Capacity Optimization Allocation of Multi-Energy-Coupled Integrated Energy System Based on Energy Storage Priority Strategy

Abstract

As the global focus on environmental conservation and energy stability intensifies, enhancing energy efficiency and mitigating pollution emissions have emerged as pivotal issues that cannot be overlooked. In order to make a multi-energy-coupled integrated energy system (IES) that can meet the demand of load diversity under low-carbon economic operation, an optimal capacity allocation model of an electricity–heat–hydrogen multi-energy-coupled IES is proposed, with the objectives of minimizing operating costs and pollutant emissions and minimizing peak-to-valley loads on the grid side. Different Energy management strategies with different storage priorities are proposed, and the proposed NSNGO algorithm is used to solve the above model. The results show that the total profit after optimization is 5.91% higher on average compared to the comparison type, and the pollutant emission scalar function is reduced by 980.64 (g), which is 7.48% lower. The peak–valley difference of the regional power system before optimization is 0.5952, and the peak–valley difference of the regional power system after optimization is 0.4142, which is reduced by 30.40%, and the proposed capacity allocation method can realize the economic operation of the multi-energy-coupled integrated energy system.

1. Introduction

With the escalating global interest in environmental conservation and securing energy supplies, the urgency to enhance energy efficiency and decrease pollutant emissions has become undeniably prominent. The advent of electric vehicles (EVs) and advancements in energy provisioning have reshaped the conventional gas station into a multifaceted integrated energy hub, integrating a wide array of innovative energy technologies. The optimization of capacity allocation within this integrated energy hub is currently a focal point of research, primarily due to its direct correlation with the economy, reliability, and environmental sustainability of the energy system. In the context of a multi-energy-coupled integrated energy system, the role of capacity allocation optimization is paramount. Researchers are actively engaged in exploring the dispatch of EVs to harness electricity from renewable energy systems and charging stations, the configuration of renewable energy sources and energy storage capacities at charging stations, and the analysis of hydrogen production via renewable energy. The intermittent and volatile nature of renewable energy generation can potentially jeopardize the stability of the main power grid [1]. To mitigate this challenge, energy storage technologies (ESTs) have emerged as a pivotal solution, offering bidirectional power flow capabilities and operational flexibility [2]. Proper allocation of capacities ensures that the energy system meets demand while minimizing costs. By fine-tuning the capacity configurations of various energy modules, the energy system can achieve efficient utilization and reduce resource wastage, ultimately enhancing the economic performance of the entire integrated energy hub.

Comprehensive energy station capacity configuration is a multifaceted and intricate endeavor that necessitates a holistic consideration of various factors, including regional energy demand patterns, renewable energy resource availability, energy storage technology advancements, grid connectivity, policy directives, and more. Through the strategic optimization of energy equipment capacity ratios, an efficient and sustainable energy system can be established. Zhao et al. [3] introduced a method for allocating rated capacity and power to a regional integrated energy system (IES)’s electric and thermal energy storage devices in both off-grid and grid-connected scenarios. Their findings revealed that an integrated energy storage model offers the greatest cost-effectiveness. However, single-objective optimization approaches have limitations, as they often overlook environmental and reliability aspects. Multi-objective optimization, which considers combinations of electric and thermal energy storage, particularly in systems like cogeneration units and solar systems, provides significant advantages [4,5]. Yan et al. [6] and Guo et al. [7] optimized the configuration of lithium-ion batteries and thermal storage tanks based on fitting functions, load aggregation models, and user behavior, taking into account seasonal variations in electricity demand. With the advancing technologies of power-to-gas (P2G) and hydrogen fuel cells, the integration of electricity and natural gas networks, along with hydrogen storage and supply, has been enhanced. Consequently, the combined form of electric–thermal–gas multi-energy systems (MESs) has garnered increasing attention. Bartolini et al. [8] optimized the capacity of batteries, thermal energy storage, hydrogen, and gas engines at minimal cost in a community with high renewable energy penetration, demonstrating that energy storage technologies are crucial in mitigating the surge in grid demand. While thermal and cold energy storage has traditionally been used in air-conditioning systems through ice storage, the combination of electricity, cooling, and heat has recently garnered significant interest. Luo and Shao et al. [9] proposed a combination of different energy storage configurations, including ice storage, to harness renewable energy sources and reduce emissions in the North China Industrial Park. However, their capacity planning was solely based on load levels and hours of operation. In recent years, with the advent of the Net Zero Energy Community (NZEC) concept, energy storage forms such as electric vehicles (EVs) and hydrogen vehicles (HVs) have been increasingly explored [10,11,12], aiming to develop more flexible and extensive multi-energy-coupled energy storage systems. Larry Orobome Agberegha et al. [13] introduced an innovative combined steam–steam cascade triplex cycle system incorporating vapor absorption refrigeration and district heating systems, which efficiently converts low-temperature thermal energy. Amir Ahmarinejad [14] proposed a multi-objective optimization framework for long-term planning of the energy center. By taking into account equipment degradation and integrated demand response plan, the goals of cost reduction, emission reduction and optimization of wheel wear were achieved, and load supply was ensured until the end of the planning period. Through energy and exergy analyses, they demonstrated significant improvements in energy efficiency and the potential to address global energy.

Li proposes an Adaptive Reference Vector Evolutionary Algorithm (ARVEA), JH, in a recent study on many-objective optimization algorithms, etc. It effectively solves a multi-objective problem by combining the Pareto dominance and the ASF function as a selection criterion and introducing an adaptive method of reference vectors to adjust the distributions of various Pareto frontier types [15]. A novel multi-objective evolutionary algorithm named ABOEA was presented by Yang, along with its effectiveness in solving multi-objective problems [16]. Jiang introduced an adaptive weighted decomposition multi-objective evolutionary method to solve intricate multi-objective problems with non-Pareto front ends [17]. An efficient reference-direction-based density estimator, a new fitness allocation scheme, and a new environment selection method were introduced by Jiang to reevaluate a computationally demanding intensity Pareto-based evolutionary algorithm for solving multi-objective and multi-objective problems [18]. Chen presented an evolutionary algorithm with an adaptive switching approach for multi-objective optimization problems to lessen selection pressure and boost variety. This method adaptively switches between two deletion criteria in the environment selection process [19]. The trial outcomes demonstrated the algorithm’s benefits and efficacy in solving common benchmarking and water resource planning issues. To tackle multi-objective optimization problems with irregular Pareto frontiers, Sun suggested a decomposition and hierarchical clustering-based selection technique. This included the introduction of uniformly distributed reference vectors, adaptive reference vectors, and a hierarchical clustering selection strategy [20]. The outcomes of the experiment show an enhanced version of Zhang’s integral dominance algorithm with adaptive selection probabilities [21]. However, better local search capabilities and quicker processing speeds are still required for the mutual feeding process between the energy storage system and the regional power grid. Multi-objective optimization algorithms usually contain two important search strategies: global search and local search. By combining the two strategies of global and local search, multi-objective optimization algorithms are able to make full use of the breadth of global search and the precision of local search during the search process, thus effectively discovering a set of high-quality solutions, providing diversified choices for decision makers, and facilitating the comprehensiveness and diversity of the problem solution. In this paper, we propose a global search convergence metric for evaluating the degree of global/local convergence of an algorithm. We combine the NSGA-III Genetic Operator (GA) and the MONGO Optimization Operator (NGO) to address this problem. We choose to combine the genetic operator (GA) in the NSGA-III algorithm with the optimization operator (NGO) in the MONGO algorithm. This is because the genetic operator of the NSGA-III algorithm has an excellent global search capability, while the NGO operator exhibits an excellent local search capability. We combine these two operators and apply CM metrics to construct a novel multi-objective hybrid algorithm (NSNGO). This can significantly improve the convergence and distribution of the algorithm [22].

This paper reviews the concepts, frameworks, and improvement strategies of capacity allocation models for integrated energy systems with multi-energy coupling and proposes the Northern Eagle algorithm based on non-dominated ordering. The contributions of this paper are summarized as follows:

(1)

A model for optimizing capacity allocation in a multi-energy-coupled integrated energy station is introduced. This model provides an improved representation of the energy management system within the IES.

(2)

The three objective functions proposed in this paper can effectively reduce the operating costs of the integrated energy station and the pollutant emissions from the station and, at the same time, reduce the peak-to-valley load difference of the regional power system, so as to achieve a balance of interests between the integrated energy system and the power grid.

(3)

A multi-objective optimization algorithm (NSNGO) based on the non-dominated sorting northern pale eagle high-latitude multi-objective optimization algorithm (NSNGO) is proposed, which is shown to be excellent in generating high-quality optimal solutions through a comparative analysis, and an evaluation index convergence metric (CM) for evaluating the extent of the global search/local search is also proposed, which is capable of reflecting whether or not the algorithm has sufficiently explored the search space.

(4)

An energy management strategy for storage prioritization is proposed to determine the optimal allocation of storage capacity by exploring the impacts of three energy sources under different storage prioritization levels, thus helping to effectively manage energy resources and ensure sustainable operation.

In the second part of this paper, the proposed integrated energy addition station and the framework are introduced; in the third part, the structure and the multi-objective optimization model of the IES battery storage system are given, respectively; in the fourth part, the NSNGO optimization algorithm is proposed, and the results of the benchmarking-function DTLZ series of problems are analyzed in comparison with those of different multi-objective algorithms; and in the fifth part, simulation experiments are conducted to solve the model and perform a typical simulation using the proposed NSNGO algorithm. And finally, the full paper is summarized.

2. Multi-Energy-Coupled Integrated Energy System Structure and Modeling

The structure of the integrated energy system constructed in this paper is shown in Figure 1, in which the electric load is provided by the on-grid wind turbine (WT), photovoltaic (PV), energy storage (ES), battery-charging station (BCS), battery-switching station (BSS), and gas turbine (GT), and the heat load is provided by the gas boiler (GB), electric boiler (GB), gas turbine (GT), gas boiler (GB), and the CO₂ generated from the grid, which will be delivered to the P2G plant. Hydrogen storage tanks (HTs) will be used to store the hydrogen produced during the P2G water electrolysis process and to charge the hydrogen vehicles (HVs). PG, HN, and HG are power grid, hydrogen network, and hot grid, respectively.

The integrated energy system proposed in this paper includes a variety of energy and conversion technologies to provide electrical, thermal, and hydrogen loads.

(1)

Power load supply:

The system provides the power load primarily through grid-connected wind turbines (WTs) and photovoltaic (PV) panels utilizing renewable energy sources. Energy storage (ES)-system integration is performed to balance supply and demand for reliability and efficiency. Battery-charging stations (BCSs) and battery-switching stations (BSSs) facilitate the charging and management of electric-vehicle batteries. The gas turbine (GT) also contributes to the power load, providing flexibility and backup power.

