-objective evaluation metrics for four algorithms.

LSDBO-WOA	IGD	GD	Spacing	Time (s)
	36368.6	1614.18	10876.9	173.818
MODBO	47039.9	1821.49	15005.2	164.777
MOPSO	38343.5	2082.62	11144.8	141.035
NSGA-Ⅱ	42821.7	1743.49	18153.3	185.869

Note: IGD denotes Inverted Generational Distance; GD denotes Generational Distance.

The table provides a systematic performance evaluation of four multi‑objective optimization algorithms across three dimensions: convergence, distribution, and computational efficiency. In terms of convergence, LSDBO‑WOA demonstrates significantly superior performance compared to the other algorithms, achieving the lowest values in both IGD (36368.6) and GD (1614.18). This indicates that its obtained solution set excels in proximity to the true Pareto front. Regarding the distribution characteristics of the solution set, the Spacing metric is used to evaluate the uniformity of non‑dominated solutions in the objective space. LSDBO‑WOA also performs best on this metric (10876.9), reflecting its ability to obtain a more evenly and broadly distributed set of solutions.

From the perspective of computational efficiency, the runtime directly reflects the computational cost of the algorithm. MOPSO ranks first with the shortest runtime of 141.035 s, exhibiting the highest computational efficiency. Although LSDBO-WOA achieves superior performance across all quality metrics, this comes at the cost of the highest computational time. However, this trade-off is considered acceptable.

Distribution analysis of the LSDBO-WOA algorithm’s pareto

The optimization conducted using the proposed LSDBO-WOA algorithm in this study revolves around four evaluation dimensions: economic performance, environmental friendliness, system efficiency, and energy utilization rate. The Pareto solution set is screened and labeled via the Technique for Order Preference by Similarity to An Ideal Solution (TOPSIS) method. In the decision-making process using TOPSIS, the objective entropy weight method is employed to determine the weight of each objective, thereby eliminating subjective bias. This approach automatically computes weights based on the variability of objective values within the Pareto set—objectives with greater dispersion receive higher weights. The resulting weight distribution is as follows: annualized cost (0.3), carbon emissions (0.3), system efficiency (0.2), and renewable curtailment rate (0.2). This allocation indicates that, under the studied scenario, the Pareto solutions exhibit the greatest diversity and dispersion along the economic dimension. The distribution of the solution set is illustrated in Fig. 10.

Fig. 10.

LSDBO-WOA Optimized Pareto Solution Set.

Figure 10 illustrates the distribution of system performance across three dimensions: annualized cost, curtailment rate, and daily carbon emissions, with point color representing negative efficiency. The collection of data points forms a three-dimensional Pareto frontier surface. This figure demonstrates that no single solution can simultaneously optimize all objectives, necessitating trade-offs between different goals. Spatially, low-emission regions significantly overlap with high-cost areas, indicating that achieving carbon reduction targets under current technological constraints incurs corresponding economic costs. The gradient of data point colors reveals a non-uniform distribution of system efficiency, with high-efficiency solutions concentrated in specific intervals of medium-to-high costs and medium-to-low emissions. To clarify the solution set, this paper selects three projection planes from Fig. 10, as shown in Fig. 11.

Fig. 11.

Comparison of 2D Projections of Pareto Solution Sets.

Figure 11 illustrates the trade-off between cost, carbon emissions, and energy utilization efficiency in multi-objective optimization of energy systems. Figure 11-(a) visually demonstrates the inverse relationship between cost and carbon emissions, known as the “green premium”: pursuing ultra-low carbon emissions requires the system to prioritize the use of expensive green hydrogen/green ammonia, while emphasizing economic efficiency leads to greater reliance on fossil fuels, thereby increasing carbon emissions. Figure 11-(b) indicates that achieving high energy utilization requires configuring large-scale energy storage or expensive backup power sources, causing costs to surge sharply. This exhibits a “trade-off between cost and utilization,” with the most significant improvement in benefits occurring within the medium-cost range. Figure 11-(c) further analyzes the relationship between environmental performance and energy utilization efficiency, revealing a “weak negative correlation” and distinct “cluster differentiation”: High-efficiency systems (dark blue cluster) achieve low-carbon, high-consumption integration through hydrogen-ammonia cycles; low-efficiency systems (yellow-orange cluster) rely on external fossil fuels, maintaining high consumption in the short term but accompanied by high emissions. A “knee point” region exists between these two extremes, where solutions achieve the optimal engineering balance across all objectives.

Through TOPSIS screening, a solution costing approximately 11.7 × 10⁸ CNY with carbon emissions of about 1.47 × 10⁶ tons was selected as optimal. This solution significantly reduces emissions at moderate cost while maintaining high system efficiency and energy utilization, offering the best overall cost-performance ratio.