(2)

Heat load supply:

The heat load uses gas boilers (GBs) and electric boilers (EBs), which can generate electricity from natural gas or electricity. Gas turbines (GTs) also have dual uses, generating electricity and heat (combined heat and power). The system takes into account the carbon dioxide emissions generated by the grid and plans to use these emissions in the electricity to gas (P2G) plant, reducing carbon emissions and utilizing the gas.

(3)

Hydrogen production and storage:

The system in this paper integrates a P2G plant to convert renewable electricity into hydrogen via hydro-electrolysis. Hydrogen storage tanks (HTs) are used to store produced hydrogen, ensuring its availability for a variety of applications. These hydrogen tanks also support the charging of hydrogen-fueled vehicles (HVs), facilitating the transition to clean and sustainable transportation.

(4)

Network Integration:

The system seamlessly integrates three key networks: power grid (PG), hydrogen network (HN), and heat network (HG). This integration allows for efficient energy distribution, optimization, and utilization across different sectors.

The multi-energy-oupled integrated energy system in this paper represents a forward-looking approach to energy management that balances the use of renewable energy, carbon reduction, and the transition to low-carbon fuels such as hydrogen. By integrating multiple energy sources and conversion technologies, it aims to improve energy security, sustainability, and efficiency.

2.1. Wind Turbine Model

Wind power is a technology that converts wind energy into electricity. It is a clean and renewable form of energy that can reduce dependence on traditional energy sources, such as fossil fuels, and minimize negative environmental impacts. The wind turbine model is as follows:

$$P_{WT}=\left\{\begin{array}{l}0\\ {\displaystyle \frac{P_R}{V_R^3-V_{ci}^3}}\cdot V^3-{\displaystyle \frac{V_{ci}^3}{V_R^3-V_{ci}^3}}\cdot P_R\\ P_R\\ 0\end{array}\right.$$

(1)

where $V$, $P_R$, $V_R$, $V_{ci}$, and $V_{co}$ are the actual wind speed measured at the hub height of the turbine (in meters per second), the rated power capacity of the turbine (in kilowatts), the rated wind speed for optimal performance (in meters per second), and the cut-in and cut-out wind speeds that define the operational range of the turbine (both in meters per second) [23].

2.2. Photovoltaic Model

Photovoltaic power generation entails the conversion of sunlight into electrical energy through the utilization of the photovoltaic effect. The power output of a PV module can be formulated based on several factors, including the solar irradiation intensity on the PV panel ($G_{\beta }$)’s surface (measured in watts per square meter), the operational temperature of the PV panel ($T_0$) (in degrees Celsius), the efficiency of the inverter (${\eta }_{inv}$), and the percentage of losses (${\eta }_{loss}$) incurred [24]:

$$P_{PV}=\left[{\eta }_{inv}\cdot {\eta }_{loss}\cdot {\eta }_{ref}\cdot \left(1-k\cdot \left(T_0-T_{ref}\right)\right)\right]\cdot A_{PV}\cdot G_{\beta }$$

(2)

where ${\eta }_{ref}$ signifies the reference efficiency of the PV module at a standard temperature of 25 °C, denoted as $T_{ref}$, with the unit being a percentage (%). The symbol $k$ represents the temperature coefficient, while $A_{PV}$ indicates the designated area of the PV array in the hybrid system, measured in square meters (m²). The parameters are shown in Supplementary Table S1.

2.3. Hydrogen Production System Model

The hydrogen production, storage, and charging system provides the hydrogen fuel demand for hydrogen-fueled vehicles. Electric power is fed into the electrolyzer through the DC bus and DC/DC module. The electrolyzer electrolyzes water to obtain hydrogen. The energy conversion relationship in the process of hydrogen production is shown in Figure 2.

In a multi-energy-coupled integrated energy system, the hydrogen production process is a key link, which involves using renewable energy sources (electricity generated by solar panels and wind turbines) as inputs to split water into hydrogen and oxygen through water electrolysis technology. In this process, the electricity is first converted into a direct current suitable for electrolysis and then supplied to the electrolytic water equipment. After possible purification and compression treatment, the produced hydrogen is stored in hydrogen storage tanks for supply to hydrogen fuel cells or other hydrogen using equipment when needed. At the same time, the entire system also includes electric energy conversion devices such as battery chargers, as well as different connection points connecting these devices, which together constitute a complete energy conversion, storage, and supply system. In this process, the electrical energy conversion and storage equipment plays a crucial role in ensuring the smooth progress of the hydrogen production process and the effective use of hydrogen.

2.3.1. Electrolyzer Model

The electrolyzer electrolyzes water to obtain hydrogen. The reaction of electrolyzer electrolysis of water is shown in Equation (3). The polymer electrolyte membrane (PEM) electrolyzer has the advantages of low operating temperature, simple structure, and high-purity hydrogen production when the pressure reaches 200 bar. The calculation model of the PEM electrolyzer electrolysis water conversion is shown in Equations (3) and (4) [25]:

$$H_{2}O+Electricity\to H_2+{\displaystyle \frac{1}{2}}{O}_2$$

(3)

$$P_t^{ELE}={\displaystyle \frac{m_t^{ELE}\cdot LH{V}_{H_2}}{{\eta }_{ELE}}}$$

(4)

where ${\eta }_{ELE}$ is the electrolyzer efficiency, $m_t^{ELE}$ is the mass flow rate of hydrogen gas at the output of the electrolyzer, $LH{V}_{H_2}$ is the lower calorific value of hydrogen, and $P_t^{ELE}$ is the power consumed by the electrolyzer at time t. Parameters are shown in Supplementary Table S2.

2.3.2. Compressor Model

A compressor is a mechanical device used to compress gases or vapors. It works by increasing the gas pressure by decreasing the volume of the gas, thus compressing the gas into a smaller space. The compressor operates in parallel with the electrolysis of hydrogen water, where a photovoltaic module, a wind module, and a parallel grid power the compressor. The compressor model is shown in Equation (5) [26].

$$P_t^{comp}=C_{comp}\cdot {\displaystyle \frac{T_{in}\times {10}^4}{{\eta }_{motor}\cdot {\eta }_{comp}\cdot \Delta t}}\left({\left({\displaystyle \frac{p_{out}^{comp}}{p_{in}^{comp}}}\right)}^{{\displaystyle \frac{r-1}{r}}}-1\right)\cdot {\displaystyle \frac{m_t^{ELE}}{3600}}$$

(5)

where $C_{comp}$ represents the constant-pressure specific heat of hydrogen; $P_t^{comp}$ signifies the power utilized by the compressor motor at a given time t; $p_{in}^{comp}$ and $p_{out}^{comp}$ designate the inlet and outlet pressures of the compressor, respectively; r is the specific heat ratio for hydrogen; $T_{in}$ represents the temperature of the hydrogen at the compressor’s inlet; ${\eta }_{comp}$ signifies the isentropic efficiency of the compressor; and ${\eta }_{motor}$ denotes its mechanical efficiency. The parameters are shown in Supplementary Table S3.

2.3.3. Hydrogen Storage Tank Model

The principle of high-pressure hydrogen storage is to compress hydrogen to a very high pressure to reduce the hydrogen volume and increase the storage density. Over-pressure hydrogen storage allows for storing a greater quantity of hydrogen in a smaller space, thus increasing the efficiency of hydrogen storage. High-pressure hydrogen storage tanks store hydrogen from a compressor and supply it to a distributor to meet the hydrogen demand of a high-pressure boiler at different times. As a result, Equation (6) demonstrates the fluctuation in hydrogen content within HT.

$$SO{C}_{t+1}^{HT}=[(1-{\phi }^{HT})\cdot SO{C}_t^{HT}+(m_t^{ELE}-m_t^{HV})\cdot C_{HT}]$$

(6)

where $SO{C}_t^{HT}$ and $SO{C}_{t+1}^{HT}$ represent the hydrogen storage levels in HT at times t’ and t + 1, respectively, both measured in percentage (%); $m_t^{HV}$ signifies the amount of hydrogen supplied to heavy vehicles (HVs) at time ‘t’; and ${\phi }^{HT}$ is the coefficient representing hydrogen loss in HT, while $C_{HT}$ denotes the total capacity of HT. The parameters are shown in Supplementary Table S4.

2.4. Heat Production Model

2.4.1. Gas Turbine Model

The gas turbine is one of the core pieces of equipment of the IES, which can satisfy the multi-stage utilization of various energies, and the rest of the heat is supplied to the heat load through the waste heat boiler. The modeled power of the gas turbine is shown in Equation (7):

$$\left\{\begin{array}{l}{P}_{\mathrm{GT}}(t)=P_{\mathrm{GTe}}(t)+P_{\mathrm{GTh}}(t)\\ P_{\mathrm{GTe}}(t)={\eta }_{\mathrm{GTe}}(t)P_{\mathrm{GTin}}(t)\\ P_{\mathrm{GTh}}(t)={\eta }_{\mathrm{GTh}}(t)P_{\mathrm{GTin}}(t)\end{array}\right.$$

(7)

where $P_{\mathrm{GT}}(t)$ is the power of the gas turbine at time t; $P_{\mathrm{GTh}}(t)$ and $P_{\mathrm{GTe}}(t)$ are the electric and thermal power of the gas turbine at time t; and ${\eta }_{\mathrm{GTe}}(t)$ and ${\eta }_{\mathrm{GTh}}(t)$, are the electric and thermal efficiency of the gas turbine at time t, respectively.

2.4.2. Gas Boiler Model

The heat energy in IES is provided by a gas boiler. Among them, the vertical boiler has low smoke emissions, a large heat exchange capacity, and high thermal efficiency, and its heat output is related to the rate of change in the load. The modeled power of the gas boiler is shown in Equation (8):

$$P_{\mathrm{GB},t}={\eta }_{\mathrm{GB}}{Q}_{{\mathrm{CH}}_4,t}^{\mathrm{GB}}{H}_{\mathrm{HV}}$$

(8)

where $P_{\mathrm{GB},t}$ is the thermal power of the gas boiler at time t, ${\eta }_{\mathrm{GB}}$ is the efficiency of the gas boiler, and $Q_{{\mathrm{CH}}_4,t}^{\mathrm{GB}}$ is the natural gas consumption at time t.