System performance analysis

Analysis of system impact from ammonia blending ratio

The operational results of seven ammonia blending scenarios are presented in Table 3; Fig. 12, ranging from the baseline scenario R-0 (0% ammonia blending) to R-6 (30% ammonia blending).By 2025, the maximum ammonia injection ratio demonstrated in engineering applications reached 70%, achieved by Japan’s IHI Corporation on a 2 MW-class gas turbine. In actual commercial operation, the maximum ammonia injection ratio is 20%, implemented and deployed commercially by IHI Corporation⁸. Integrating commercial and engineering application results, this study sets the ammonia injection ratio range as , with the baseline scenario defaulting to no ammonia loop.

Table 3.

Comparison of cost carbon emissions and energy utilization rate under scenarios R0 to R6 with ammonia blending ratios ranging from 0 to 30%.

Scenario	Parameter
	Ammonia Blending Ratio (%)	Total Operating Cost(10⁴ CNY)	Carbon Emissions (tons)	Cost of Synthetic Ammonia (10⁴ CNY)	Carbon Emission Cost (10⁴ CNY)	Energy Procurement Cost (10⁴ CNY)	Energy Utilization Rate (%)
R-0	0	400.83	4356.84	0	8.95	195.36	83.60
R-1	5	383.94	4280.86	4.42	7.71	168.45	90.89
R-2	10	381.69	4257.35	5.61	7.66	145.28	93.12
R-3	15	380.57	4043.15	5.89	7.28	125.64	97.66
R-4	20	380.67	4186.58	7.20	7.53	132.36	98.03
R-5	25	379.78	4193.62	9.96	7.65	158.42	98.10
R-6	30	378.52	4216.75	10.84	7.69	180.06	97.45

Fig. 12.

Comparison of cost carbon emissions and energy utilization rate under scenarios R0 to R6 with ammonia blending ratios ranging from 0 to 30%.

As the ammonia blending ratio increased from 0% (R-0) to 30% (R-6), the total operating cost of the system gradually decreased from 4.0083 million yuan to 3.7852 million yuan, representing a cumulative reduction of 5.6%. This demonstrates the economic improvement potential of ammonia blending technology. However, the cost reduction is not linear: the synthetic ammonia system’s operation and maintenance costs monotonically increase with the ammonia blending ratio, peaking at 108,400 yuan at R-6. Meanwhile, both purchased energy costs and carbon emission costs reach their lowest points at a 15% ammonia blending ratio (R-3), amounting to 1,256,400 yuan and 72,800 yuan respectively—representing reductions of 35.7% and 18.6% compared to the baseline scenario. This indicates that moderate ammonia blending enhances economic viability by optimizing energy structure and reducing environmental costs, while excessively high ratios diminish overall benefits due to increased operational expenses. Regarding environmental impact, carbon emissions reached their lowest point at 4,043.15 tons under the R-3 scenario, representing a 7.3% reduction from the baseline. However, emissions increased beyond this ratio, rising to 4,216.75 tons at R-6, indicating that excessively high ammonia blending may trigger new carbon emission patterns. Energy utilization efficiency continuously improves with increasing ammonia blending ratios, rising from 83.60% to 98.10% in R-5, demonstrating the ammonia energy system’s enhanced capacity to absorb renewable energy. It slightly declines to 97.45% in R-6, indicating the existence of an improvement threshold.

Dispatch impact analysis of ammonia blending ratio

The aforementioned analysis indicates that an ammonia blending ratio of 15% achieves the optimal balance between system economy and low-carbon performance. To gain deeper insight into the specific impact of hydrogen-ammonia synergy on system operation under this ratio, a visual analysis based on the dispatch process of a typical day is further conducted below.

Figure 13 presents the 24‑hour thermal dispatch results under the benchmark scenario (R‑0, ρ = 0%) in subfigure (a) and the optimally configured scenario (R‑3, ρ = 15%)—which achieves the best economic and carbon emission performance—in subfigure (b). The comparison visually demonstrates the substantial impact of hydrogen–ammonia synergy on the system’s heating strategy and operational flexibility.

Fig. 13.

Heat output balance between baseline scenario (R-0) and scenario (R-3). Note: Abbreviations of system components in the figure are elaborated in detail in Sect. 2.2 and 3.2.2.

As shown in Fig. 13-(a), under the baseline scenario (R-0), the thermal load is primarily borne by boilers and combined heat and power (CHP) units, whose output curves are smooth and closely follow changes in the total thermal load. This indicates that in the absence of flexible electricity-hydrogen-ammonia conversion resources, the system must rely heavily on traditional fossil fuel facilities to meet thermal demands, employing a relatively straightforward scheduling strategy that lacks flexibility. However, as shown in Fig. 13-(b), the optimized scenario (R-3) incorporating the hydrogen-ammonia synergistic chain brings significant changes to the heating structure. First, the output variability of boilers and CHP units markedly increases. Between 00:00 and 06:00, ammonia production within the system substantially elevates the output share of ammonia-blended gas turbines integrated into CHP. This directly reflects the carbon reduction benefits of ammonia-blended combustion, enabling the system to adjust conventional heat source operations more flexibly while meeting environmental constraints. Second, thermal storage systems operate at higher intensity, absorbing excess heat during low-demand periods and rapidly releasing energy during peak demand.

To illustrate the impact of ammonia blending on power dispatch, Fig. 14-(a) and (b) compare 24-hour power dispatch under the baseline scenario (R-0) and the optimized scenario (R-3), respectively.

Fig. 14.

Power output balance between baseline scenario (R-0) and scenario (R-3). Note: Abbreviations of system components in the figure are elaborated in detail in Sect. 2.2 and 3.2.2.

In the baseline scenario (R-0), the system exhibits typical characteristics of conventional operation. Power supply primarily relies on renewable energy and gas turbines. When electricity demand significantly increases, the system requires power input from the grid to meet load requirements. Renewable energy output peaks during the 00:00–05:00 and 23:00–00:00 periods when electricity demand is low. EL enhances the integration capacity of wind and solar power as flexible, adjustable equipment. However, without the ammonia cycle in operation, the overall scale of energy conversion within the system is limited, significantly reducing its regulation capability. The ORC system provides stable auxiliary power generation, but the system operation remains passive and exhibits strong dependence on the external grid.

In the optimized scenario (R-3), the power dispatch pattern undergoes a significant transformation, driven by the flexible regulation of the hydrogen-ammonia synergy chain: During peak renewable energy output periods, the large-scale operation of electrolysers and ammonia synthesis units effectively absorbs surplus electricity. When output is insufficient, ammonia fuel cells and hydrogen fuel cells efficiently convert stored chemical energy back into electricity. Gas turbines continue to provide baseload power, demonstrating higher output than the baseline scenario during most periods. This reflects the enhanced scheduling priority of gas turbines after ammonia blending reduces carbon costs, optimizing their operational mode. Concurrently, increased output from gas turbines and fuel cells enables active and stable operation of the ORC system, boosting overall energy utilization efficiency. By establishing a multi-energy complementary conversion platform, the optimized scenario not only achieves efficient integration of intermittent renewable energy but also significantly enhances the economic viability and operational flexibility of the system.

Comparison analysis of different uncertainty optimization methods

The selection of uncertainty handling methods in integrated energy system optimization is crucial for influencing the economic efficiency and robustness of scheduling strategies. In response to source load uncertainty optimization models regulate the risk level of decisions by introducing key conservativeness parameters which directly affect the utilization of renewable energy and system operation strategies. This section conducts a comparative analysis under the same system architecture identical equipment parameters and source load data comparing the Stochastic Programming (SP) method adopted in this paper with classical Robust Optimization (RO) and Distributionally Robust Optimization (DRO). To ensure a fair comparison the capacity planning results from Sect. 5.2 with the optimal configuration 15 ammonia blending ratio are used for the upper layer The comparative results are presented in Figs. 15 and 16, and 17.

Fig. 15.

Annualized cost comparison of SP RO and DRO. Note: SP stands for stochastic programming; RO stands for robust optimization; DRO stands for distributionally robust optimization, respectively. Note: SP stands for Stochastic Programming; RO stands for Robust Optimization; DRO stands for Distributionally Robust Optimization, respectively.

Fig. 16.

Annual carbon emission comparison of SP RO and DRO. Note: SP stands for stochastic programming; RO stands for robust optimization; dro stands for distributionally robust optimization, respectively. Note: SP stands for Stochastic Programming; RO stands for Robust Optimization; DRO stands for Distributionally Robust Optimization, respectively.

Fig. 17.

Curtailment rate comparison of SP RO and DRO. Note: SP stands for stochastic programming; RO stands for robust optimization; DRO stands for distributionally robust optimization, respectively. Note: SP stands for Stochastic Programming; RO stands for Robust Optimization; DRO stands for Distributionally Robust Optimization, respectively.

Figures 15 and 16, and 17 each contain three subplots, respectively illustrating the relationship between the key conservativeness parameters and operational outcomes for three different optimization methods when handling system uncertainty. The SP method demonstrates superior performance in terms of cost and carbon emission control. Particularly when the confidence level α is appropriately set, it can achieve lower operational expenditure and carbon footprint. However, this comes at the cost of a relatively higher renewable curtailment rate, indicating a weaker capability for accommodating volatile renewable energy and potentially lower operational reliability. Conversely, RO and its derivative, DRO, can significantly enhance the system’s ability to cope with uncertainty by increasing the robustness parameters Γ and ε. This effectively minimizes the curtailment rate, thereby ensuring power supply security and maximizing renewable energy utilization. Nevertheless, this advantage is traded for substantially increased economic costs and higher carbon emissions.