2.4.3. Waste Heat Boiler Model

The waste heat boiler recovers the flue gas heat after the gas turbine generates electricity and produces heat from it, and its mathematical model is as follows:

$$P_{\mathrm{YR},t}={\eta }_{\mathrm{YR}}{P}_{\mathrm{YR},t}^{\mathrm{in}}$$

(9)

where $P_{\mathrm{YR},t}$ is the waste heat power of the system at time t, ${\eta }_{\mathrm{YR}}$ is the heat production efficiency of the waste heat boiler, and $P_{\mathrm{YR},t}^{\mathrm{in}}$ is the heat power recovered by the waste heat boiler at time t.

2.5. Battery Energy Storage System Model

2.5.1. Battery Charging Station

Equation (7) illustrates the process of battery charging and discharging during the charging mode of the Battery Energy Storage System (BESS),

$$SO{C}_t^{BCS}={\displaystyle \frac{\left[E_{t-1}^{BCS}\times \left(1-\sigma \right)+P_{charge,t}\times {\eta }_{charge}\times \Delta t_1-P_{disharge,t}\times {\eta }_{disharge}\times \Delta t_2\right]}{C_{BCS}}}$$

(10)

where $SO{C}_t^{BCS}$ is the SOC state of BCS at time t; $E_{t-1}^{BCS}$ is the charge of BCS at time t – 1; $\sigma$ is the self-discharge rate of the battery; $P_{charge,t}$ is the charging power of the battery at time t; ${\eta }_{charge}$ is the charging efficiency of battery; $P_{disharge,t}$ is the discharge power of the cell at time t; ${\eta }_{disharge}$ is the discharge power of battery; $\Delta t_1$ and $\Delta t_2$ are the charge interval and discharge interval of the battery, respectively; and $C_{BCS}$ is the total battery capacity of BCS.

2.5.2. Battery-Switching Station

In the swapping mode of the Battery Energy Storage System (BESS), the battery can be in either a charged or fully charged state. Here, $N_t^{full}$ represents the number of fully charged cells, while $N_t^{charge}$ denotes the number of batteries in the charging state. The following equation presents the dynamic model of the battery-swapping station [27].

$$\left\{\begin{array}{l}{N}_t^{full}=N_{t-1}^{full}-N_{t-1}^{EV,BSS}\\ W_t^{BSS}={\displaystyle \sum _n^N\left[\left(0.9-SO{C}_{t-1,n}^{EV,BSS}\right)\times C_{Battery}\right]}\end{array}\right.$$

(11)

In this context, $N_{t-1}^{EV,BSS}$ signifies the number of electric vehicles that were exchanged for electricity at the previous time step (t − 1); $W_t^{BSS}$ represents the electricity consumed by the battery after both the swapping station and the electric vehicles have been fully charged at the current time step (t); $SO{C}_{t-1,n}^{EV,BSS}$ denotes the state of charge (SOC) of the battery when the n-th electric car undergoes swapping at the previous time step (t − 1); and $C_{Battery}$ indicates the capacity of a single.

2.6. Objective Function

The three objective functions pursued by the multi-energy-coupled integrated energy system are maximization of total profit, minimization of total emissions, and minimization of peak-to-valley load spread on the grid side.

2.6.1. Total Profit

From the operational point of view of the integrated energy system, the total profit of the integrated energy system is a fundamental goal.

$$f_1=\min \left(m_{\mathrm{e}}+m_{\mathrm{g}}\right)$$

(12)

$$m_{\mathrm{e}}=\sum _{t=1}^{24}\left[p_{\mathrm{e}}\left(t\right)P_{\mathrm{in}}\left(t\right)\Delta t\right]$$

(13)

$$m_{\mathrm{g}}=p_{\mathrm{g}}\sum _{t=1}^{24}\left[{\displaystyle \frac{P_{\mathrm{ge}}\left(t\right)}{{\eta }_{\mathrm{ge}}}}+{\displaystyle \frac{P_{\mathrm{gb}}\left(t\right)}{{\eta }_{\mathrm{gb}}}}\right]\Delta t$$

(14)

where $m_{\mathrm{e}}$ and $m_{\mathrm{g}}$, respectively, represent the cost of purchasing electricity and gas; $P_{\mathrm{in}}\left(t\right)$ represents the actual power of the power grid; $p_{\mathrm{e}}\left(t\right)$ represents the price of electricity at time t; $p_{\mathrm{g}}$ represents the price of gas; ${\eta }_{\mathrm{ge}}$ is the gas turbine power generation efficiency; $P_{\mathrm{gb}}\left(t\right)$ is the power generation of the gas boiler at time t; ${\eta }_{\mathrm{gb}}$ is the heat production efficiency of the gas boiler; and $P_{\mathrm{gb}}\left(t\right)$ is the heat production power of the gas turbine at time t.

2.6.2. Total Emissions

The primary power sources for the IES are WT and PV. In this research, a majority of the environmental pollution emissions from the station stem from the electricity it purchases from the grid. Therefore, the objective function is to minimize the emissions of $S{O}_2$, $N{O}_x$, and $C{O}_2$. The objective function is as follows:

$$\min F_{C{O}_2,S{O}_2,N{O}_x}={\displaystyle \sum _{t=1}^T{W}_{buy,t}^{Grid}\times \left(e_{C{O}_2}+e_{S{O}_2}+e_{N{O}_x}\right)}$$

(15)

$$W_{buy,t}^{Grid}=P_{charge,t}^{BCS}\times \Delta t_1+W_t^{BSS}+W_{charge,t}^{EV}+{\displaystyle \frac{\Delta SO{C}_{t,t-1}^{HT}\times C_{HT}}{{\eta }_{H_2}}}-W_t^{WP}$$

(16)

where $W_{buy,t}^{Grid}$ is the amount of electricity purchased from the grid in time period t; $e_{C{O}_2}$, $e_{S{O}_2}$, and $e_{N{O}_x}$ are the emission factors of $S{O}_2$, $N{O}_x$, and $C{O}_2$ per kW·h from the utility grid, respectively; and $W_t^{WP}$ is the amount of wind and photovoltaic power generated at time t.

2.6.3. Rate of Peak–Valley

As a distributed energy storage unit, the charging and discharging operations of the Battery Energy Storage System (BESS) can influence the regional power system’s load to a certain degree. Therefore, optimal scheduling and rational charging/discharging arrangements of the BESS can help reduce the grid’s peak load and fill in the trough periods, thereby enhancing the grid’s safe and stable operation. The grid-side peak-to-valley load difference ratio serves as an effective indicator to reflect changes in the grid’s peak-to-valley load difference. The formula for calculating the grid-side peak-to-valley ratio is provided in References [28,29,30,31]:

$$P_{load}=(P_{load}(1),P_{load}(2),P_{load}(3),\cdot \cdot \cdot ,P_{load}(24))$$

(17)

$$Z_{load}^{rate}={\displaystyle \frac{\max (P_{load})-\min (P_{load})}{\max (P_{load})}}$$

(18)

where $Z_{load}^{rate}$ is the peak-to-valley difference rate of the load profile. Therefore, this paper establishes the objective function for minimizing the peak-to-valley difference rate of load on the grid side:

$$\min Z_{load}^{rate}={\displaystyle \frac{P_{peak}^t-P_{valley}^t}{P_{peak}^t}}$$

(19)

where $P_{peak}^t$ is the peak hour grid load value after optimization of the energy storage system, and $P_{valley}^t$ is the value of grid load at valley time after optimization of energy storage system.

2.7. Constraints

2.7.1. Power Constraint

The IES shall satisfy thermal, electrical, and gas balance constraints during operation, expressed as follows.

$$\left\{\begin{array}{l}{P}_{\mathrm{esup}}\left(t\right)-P_{\mathrm{ECin}}\left(t\right)+P_{\mathrm{HFCe}}\left(t\right)+P_{\mathrm{GTe}}\left(t\right)+P_{\mathrm{ORC}}\left(t\right)=P_{\mathrm{el}}\left(t\right)\\ P_{\mathrm{GT}2\mathrm{hl}}\left(t\right)+P_{\mathrm{HFC}2\mathrm{hl}}\left(t\right)+P_{\mathrm{GB}}\left(t\right)=P_{\mathrm{hl}}\left(t\right)\\ P_{{\mathrm{H}}_2\mathrm{in}}\left(t\right)=P_{{\mathrm{H}}_2\mathrm{load}}\end{array}\right.$$

(20)

where $P_{\mathrm{esup}}\left(t\right)$ is the electrical output of the supply side at time t; $P_{\mathrm{ECin}}\left(t\right)$ is the electrolyzer input; $P_{\mathrm{HFCe}}\left(t\right)$ is the fuel cell output; $P_{\mathrm{GTe}}\left(t\right)$ is the gas turbine electrical output; $P_{\mathrm{ORC}}\left(t\right)$ is the waste heat generation output; $P_{\mathrm{el}}\left(t\right)$ is the electrical load; $P_{\mathrm{GT}2\mathrm{hl}}\left(t\right)$ is the gas turbine heat output; $P_{\mathrm{HFC}2\mathrm{hl}}\left(t\right)$ is the fuel cell heat output; $P_{\mathrm{GB}}\left(t\right)$ is the boiler output; $P_{\mathrm{hl}}\left(t\right)$ is the heat load; $P_{{\mathrm{H}}_2\mathrm{in}}\left(t\right)$ is the hydrogen storage tank output; and $P_{{\mathrm{H}}_2\mathrm{load}}$ is the hydrogen load.

2.7.2. Electricity and Gas Purchase Constraints

This constraint is for the integrated energy system and grid power purchase and sale, and the constraint equation is shown below.

$$\left\{\begin{array}{c}0\le P_{\mathrm{ebuy}}\left(t\right)\le P_{\mathrm{emet}-\max }\\ 0\le V_{\mathrm{ebuy}}\left(t\right)\le V_{\mathrm{gnet}-\max }\end{array}\right.$$

(21)

where $P_{\mathrm{emet}-\max }$ is the upper limit for the purchase and sale of electricity from the grid by the integrated energy system; and $V_{\mathrm{gnet}-\max }$ is the upper limit for the purchase and sale of gas from the gas grid.