This section, through systematic comparative experiments, demonstrates that the selection of an uncertainty optimization method is ultimately a decision based on risk preference and data availability. The two-layer framework and the LSDBO-WOA algorithm constructed in this study exhibit good generality and can be adapted to different paradigms such as SP and RO. For the park-level integrated energy system targeted in this research, given the condition of possessing relatively comprehensive historical data, employing SP and making decisions within the α∈[0.85, 0.90] interval can achieve lower carbon emissions and an acceptable curtailment rate under controllable costs.

Discussion and limitations

(1) The proposed LSDBO-WOA algorithm and the bi‑level optimization framework demonstrate satisfactory performance when applied to the park‑scale integrated energy system considered in this study. However, as system scale expands substantially, or when more refined device dynamics and complex network topologies are incorporated, the convergence time and solution stability of the algorithm may face significant challenges. Future research should explore more efficient hierarchical or distributed solution strategies, as well as data‑driven approaches such as reinforcement learning, to enhance computational scalability for large‑scale systems.

(2) In practical engineering contexts, the long‑term safe storage of liquid ammonia—entailing risks of toxicity, corrosion, and leakage—as well as its transportation, pose critical technical and managerial hurdles. Additionally, ammonia co‑firing introduces challenges including NOₓ emission control, flame stability, and turbine corrosion, all of which must be addressed prior to real‑world deployment. These factors warrant explicit consideration in future investigations.

(3) The cost‑benefit analysis conducted in this study is based on current equipment cost estimates and prevailing market prices. However, the hydrogen–ammonia industrial chain remains in an early stage of commercialization, and substantial uncertainties persist regarding the capital costs, operational lifespans, and maintenance expenses of key components. Such uncertainties may significantly influence the feasibility and economic viability of the proposed scheduling strategies in actual systems.

Conclusion

This study addresses the challenges of integration and operational flexibility in high-penetration renewable energy systems by establishing an integrated energy system optimization framework that synergizes electricity, hydrogen, ammonia, and heat flows while effectively managing source–load uncertainties. Through systematic modeling, algorithmic innovation, and simulation validation, the following conclusions are drawn:

(1) The proposed system framework, with liquid ammonia as the core energy storage and conversion hub, forms an organically coordinated energy cycle through three energy release pathways: fuel cell power generation, cracking, and direct utilization. Case study results show that this architecture increases the energy utilization efficiency from 83.60% in the baseline scenario to over 97.66%. Moreover, the introduction of the ammonia loop achieves approximately 7.3% reduction in carbon emissions.

(2) To overcome the slow convergence and local optimum issues of traditional algorithms in solving high-dimensional nonlinear multi-objective problems, this paper innovatively proposes the LSDBO-WOA algorithm by integrating enhanced dung beetle optimization and whale optimization mechanisms. Performance comparisons show that the algorithm improves convergence accuracy by an average of 23.3% and enhances distribution uniformity by 35%.

(3) The dual-layer model developed in this paper combines upper-layer multi-objective capacity planning with lower-layer stochastic chance-constrained scheduling. By incorporating operational metric feedback and an upper-layer adaptive correction mechanism, it overcomes the traditional unidirectional “planning-to-scheduling” limitation. Simulation results reveal trade-offs among economy, environmental performance, and energy utilization at different ammonia blending ratios, with 15% identified as the optimal operating point. Furthermore, to address source–load uncertainty, an optimal confidence level range of 0.85–0.9 is identified. Within this range, the system achieves low carbon emissions and acceptable energy utilization at controllable costs, providing quantitative support for risk-informed decision-making in practical engineering applications.

(4) Comparing dispatch results between the baseline and optimized scenarios shows that the hydrogen–ammonia loop transforms the system from a passive mode reliant on external grids and conventional units to an active, self-sufficient mode that leverages internal multi-energy conversion and storage. The system stores surplus renewable energy as hydrogen and ammonia during periods of excess generation, and stabilizes supply via fuel cells and ammonia-blended gas turbines during periods of insufficient output. This fundamentally enhances the system’s renewable energy absorption capacity and supply flexibility.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Naiwei Tu: Methodology, Formal analysis, Writing – review & editing.Jinda Yang: Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing – original draft, Visualization.Xin Yan: Conceptualization, Supervision, Project administration.Zuhao Fan: Writing – review & editing, Funding acquisition.

Data availability

The datasets generated and analyzed during the current study are not publicly available due to our laboratory’s internal policies and confidentiality agreements, but are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.