2.7.3. Capacity Constraint

The constraints involve the BESS and HT. Ensure that the energy storage capacity of the system does not exceed the maximum capacity or fall below the minimum capacity. The corresponding formula is presented below:

$$SO{C}_{\min }^{HT}\le SO{C}_t^{HT}\le SO{C}_{\max }^{HT}$$

(22)

$$SO{C}_{\min }^{BESS}\le SO{C}_t^{BESS}\le SO{C}_{\max }^{BESS}$$

(23)

$$SO{C}_{\min }^{BESS}=\left(1-DOD\right)\times SO{C}_{\max }^{BESS}$$

(24)

$$SO{C}_{\min }^{HT}=0,SO{C}_{\max }^{HT}=1,SO{C}_{\min }^{BESS}=0.9,SO{C}_{\max }^{BESS}=0.2$$

(25)

where $SO{C}_{\min }^{HT}$ and $SO{C}_{\max }^{HT}$ are the minimum and maximum capacity states of the hydrogen storage tank, respectively; $SO{C}_{\min }^{BESS}$ and $SO{C}_{\max }^{BESS}$ are the minimum load state and maximum load state of electric vehicle battery, respectively; and DOD is the maximum depth of discharge allowed for the battery.

$$SO{C}_0^{HT}=SO{C}_T^{HT}$$

(26)

$$SO{C}_0^{BCS}=SO{C}_T^{BCS}$$

(27)

$$N_0^{full}=N_T^{full}$$

(28)

where $SO{C}_0^{HT}$ and $SO{C}_T^{HT}$ are the capacity states of HT at the beginning and end of the day, respectively; $SO{C}_0^{BCS}$ and $SO{C}_T^{BCS}$ are the load states of the cells in the BCS at the beginning and end of the day, respectively; and $N_0^{full}$ and $N_T^{full}$ are the number of fully charged cells in the BSS at the beginning and end of the day, respectively.

2.8. Energy Storage Prioritization Strategy

The energy management strategies employed by various multi-energy-coupled integrated energy stations will influence the outcomes of energy storage configurations. In this study, the system’s capacity configuration is established based on the following considerations: (1) giving priority to the direct storage of the most crucial and high-quality energy forms, such as electricity; (2) prioritizing the storage of energy forms with longer durations, like hydrogen; and (3) preferring energy forms with storage densities that exceed energy demand, such as thermal energy. Consequently, an energy storage prioritization strategy is proposed (Figure 3), adhering to the sequence of battery energy storage, hydrogen energy storage, and thermal energy storage. According to this strategy, surplus renewable energy is initially utilized to charge the battery. If the battery is unable to accept further charging, the remaining energy is sequentially directed towards hydrogen storage, followed by thermal energy storage. Any remaining energy shortfall will be addressed by importing power from the grid.

3. Solution Method

3.1. Northern Goshawk Optimization

Northern Goshawk Optimization (NGO) was proposed 2022 by Mohammad Dehghani et al. [32]. This algorithm simulates the behavior of the Northern Goshawk during the hunting process, precisely prey recognition and attack, pursuit, and escape [32,33].

The first stage of hunting, in which the northern goshawk randomly selects its prey and then quickly attacks it, is the global search stage and can be described by the following mathematical model:

$$x_{i,j}^{new,P1}=\left\{\begin{array}{ll}{x}_{i,j}+\left(p_{i,j}-I{x}_{i,j}\right)\hfill & \hspace{1em}F{p}_i<F_i\hfill \\ x_{i,j}+\left(x_{i,j}-p_{i,j}\right)\hfill & \hspace{1em}F{p}_i\ge F_i\hfill \end{array}\right.$$

(29)

$$X_i=\left\{\begin{array}{l}\hspace{1em}{X}_i^{new,P1},\hspace{1em}{F}_i^{new,P1}<F_i\hfill \\ X_i,\hspace{1em}{F}_i^{new,P1}\ge F_i\hfill \end{array}\right.$$

(30)

Pursuit and escape (localized search):

$$x_{i,j}^{new,P2}=x_{i,j}+R(2r-1)x_{i,j}$$

(31)

$$R=0.02\left(1-{\displaystyle \frac{t}{\tau }}\right)$$

(32)

$$X_i=\left\{\begin{array}{l}{X}_i^{new,P2},\hspace{1em}{F}_i^{new,P2}<F_i\hfill \\ X_i,\hspace{1em}{F}_i^{new,P2}\ge F_i\hfill \end{array}\right.$$

(33)

The excellent strategy of the Northern Eagle optimization algorithm is combined with the idea of high-dimensional multi-objective optimization, which draws on NSGA-III’s use of distributional reference points to maintain the diversity of the population under high-dimensional objectives and introduces evaluation indexes for evaluating the extent of the global search/local search to improve the algorithm’s convergence and diversity in the face of three and more multi-objective optimization problems and to make the computed Pareto solution set closer to the absolute Pareto frontiers.

3.2. Convergence Metric

In multi-objective optimization algorithms, the degree of convergence of the global search reflects whether the algorithm has sufficiently explored the search space, so it is crucial to evaluate the degree of convergence of the algorithm’s global search. In this paper, we propose an evaluation metric, the convergence metric (CM), to evaluate the degree of global search/local search, which is based on the average Euclidean distance between the individuals in the population and the reference point to measure the progress of the algorithm’s global search and evaluates the degree of convergence of the algorithm’s population and the form of the search during iteration. The specific formula is as follows: The position of the individuals in the population is set to be $x_i$, uniformly distributed. The position of the reference point is $r_j$, the population size is $N$, and the number of reference points is $M$.

• Calculate the Euclidean distance from the individual $x_i$ to all reference points, $r_j$:

  $$d_{ij}=\sqrt{{\displaystyle \sum _{k=1}^D{\left(x_{ik}-r_{jk}\right)}^2}}$$

  (34)

  where $D$ is the dimension of the problem.
• For each individual $x_i$, calculate its average distance to all reference points:

  $$\overline{d_i}={\displaystyle \frac{1}{M}}{\displaystyle \sum _{j=1}^M{d}_{ij}}$$

  (35)
• Calculate the average distance across the population:

  $$\overline{d}={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N\overline{d_i}}$$

  (36)

The obtained $\overline{d}$ is an indicator of the degree of convergence of the global search of the algorithm. This indicator represents the average distance from each individual in the population to a uniformly distributed reference point. When this average distance is smaller, it means that the individuals in the population are more evenly distributed. That is, the algorithm’s global search has a high degree of convergence, which is conducive to subsequent local searches and improves the algorithm’s convergence speed and accuracy.

We use the NSNGO algorithm to conduct CM metrics experiments to verify the metrics feasibility. Set the maximum number of iterations to MaxGen = 400, the target dimension to M = 4, the number of populations to N = 500, and use the NSNGO algorithm to solve the test function DTLZ1; after the algorithm is run once, record the changes in the CM indexes of the whole iteration process of the algorithm, and the changes in the CM indexes are shown in the following Figure 4.

The algorithm is in a state of continuous reduction in the CM metrics during the iterations, and at about Gen = 40, i.e., the 40th iteration, there is no further significant reduction in the CM values, which have been in a trend of significant reduction until the 40th iteration. The CM values from the 20th iteration to the 50th iteration are shown in the table below.

From the

Table 1. Twenty-to-fifty generations of CM values.

Norm	Number of Iterations
CM	20	21	22	23	24	25	26
	8.11	7.89	6.49	6.33	6.21	5.45	4.23
CM	27	28	29	30	31	32	33
	4.22	4.23	4.20	3.43	3.43	2.86	2.86
CM	34	35	36	37	38	39	40
	2.86	2.27	2.27	2.27	0.98	0.97	0.97
CM	41	42	43	44	45	46	47
	0.98	0.98	0.98	0.98	0.98	0.98	0.98
CM	48	49	50
	0.98	0.98	0.93

, it can be seen that, after the 37th iteration, there is no further significant decrease in the CM metric value. Therefore, it can be proved that the NSNGO algorithm is in the process of global search before about the 37th iteration and in the process of local search after the 37th iteration when solving the DLTZ1 test function.

3.3. Parameter Sensitivity Analysis

In the previous section, we discussed the computation of CM metrics in detail. In this section, we explore a new multi-objective hybrid algorithm that combines CM into the operators of the hybrid algorithm. We combine the genetic operator (GA) of NSGA-III with the optimization operator (NGO) in MONGO. This is because the genetic operator in NSGA-III performs well in the global search, while the optimization operator in NGO excels in local search. By combining these two operators and applying CM metrics, we construct a novel high-latitude multi-objective hybrid algorithm by introducing the non-dominated sorting genetic Northern Goshawk Optimization (NSNGO), or NSNGO for short.

In our proposed NSNGO, we utilize CM metrics to evaluate the algorithm’s search process. The GA algorithm, which is more capable of a global search, is used in the global-search phase, while the NGO algorithm, which is more capable of a local search, is used in the local search phase. This strategy can effectively improve the convergence and distribution of the algorithm.

In order to investigate what value the convergence-index CM reaches when it enters the local search, we solve the DTLZ series of problems with the internationally used benchmark function, take different parameter values as the judgment conditions to judge whether CM reaches the value to enter the local search strategy, and set the maximum population size to N = 400. Then, we consider five cases of the number of objective functions, M = 3, M = 5, M = 8, M = 10, and M = 15; different DTLZs; and different DTLZs for the number of objective functions. The number of iterations for different DTLZ functions with different objective dimensions, m, varies. For each set of parameter values, we perform 30 experiments, and the results of solving the NSNGO proposed in this paper under different parameters, 0.01, 0.05, 0.1, 0.5, and 1, in the DTLZ series of problems are given in Table 1, which gives the maximum, minimum, and the median IGD values for the 30 experiments.

From

Table 2. NSNGO’s maximum, minimum, and median IGD values on the DTLZ1–4 problem at different parameter values (bold is the better value for comparison).

Function	Dimension	MAX Gen	0.01	0.05	0.1	0.5	1
DTLZ1	3	400	2.15 × 10−4	1.92 × 10−4	2.09 × 10−4	4.90 × 10−4	3.18 × 10−4
			1.72 × 10−4	1.68 × 10−4	1.64 × 10−4	1.69 × 10−4	1.75 × 10−4
			1.83 × 10−4	1.80 × 10−4	1.80 × 10−4	2.20 × 10−4	2.00 × 10−4
	5	600	1.09 × 10−3	1.25 × 10−3	4.22 × 10−4	3.89 × 10−4	5.99 × 10−4
			3.24 × 10−4	2.72 × 10−4	2.57 × 10−4	2.68 × 10−4	2.79 × 10−4
			4.46 × 10−4	4.80 × 10−4	3.32 × 10−4	3.44 × 10−4	3.82 × 10−4
	8	750	1.05 × 10−1	7.50 × 10−2	6.74 × 10−2	9.89 × 10−2	8.44 × 10−2
			1.87 × 10−3	1.99 × 10−3	1.86 × 10−3	2.37 × 10−3	1.96 × 10−3
			1.28 × 10−2	1.45 × 10−2	8.98 × 10−3	2.07 × 10−2	1.42 × 10−2
	10	1000	2.12 × 10−1	1.00 × 10−1	8.80 × 10−2	2.90 × 10−1	8.97 × 10−2
			3.56 × 10−3	3.32 × 10−3	3.01 × 10−3	3.88 × 10−3	3.52 × 10−3
			4.04 × 10−2	2.15 × 10−2	3.19 × 10−2	4.73 × 10−2	1.77 × 10−2
	15	1500	2.09 × 10−1	2.30 × 10−1	2.06 × 10−1	2.21 × 10−1	2.34 × 10−1
			8.12 × 10−3	3.73 × 10−3	3.38 × 10−3	6.31 × 10−3	7.99 × 10−3
			1.22 × 10−1	1.36 × 10−1	1.20 × 10−1	1.00 × 10−1	9.70 × 10−2
DTLZ2	3	250	5.78 × 10−4	5.93 × 10−4	5.34 × 10−4	6.25 × 10−4	5.75 × 10−4
			4.53 × 10−4	4.74 × 10−4	4.04 × 10−4	4.27 × 10−4	4.37 × 10−4
			4.90 × 10−4	5.19 × 10−4	4.82 × 10−4	5.01 × 10−4	5.02 × 10−4
	5	350	1.29 × 10−3	1.21 × 10−3	1.13 × 10−3	1.23 × 10−3	1.09 × 10−3
			8.71 × 10−4	9.31 × 10−4	7.92 × 10−4	9.39 × 10−4	9.34 × 10−4
			1.06 × 10−3	1.08 × 10−3	9.51 × 10−4	1.10 × 10−3	1.01 × 10−3
	8	500	2.73 × 10−2	5.23 × 10−3	4.83 × 10−3	5.38 × 10−3	5.45 × 10−3
			4.61 × 10−3	4.37 × 10−3	4.02 × 10−3	4.52 × 10−3	4.16 × 10−3
			7.32 × 10−3	4.81 × 10−3	4.50 × 10−3	4.87 × 10−3	4.57 × 10−3
	10	750	3.49 × 10−1	1.08 × 10−2	1.03 × 10−2	3.79 × 10−1	4.05 × 10−1
			7.78 × 10−3	7.43 × 10−3	7.29 × 10−3	7.99 × 10−3	7.64 × 10−3
			4.28 × 10−2	8.56 × 10−3	8.33 × 10−3	8.25 × 10−2	1.11 × 10−1
	15	1000	4.84 × 10−1	3.98 × 10−1	2.33 × 10−1	2.38 × 10−1	3.44 × 10−1
			9.80 × 10−3	1.03 × 10−2	1.00 × 10−2	9.33 × 10−3	9.27 × 10−3
			1.67 × 10−1	1.71 × 10−1	3.60 × 10−2	5.10 × 10−2	1.34 × 10−1
DTLZ3	3	1000	1.52 × 10−3	1.27 × 10−3	2.47 × 10−4	2.49 × 10−4	3.12 × 10−4
			2.00 × 10−4	2.01 × 10−4	1.18 × 10−4	1.84 × 10−4	1.80 × 10−4
			4.24 × 10−4	3.51 × 10−4	1.98 × 10−4	2.01 × 10−4	2.07 × 10−4
	5	1000	1.84 × 10−3	1.56 × 10−3	6.94 × 10−4	6.66 × 10−4	6.83 × 10−4
			6.79 × 10−4	5.97 × 10−4	4.03 × 10−4	5.77 × 10−4	5.92 × 10−4
			8.69 × 10−4	7.75 × 10−4	6.03 × 10−4	6.09 × 10−4	6.31 × 10−4
	8	1000	8.71 × 10−3	6.33 × 10−3	5.59 × 10−3	6.20 × 10−3	4.25 × 10−1
			5.06 × 10−3	4.44 × 10−3	4.06 × 10−3	4.82 × 10−3	4.45 × 10−3
			6.40 × 10−3	5.09 × 10−3	4.84 × 10−3	5.39 × 10−3	4.70 × 10−2
	10	1500	5.97 × 10−1	8.05 × 10−1	5.43 × 10−1	5.66 × 10−1	5.48 × 10−1
			7.01 × 10−3	7.43 × 10−3	6.61 × 10−3	7.18 × 10−3	7.07 × 10−3
			2.73 × 10−1	3.98 × 10−1	2.54 × 10−1	2.71 × 10−1	3.63 × 10−1
	15	2000	5.34 × 10−1	5.23 × 10−1	5.44 × 10−1	5.56 × 10−1	5.82 × 10−1
			4.68 × 10−1	4.31 × 10−1	9.66 × 10−2	1.10 × 10−1	4.95 × 10−1
			4.99 × 10−1	4.91 × 10−1	4.65 × 10−1	4.83 × 10−1	5.26 × 10−1
DTLZ4	3	600	1.62 × 10−3	1.90 × 10−3	1.36 × 10−3	1.57 × 10−3	9.48 × 10−1
			3.11 × 10−4	2.63 × 10−4	2.51 × 10−4	2.85 × 10−4	5.37 × 10−1
			8.22 × 10−4	7.08 × 10−4	7.21 × 10−4	8.08 × 10−4	7.83 × 10−1
	5	1000	1.45 × 10−3	1.60 × 10−3	1.24 × 10−3	1.37 × 10−3	4.04 × 10−1
			9.17 × 10−4	8.27 × 10−4	8.03 × 10−4	1.02 × 10−3	9.41 × 10−4
			1.16 × 10−3	1.07 × 10−3	1.06 × 10−3	1.22 × 10−3	7.77 × 10−2
	8	1250	4.74 × 10−3	4.41 × 10−3	4.24 × 10−3	4.86 × 10−3	4.36 × 10−3
			3.64 × 10−3	3.50 × 10−3	2.72 × 10−3	3.45 × 10−3	3.46 × 10−3
			4.15 × 10−3	3.98 × 10−3	3.84 × 10−3	4.19 × 10−3	3.92 × 10−3
	10	2000	5.51 × 10−3	5.34 × 10−3	5.93 × 10−3	5.19 × 10−3	5.49 × 10−3
			4.45 × 10−3	4.05 × 10−3	4.01 × 10−3	4.29 × 10−3	4.32 × 10−3
			5.09 × 10−3	4.68 × 10−3	4.61 × 10−3	4.65 × 10−3	4.89 × 10−3
	15	3000	6.83 × 10−3	6.70 × 10−3	6.54 × 10−3	6.92 × 10−3	7.81 × 10−3
			4.97 × 10−3	5.31 × 10−3	5.21 × 10−3	5.35 × 10−3	5.02 × 10−3
			5.99 × 10−3	5.85 × 10−3	5.80 × 10−3	6.16 × 10−3	6.00 × 10−3

, it can be seen that the sensitivity parameter is 0.1 in the DTLZ1–4 test functions, and almost all of them are better than the other parameters of the results. In the DTLZ1 m = 10 and m = 15 case, the median value of the IGD results in worse; in the DTLZ3 m = 5 case, the maximum value of the IGD results in worse than the rest of them; in the DTLZ4 m = 15 case, the result of the minimum value of IGD is worse than the rest; and in DTLZ4 series, all values of IGD are to be due to the parameter 1. In summary, a parameter of 0.1 will be used as the judgment condition for whether CM will enter into the local search strategy or not.

3.4. Non-Dominated Sorting Genetic Northern Goshawk Optimization

We detailed the computation of the CM (convergence metric) and demonstrated its effectiveness in evaluating the convergence properties of the algorithm’s search during iterations through experimental results. In this section, we explore a new multi-objective hybrid algorithm that applies CM to the operators of the hybrid algorithm. We choose to combine the genetic operator (GA) in the NSGA-III algorithm with the optimization operator (NGO) in the MONGO algorithm. This is because the genetic operator in the NSGA-III algorithm has excellent global search capability, while the hyperparameter optimization operator in the NGO algorithm exhibits excellent local search capability. We combine these two operators and apply CM metrics to construct a novel multi-objective hybrid algorithm named NSNGO algorithm. In the proposed NSNGO algorithm, we use CM metrics to judge the search process during the iteration of the algorithm, using the GA operator with stronger global search capability in the global search phase, and the NGO operator with stronger local search capability in the local search phase, which greatly improves the convergence and distribution of the algorithm.

The NSNGO pseudo-code is as follows (Algorithm 1):

Algorithm 1 Implementation process of the NSNGO algorithm

Input: Define the initial number of populations, $N_P$; the maximum number of iterations, $T_{\max }$; the parent population, $N_t$; and the iterated offspring population, $N_{np}$    1: for $t=1:T_{\max }$ then    2: elseif flag = 0    3: % Combining Survival Strategies in DOA with NGO Algorithms    4:   for $N=1$:$N_P$ do    5:     $C=1-it(0.98/MaxIt)$ % C is a balancing parameter between exploration and exploitation    6:     if k > 0.6 && rand1 < 0.5 do      Then, update all individuals in the population    7:    $x(t+1)=x(t)+0.5\left[(2CZ{P}_{pos}-x(t))+(2(1-C)Z\mu (j)-x(t))\right]$    8:     elseif k > 0.6 && rand1 > 0.5    9:      $x(t+1)=T_{pos}+CZ\cos (2\pi R_4)\times (T_{pos}-x(t))$  10:    elseif k < 0.6 && rand1 < 0.5  11:      $x(t+1)=0.5\ast \left[e^{{\alpha }_1}\ast x_i\left(t\right)-{\left(-1\right)}^{{\alpha }_2}x\left(t\right)\right]$ % ${\alpha }_1$ is a uniformly generated random number in the interval [−1, 1], $x_i\left(t\right)$ is the ith randomly selected individual, ${\alpha }_2$ is a randomly generated binary number  12:    elseif k < 0.6 && rand1 > 0.5         $x(t+1)=x_{\ast }(t)+0.5\ast \left[x_i\left(t\right)-{\left(-1\right)}^{{\alpha }_2}\ast x_{i_2}\left(t\right)\right]$ % $x_{\ast }(t)$ is the best individual found in the previous iteration, the, $x_{i_2}\left(t\right)$ was the $i_2$th randomly selected individua.  13:    end if  14:     $HPposfiness=fitness(x(t))$ % Calculating the fitness of a population  15:   Find the most adapted individual in the population $HPposfiness$, and record the coordinates of the individual with the best individual weight.  16:     end for  17: elseif flag = 1  18: % GA  19:    $N_{np}=Recombination+Mutation\left(N_t\right)$% Crossover + Mutation  20:     end  21:    After $N_P\leftarrow HPO\left(N_t\right)$ is performed, $N_{pop}=N_t\cup N_{np}$,  22:    $(F1,F2,\dots )=\mathrm{Non}\text{-}\mathrm{dominated}\text{-}\mathrm{sort}(N_{pop})$,  23:    $S_t\leftarrow \varnothing ,i=1$  24:    Repeat  25:     $S_t=S_t\cup F_i and i=i+1$  26:    Until $\left|S_t\right|\ge N_p$  27:    Last front to be included: $F_l=F_i$  28:    if $\left|S_t\right|=N_p$ then  29:     $N_{t+1}=S_t$  30:     break  31:    else  32:     $N_{t+1}=sum(F_i),i=1,2,\dots ,t-1$  33:     Point to be chosen from $F_l:k=N_p-\left|N_t+1\right|$,  34:     Normalize the objective function and create a reference set $Z^r$,  35:     $S_t$ and associated elements of reference points,  36:     Select $K$ individuals from $N_{t+1}$ at a time to form $N_{t+1}$  37:    end if  38: end for

Determination conditions for localized search strategies

Input: Parent stock, $N_t$; iterated population of offspring, $N_{np}$; current number of iterations; current indicator value, $C{M}_t$ Output: Local search operator flag  1: if t ≥ 2 then  2: Calculate the $C{M}_t$ for the current iteration number t  3: if $C{M}_t$ ≤ 0.1 then  4: flag = 1  5: else  6: flag = 0  7: end if  8: end if

The specific steps for the operation of NSNGO are as follows:

Step 1: Initialize parameters: number of individuals in the population, $N_p$, and total number of iterations, $T_{\max }$.

Step 2: Generate the first generation of decision variables, $N_p$, and label the parent population, $N_t$.

Step 3: Calculate the global search convergence index of the current population before each iteration and determine whether the judgment condition of entering the local search strategy is reached; if the condition is not reached, iterate using the iterative mechanism and rules of the GA operator; if the condition is reached, generate a new generation of populations labeled with $N_{t+1}$ by the iterative mechanism of the combination of the NGO operator and the survival mechanism. Check whether the iterated population is beyond the boundary, and if it is beyond the boundary, then pull the individuals back to the boundary. Calculate the three objective function values for each individual in the population. Finally, merge the parent population with the child population, labeled $N_{pop}$.

The flowchart for the operation of the NSNGO algorithm is shown in Figure 5.

3.5. Comparison of Experimental Results

In this section, we compare the IGD values after solving the NSGA-III, θ-DEA, and MOEA/D-PBI algorithms with the NSNGO proposed in this paper by solving the DTLZ series of problems with internationally generalized benchmarking functions, respectively. We set the maximum population mode to N = 400 and consider five cases for the number of objective functions, namely M = 3, M = 5, M = 8, M = 10, and M = 15, and the number of iterations varies for different DTLZ functions with different objective dimensions, m. We also consider the number of iterations for different DTLZ functions with different objective dimensions m. The number of iterations for different DTLZ functions varies for different objective dimensions. For each group, we conducted 20 trials. The results of solving the multi-objective hybrid algorithm proposed in this paper, and the NSGA-III, θ-DEA, and MOEA/D-PBI algorithms on the DTLZ family of problems are given in

Table 3. Best, median, and worst IGDs of the NSNGO algorithm and other algorithms for the DTLZ1–7 problem with m objectives (better values compared in bold).

Functions	m	Maxgen	NSNGO	NSGA-III	θ-DEA	MOEA/D-PBI
DTLZ1	3	400	1.74 × 10−4	4.88 × 10−4	5.66 × 10−4	4.10 × 10−4
			1.85 × 10−4	1.31 × 10−3	1.31 × 10−3	1.50 × 10−3
			2.01 × 10−4	4.88 × 10−3	9.45 × 10−3	4.74 × 10−3
	5	600	1.71 × 10−5	5.12 × 10−4	4.43 × 10−4	3.18 × 10−4
			2.92 × 10−4	9.79 × 10−4	7.33 × 10−4	6.37 × 10−4
			3.17 × 10−4	1.98 × 10−3	2.14 × 10−3	1.64 × 10−3
	8	750	1.30 × 10−3	2.04 × 10−3	1.98 × 10−3	3.91 × 10−3
			1.60 × 10−3	3.89 × 10−3	2.70 × 10−3	6.11 × 10−3
			2.00 × 10−3	8.72 × 10−3	4.62 × 10−3	8.54 × 10−3
	10	1000	2.00 × 10−3	2.22 × 10−3	2.10 × 10−3	3.87 × 10−3
			4.05 × 10−3	3.46 × 10−3	2.45 × 10−3	5.07 × 10−3
			6.50 × 10−3	6.87 × 10−3	3.94 × 10−3	6.03 × 10−3
	15	1500	4.70 × 10−3	2.65 × 10−3	2.44 × 10−3	1.24 × 10−2
			4.404 × 10−3	5.06 × 10−2	8.15 × 10−3	1.53 × 10−2
			9.97 × 10−2	1.12 × 10−2	2.24 × 10−1	1.69 × 10−2
DTLZ2	3	400	8.71 × 10−4	1.26 × 10−3	1.04 × 10−3	5.43 × 10−4
			9.84 × 10−4	1.36 × 10−3	1.57 × 10−3	6.41 × 10−4
			1.05 × 10−3	2.11 × 10−3	5.50 × 10−3	8.01 × 10−4
	5	600	1.22 × 10−3	4.25 × 10−3	2.72 × 10−3	1.14 × 10−3
			1.44 × 10−3	4.98 × 10−3	3.25 × 10−3	2.26 × 10−3
			1.73 × 10−3	5.86 × 10−3	5.33 × 10−3	2.65 × 10−3
	8	750	4.98 × 10−3	1.37 × 10−2	7.79 × 10−3	3.10 × 10−3
			6.00 × 10−3	1.57 × 10−2	8.99 × 10−3	3.76 × 10−3
			3.18 × 10−1	1.81 × 10−2	1.14 × 10−2	5.20 × 10−3
	10	1000	4.60 × 10−3	1.35 × 10−2	7.56 × 10−3	2.47 × 10−3
			8.55 × 10−3	1.53 × 10−2	8.81 × 10−3	2.78 × 10−3
			5.65 × 10−1	1.70 × 10−2	1.02 × 10−2	3.24 × 10−3
	15	1500	1.67 × 10−2	1.36 × 10−2	8.82 × 10−3	5.25 × 10−3
			4.02 × 10−1	1.73 × 10−2	1.13 × 10−2	6.01 × 10−3
			4.80 × 10−1	2.11 × 10−2	1.48 × 10−2	9.41 × 10−3
DTLZ3	3	400	2.03 × 10−4	9.75 × 10−4	1.34 × 10−3	9.77 × 10−4
			2.30 × 10−4	4.01 × 10−3	3.54 × 10−3	3.43 × 10−3
			5.73 × 10−4	6.67 × 10−3	5.53 × 10−3	9.11 × 10−3
	5	600	5.83 × 10−4	3.09 × 10−3	1.98 × 10−3	1.13 × 10−3
			6.65 × 10−4	5.96 × 10−3	4.27 × 10−3	2.21 × 10−3
			7.87 × 10−3	1.20 × 10−2	1.91 × 10−2	6.15 × 10−3
	8	750	2.79 × 10−3	1.24 × 10−2	8.77 × 10−3	6.46 × 10−3
			3.11 × 10−3	2.38 × 10−2	1.54 × 10−2	1.95 × 10−2
			4.04 × 10−3	9.65 × 10−2	3.83 × 10−2	1.12 × 100
	10	1000	3.50 × 10−3	8.85 × 10−3	5.97 × 10−3	2.79 × 10−3
			5.75 × 10−2	1.19 × 10−2	7.24 × 10−3	4.32 × 10−3
			6.22 × 10−1	2.08 × 10−2	2.32 × 10−2	1.01 × 100
	15	1500	1.28 × 10−2	1.40 × 10−2	9.83 × 10−3	4.36 × 10−3
			5.56 × 10−1	2.15 × 10−2	1.92 × 10−2	1.66 × 10−2
			6.38 × 10−1	4.20 × 10−2	6.21 × 10−1	1.26 × 100
DTLZ4	3	400	3.09 × 10−4	2.92 × 10−4	1.87 × 10−4	2.93 × 10−1
			5.70 × 10−4	5.97 × 10−4	2.51 × 10−4	4.28 × 10−1
			3.56 × 10−3	4.29 × 10−1	5.32 × 10−1	5.23 × 10−1
	5	600	7.81 × 10−4	9.85 × 10−4	2.62 × 10−4	1.08 × 10−1
			1.05 × 10−3	1.26 × 10−3	3.79 × 10−4	5.79 × 10−1
			1.70 × 10−3	1.72 × 10−3	4.11 × 10−4	7.35 × 10−1
	8	750	2.38 × 10−3	5.08 × 10−3	2.78 × 10−3	5.30 × 10−1
			3.05 × 10−3	7.05 × 10−3	3.10 × 10−3	8.82 × 10−1
			3.41 × 10−3	6.05 × 10−1	3.57 × 10−3	9.72 × 10−1
	10	1000	2.62 × 10−3	5.69 × 10−3	2.75 × 10−3	3.97 × 10−1
			3.50 × 10−3	6.34 × 10−3	3.34 × 10−3	9.20 × 10−1
			4.82 × 10−3	1.08 × 10−1	3.91 × 10−3	1.08 × 100
	15	1500	5.37 × 10−3	7.11 × 10−3	4.14 × 10−3	5.89 × 10−1
			5.86 × 10−3	3.43 × 10−1	5.90 × 10−3	1.13 × 100
			6.88 × 10−3	1.073 × 10+	7.68 × 10−3	1.25 × 100
DTLZ5	3	600	2.09 × 10−3	3.59 × 10−3	1.14 × 10−2	2.38 × 10−3
			2.60 × 10−3	4.37 × 10−3	1.30 × 10−2	2.80 × 10−3
			3.46 × 10−3	4.85 × 10−3	1.36 × 10−2	3.76 × 10−3
	5	1000	2.73 × 10−2	4.35 × 10−2	4.50 × 10−2	2.05 × 10−2
			4.78 × 10−2	5.51 × 10−2	8.75 × 10−2	4.87 × 10−2
			6.12 × 10−2	6.94 × 10−2	1.28 × 10−1	6.76 × 10−2
	8	1250	1.10 × 10−1	1.44 × 10−1	1.28 × 10−1	3.87 × 10−2
			1.83 × 10−1	3.03 × 10−1	1.47 × 10−1	9.64 × 10−2
			2.30 × 10−1	4.85 × 10−1	1.97 × 10−1	2.56 × 10−1
	10	2000	1.60 × 10−1	2.15 × 10−1	1.10 × 10−1	4.78 × 10−2
			2.47 × 10−1	3.90 × 10−1	1.47 × 10−1	3.20 × 10−1
			3.85 × 10−1	5.94 × 10−1	1.97 × 10−1	5.41 × 10−1
	15	3000	1.47 × 10−1	2.19 × 10−1	1.36 × 10−1	7.49 × 10−2
			2.69 × 10−1	3.30 × 10−1	2.87 × 10−1	3.38 × 10−1
			3.71 × 10−1	5.49 × 10−1	4.22 × 10−1	4.58 × 10−1
DTLZ6	3	600	3.95 × 10−3	4.38 × 10−3	1.37 × 10−2	1.38 × 10−3
			4.40 × 10−3	4.56 × 10−3	1.55 × 10−2	1.42 × 10−3
			5.02 × 10−3	4.79 × 10−3	1.69 × 10−2	1.49 × 10−3
	5	1000	2.24 × 10−2	4.58 × 10−2	1.35 × 10−1	5.69 × 10−2
			4.51 × 10−2	5.77 × 10−2	1.45 × 10−1	9.85 × 10−2
			8.16 × 10−2	7.96 × 10−2	1.59 × 10−1	1.77 × 10−1
	8	1250	1.23 × 10−1	2.88 × 10−1	1.99 × 10−1	2.27 × 100
			2.41 × 10−1	5.50 × 10−1	2.66 × 10−1	3.70 × 100
			3.46 × 10−1	7.42 × 10−1	3.39 × 10−1	4.39 × 100
	10	2000	1.55 × 10−1	3.29 × 10−1	2.50 × 10−1	3.30 × 100
			2.31 × 10−1	5.31 × 10−1	2.86 × 10−1	4.93 × 100
			3.04 × 10−1	7.42 × 10−1	3.33 × 10−1	6.08 × 100
	15	3000	1.83 × 10−1	2.58 × 10−1	2.39 × 10−1	4.21 × 100
			2.80 × 10−1	6.10 × 10−1	3.04 × 10−1	4.75 × 100
			3.55 × 10−1	7.42 × 10−1	3.51 × 10−1	5.30 × 100
DTLZ7	3	600	4.76 × 10−2	3.30 × 10−2	5.94 × 10−2	3.40 × 10−1
			1.85 × 10−1	3.37 × 10−2	7.06 × 10−2	3.53 × 10−1
			7.31 × 10−1	3.43 × 10−2	9.13 × 10−2	3.68 × 10−1
	5	1000	1.48 × 10−1	2.05 × 10−1	2.59 × 10−1	2.43 × 10−1
			1.92 × 10−1	2.23 × 10−1	2.65 × 10−1	2.52 × 10−1
			2.46 × 10−1	2.45 × 10−1	2.74 × 10−1	2.60 × 10−1
	8	1250	2.59 × 10−1	5.64 × 10−1	5.69 × 10−1	1.04 × 100
			3.17 × 10−1	6.05 × 10−1	6.01 × 10−1	1.09 × 100
			4.82 × 10−1	6.89 × 10−1	6.46 × 10−1	1.14 × 100
	10	2000	3.28 × 10−1	1.06 × 100	8.72 × 10−1	1.59 × 100
			4.69 × 10−1	1.22 × 100	9.86 × 10−1	1.65 × 100
			7.10 × 10−1	1.43 × 100	1.09 × 100	1.69 × 100
	15	3000	3.75 × 10−1	1.88 × 100	3.20 × 100	2.20 × 100
			5.80 × 10−1	1.96 × 100	3.75 × 100	2.31 × 100
			8.76 × 10−1	2.16 × 100	4.31 × 100	2.41 × 100

, which give the best, median, and worst IGD values for the 20 trials.

From Table 3, the NSNGO algorithm proposed in this paper almost always gives better results than NSGA-III in DTLZ1–7 test functions, while IGD results are slightly worse when m = 15 in DTLZ2. As can be seen from Table 3, compared with the theta-DEA algorithm, the “optimal”, “median”, and “worst” values of the DTLZ3 test function are worse when m = 15, while the other three values are worse. For all the objective function dimensions of the DTLZ1, DTLZ2, and DTLZ4 test functions, the IGD values solved by the NSNGO method are better. Under the DTLZ2 test function, the MOEA/D-PBI algorithm outperforms NSNGO in all objective dimensions compared with the MOEA/D-PBI algorithm. However, the NSNGO outperformed the MOEA/D-PBI algorithm on all test functions of DTLZ1, DTLZ3, and DTLZ4. In summary, the NSNGO algorithm proposed in this paper has better comprehensive ability than the other three algorithms in solving DTLZ series problems, which can verify the advantages of NSNGO algorithm and the feasibility of the global search convergence index.

The running times of the NSNGO and the comparison algorithms in solving the model are as follows. As can be seen from the Figure 6, the running speed of NSNGO algorithm is superior to other algorithms in terms of optimal, worst, or average value.

As can be seen from

Table 4. Time taken to solve the IES model with different algorithms.

Algorithm	Running Time
	Best	Average	Worst
NSGA-III	11.7522	12.3023	12.6647
ANSGA-III	13.6241	14.4933	14.9921
θ-DEA	12.9632	13.6102	14.2424
PREA	21.8641	26.5847	30.2021
NSNGO	11.2712	11.6442	11.8733

, The NSNGO algorithm proposed in this paper basically outperforms the other comparative algorithms in terms of IGD value under the DTLZ test function, and it also outperforms the other algorithms in terms of running speed under the test function. In summary, the comprehensive capability of the NSNGO algorithm proposed in this paper is better than the other three algorithms, which can verify the advantages of NSNGO and the feasibility of the global search convergence metrics.

4. Experiments and Analysis of Results

4.1. Introduction to the Algorithm

In this section, we focus on a comprehensive energy-planning initiative incorporating hydrogen storage in Wuhan City as our research subject. Utilizing historical load data and meteorological records, we have identified a typical day and optimized the hourly capacity of each unit within the integrated energy system through the application of a well-established capacity-allocation model. Additionally, we have plotted the light intensity, wind speed, and electrical load curves, and utilized the region’s typical daily load curve for simulation purposes. The daily load profile and time-of-use (TOU) data for Wuhan are presented in Supplementary Table S5. Furthermore, the simulated power generation from photovoltaic (PV) and wind sources in the area is illustrated in Figure 7a. The detailed parameters of each component within the energy system of the integrated energy station are outlined in

Table 5. Parameterization of individual devices.

Installations	Life Span/a	Investment Cost/(yuan·kW−1)	Maintenance Cost/(yuan·kW−1)	Efficiency
WT	25	10,000	0.01
PV	25	12,000	0.01
ES	20	800	0.15	0.9
P2G	15	3500	0.02	0.75
HT	10	300	0.02	0.9
GT	15	7800	0.01	0.7
WHB	15	200	0.05	0.4
EB	15	7500	0.01	0.9
HS	20	50	0.05	0.95

. The specific light intensity, temperature, and wind-speed data provided by the local meteorological office were used to calculate the output of the PV and turbine fan systems within the integrated energy system (IES) model. A comprehensive description of the PV and turbine fan system model, along with the corresponding mathematical framework, is provided in Section 2. The typical daily loads for electricity, heat, and hydrogen within the IES are depicted in Figure 7b. Notably, the specific light intensities, temperatures, and wind speeds supplied by the meteorological office were instrumental in determining the PV and turbofan outputs within the IES model. Specifically, Figure 7a displays the output curves for individual PV panels and turbofans, while Figure 7b showcases the typical daily loads for electricity, heat, and hydrogen within the IES.

Over a one-month period, we simulated the initial state of charge (SOC) for car users upon their arrival at the IES. The charging and swapping preferences of electric vehicle (EV) users were taken into account, and the resulting SOC data adhered to a normal distribution, as referenced in [33]. Upon arrival at the IES, both EVs and hydrogen vehicles (HVs) exhibited random SOC states. For simplicity, it was assumed that the SOC states of all vehicles arriving at the station followed a uniform distribution. EVs had the option of utilizing either charging or swapping services at the integrated energy station, with the choice being influenced by the time costs associated with each mode. Specifically, when the vehicle’s SOC was below 0.2, users often choose battery swapping because fast charging involves a higher time expenditure, which could also result in excessive battery wear. Consequently, vehicles arriving at the station with an SOC below 0.2 were allocated to the battery-swapping service. The integrated energy station set an initial SOC threshold of 0.2 for incoming EVs; if the SOC was below this threshold, the vehicle was classified for battery swapping, and if it was above, it was classified for charging. The simulated hourly charging loads for EVs, power exchange loads for EVs (battery swapping), and hourly hydrogen charging demand for HVs are presented in Figure 8. These simulations provide insights into the energy demands of various vehicle types at the integrated energy station and can inform the optimization of energy-management strategies.

Multi-objective optimization problems are characterized by multi-objective, non-linear, and multi-constraints. In this paper, a high-latitude multi-objective algorithm, NSNGO, is proposed to solve the above problem and verify the model’s feasibility. The specific flow of the NSNGO algorithm solution is as follows; the parameters are listed in

Table 6. Algorithm- and model-specific parameters.

	${\mathit{N}}_{\mathit{p}}$	${\mathit{T}}_{\mathbf{max}}$	${\mathit{C}}_{\mathit{r}}$	m	${\mathit{m}}_{\mathit{B}\mathit{C}\mathit{S}}$	${\mathit{m}}_{\mathit{B}\mathit{S}\mathit{S}}$	${\mathit{C}}_{\mathit{H}\mathit{V}}$	${\mathit{C}}_{\mathit{H}\mathit{T}}$	${\mathit{P}}_{{\mathit{H}}_2}^{\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}}$
Value	400	1000	60 kW·h	20	15	5	50 Kg	50 Kg	60 Yuan/Kg

.

Step 1: Based on historical data on wind and photovoltaic power generation and weather forecasts, obtain the output power of the wind and photovoltaic system at each moment in the next 24 h.

Step 2: Determine the aggregate charging capacity required for electric vehicles, conduct a comprehensive analysis and document the monthly travel patterns of both electric and hydrogen-powered vehicles, and model the initial state of charge (SOC) for vehicle users upon their arrival at the integrated energy station.

Step 3: Randomly generate the electrolyzer hydrogen production power, $P_t^{ELE}$, for each time period according to the constraints and then randomly generate the battery pack charging and discharging power, $P_{charge,t}$, for each moment. Based on the hydrogen production power in each time period, the hydrogen production power in a day is obtained, and the SOC of the battery at moment i is found.

Step 4: According to the power-balance relationship, solve for the power ($P_{ri}$) supplied by the AC distribution network at moment i.

Step 5: Calculate the integrated operating cost in the objective function. Obtain the charging cost, switching cost, and electric vehicle-charging module’s charge for purchasing electricity from the grid and the charge for selling hydrogen from Steps 1 to 3 to obtain the comprehensive operating cost.

Step 6: Calculate the battery cell loss in the objective function. Obtain the battery cell loss for a day based on the $P_{charge,t}^{BCS}$ and $P_{discharge,t}^{BCS}$ states of each time period.

Step 7: Calculate the peak-to-valley ratio of the grid-side load in the objective function. The peak-to-valley difference of the grid-side load is obtained by calculating the peak–time grid load value of the energy storage system, $P_{peak}^t$, and the valley–time grid load value, $P_{valley}^t$, of the energy storage system.

Step 8: Take Steps 1 to 6 as the theoretical basis and use the high-dimensional multi-objective algorithm NSNGO proposed in this paper to solve the problem until the optimal solution is obtained.

4.2. Model Comparison Experiment

In order to verify the feasibility of the renewable energy multi-coupled integrated energy addition station model proposed in this paper, this paper uses the proposed high-dimensional multi-objective algorithm, NSNGO, to solve the model. The comparison model uses IES without considering priority policies. The Pareto frontier of the two models is shown in Figure 9.

• Case (1)

The multi-energy coupling model presented in this paper, which incorporates a strategy prioritizing energy storage, is designated as Case 1 and illustrated in Figure 10a. This model comprehensively considers the load requirements of both the integrated energy system (IES) and the Battery Energy Storage System (BESS). When the IES fulfills the load demand, it prioritizes supplying power to the grid. Subsequently, the BESS opts to sell any surplus electricity to the grid, thereby minimizing the cost of grid power purchases. To gain a clearer understanding of the pollution emissions in Case 1, as depicted in Figure 10b, the system generates pollution during specific ten-hour intervals (1:00–3:00, 4:00–7:00, 10:00–12:00, 18:00–19:00, and 23:00–24:00). During these periods, the IES also purchases power. An analysis of Figure 10 reveals that the system sells more electricity than it purchases in a single day, indicating that it is designed with an excess supply capacity.

• Case (2)

An integrated energy system in Wuhan is set as Case 2. The optimized scheduling scheme reveals that when electricity prices are low (from 1:00 to 8:00 and from 20:00 to 24:00), the integrated energy system (IES) will purchase electricity from the grid to meet the load demand of electric vehicles (EVs). When the electricity price is high (from 13:00 to 19:00), the Battery Energy Storage System (BESS) will sell electricity to the grid to enhance its profit. Based on the system configuration and the planning of the objective function, when the system buys electricity from the grid, a negative profit will be incurred, thereby reducing the value of F1. Conversely, when the system sells electricity to the grid, it generates a positive profit, thus increasing the value of F1, as depicted in Figure 11a. As presented in Figure 11b, the relationship between load variation and pollution emission can be more explicitly observed. Firstly, in accordance with the analysis of the objective function and its constraints, pollution emission accompanies the purchase of electricity from the system. Therefore, it can be noticed that during the 13 h when BESS does not produce pollution emissions (from 4:00 to 6:00, from 7:00 to 9:00, from 12:00 to 17:00, from 21:00 to 22:00, and from 23:00 to 24:00), the amount of electricity purchased during this period is negative (a negative number indicates that FEVS sells electricity to the grid instead of purchasing it). Therefore, no pollution was emitted during that time.

Comparing the gap between the multi-energy-coupled integrated energy system with the energy storage priority strategy and the comparison model, the overall revenue increased by 6.3%, and the pollution emissions decreased by 46.9%. Therefore, the method and model proposed in this paper have good practicability and application value for promoting the development of an integrated energy system in the future.

From Figure 9, it can be seen that the Pareto frontier distribution for solving the integrated refueling station model considering the prioritization strategy is more homogeneous compared to the comparative model, using the following three objective functions for the two models.

From Figure 12, we can see that the TOTAL PROFIT exhibits an increase of 2532 yuan when compared to the benchmark model. This translates to an average increase of 5.91% in total profit. Furthermore, the grid-side-load peak-to-valley differential ratio, which serves as an objective function, decreases by 0.12 in the IES model, indicating a 15.72% reduction in the grid’s load peak-to-valley ratio compared to the benchmark. Additionally, the total emissions, another objective function, decrease by 980.64 g, resulting in a 7.48% reduction in pollutant emissions relative to the benchmark model. The aforementioned data demonstrate that the IES model outperforms the benchmark model in terms of all three objective function values, and its Pareto solution set is superior to that of the benchmark. Consequently, it is reasonable to conclude that the IES model is advantageous over the benchmark model.

4.3. Typical Solution Analysis

Fuzzy comprehensive evaluation (FCE) is a decision analysis method for dealing with uncertain and ambiguous information. It is usually used to solve complex multi-indicator decision-making problems in which cross-influence and ambiguity among the indicators may exist. Fuzzy comprehensive evaluation assists decision-making by quantifying uncertainty and ambiguity and synthesizing information from multiple indicators to produce a comprehensive evaluation result. We can understand and process complex information more comprehensively through fuzzy comprehensive evaluation to make accurate decisions. The steps of a fuzzy comprehensive evaluation to solve the decision-making of the comprehensive energy-adding station model are as follows.

(1)

Establish the virtual matrix:

$$U=\{u_1,u_2,u_3,\dots ,u_m\}$$

(37)

(2)

Establishment of relative deviation fuzzy matrix:

$$R={({\mathrm{r}}_{\mathrm{ij}})}_{\mathrm{m}<\mathrm{n}}=\left(\begin{array}{cccc}{r}_{11}& r_{12}& \dots & r_{1n}\\ r_{21}& r_{22}& \cdots & r_{2n}\\ ⋮& ⋮& ⋮& ⋮\\ r_{m1}& r_{m2}& \cdots & r_{mn}\end{array}\right)$$

(38)

$$r_{ij}={\displaystyle \frac{|a_{ij}-u_j|}{\underset{j}{\max }\{a_{ij}\}-\underset{j}{\min }\{a_{ij}\}}}$$

(39)

(3)

Coefficient of variation method to determine the weight vector:

$$v_i={\displaystyle \frac{s_i}{\left|\overline{x_i}\right|}}$$

(40)

$$w_i=\{v_1,v_2,v_3,\cdots ,v_m\}$$

(41)

(4)

Weighting the deviations of the programs:

$$F_j=\sum _{i=1}^m{w}_i{r}_{ij}(j=1,2,\cdots ,n)$$

(42)

Upon applying fuzzy comprehensive evaluation, the derived objective weights are [0.4421, 0.3701, 0.1877]. The best solutions are as follows: F1 (total profit) = −41,369.70434, F2 (total emissions) = 36.73207, and F3 (peak-to-valley difference rate of grid-side loads) = 0.6349. The subsequent step involves summarizing the optimal solution determined through fuzzy comprehensive evaluation, examining the operational conditions of this solution, and discussing the rationale behind the integrated energy station model presented in this paper.

4.4. Analysis of the Results of the Optimized Scheduling Scheme

The results of the optimal solution determined by the fuzzy comprehensive evaluation are shown in the figure below. Figure 13 illustrates the daily variations in the charging status of both the BESS and HT modules. Meanwhile, Figure 14 displays the quantity of charged and uncharged batteries within the BSS at every point in time throughout the day.

Figure 15 depicts the HT, BESS, and EV purchases over the course of a day. It is worth noting that large power purchases were observed only at 12:00 and 19:00. These times correspond to peak demands for high-pressure hydrogen production. Consequently, the HT module incurs substantial power purchases during these tariff peak hours. With the hydrogen constraint in place, the absence of significant power purchases during the other peak hours, namely 13:00–14:00, 16:00–18:00, and 20:00–21:00, leads to a substantial reduction in hydrogen production costs at the integrated energy station, ultimately boosting overall revenue. Figure 16 displays the return on investment for each period for both EVs and hybrid vehicles HVs.

Figure 17 illustrates the charging and discharging status of the Battery Energy Storage System (BESS) across various time periods, encompassing the cumulative charging and discharging activities of all batteries within both the battery charging station (BCS) and battery storage station (BSS) modules. It is worth noting that a positive value indicates the amount of charge, while a negative value indicates the amount of discharge. During peak hours (13:00–16:00 and 19:00–22:00), electric vehicle batteries are collectively discharged to charge electric vehicles or sell electricity to the grid. This approach minimizes grid power purchases, thereby reducing costs and boosting the total revenue of IES. In addition, the graph shows the discharge activity during the period of low electricity prices between 3 p.m. and 6 p.m. This was due to increased generation from wind and PV during this period, coupled with lower loads from electric vehicles, which resulted in discharges during these off-peak tariff periods.

Based on the results of the electric-load day-ahead dispatch (shown in Figure 18a), it can be seen that, due to the impact of the peak and valley tariffs, power purchases during the peak hours from 8:00 to 10:00 are relatively low, and this period relies mainly on wind, solar, and gas turbines to provide power. During the peak and valley hours, by coordinating the output of each generating unit, part of the load can be dispatched, thus relieving the pressure on the output of the unit. In the analysis of the energy consumption of the electric hydrogen production equipment, it is found that its main operating hours are concentrated in the morning, from 2:00 a.m. to 8:00 a.m. The higher operation volume of hydrogen production in this period is due to the increase in the market demand for hydrogen and the lower price of electricity at this time, which is conducive to the improvement of economic efficiency.

Figure 18b shows the heat load scheduling diagram, it can be seen that, in the period from 18:00 to 20:00, the electric load is larger; the electric power required for electric heating is reduced, resulting in a decrease in the amount of heat supplied by electric heating; and, at this time, the heat shortfall is mainly supplied by the heat storage tank. At the same time, in order to alleviate the pressure of regulation, the heat storage tank will also transfer some heat to the system. When there is excess heat in the system, the storage tank is able to store the excess heat, which not only helps to reduce the heating cost of the system but also improves the efficiency of energy utilization.

As shown in Figure 19, the gas turbine consumes more gas in the morning and evening hours because the pressure on the gas turbine increases due to the decrease in wind power during these hours. At noon, when the wind power is sufficient, the gas turbine consumes less gas. During 18:00–20:00, the MET process is utilized to provide natural gas and shift a small amount of hydrogen load to meet the overall supply/demand balance.

In summary, by analyzing the operation results of the multi-coupled integrated energy system, it can be seen that the system scheduling results are more complicated due to the coupling between multiple devices and the interconnection between different systems. In this calculation example, under the premise of meeting the demand of three different loads, namely electricity, hydrogen, and heat, the capacity of distributed energy equipment is optimized to achieve the lowest operating cost with the lowest pollutant emission and the smallest peak-to-valley difference rate of the load on the grid side in a typical daily cycle of the regional integrated energy system, and the results of the capacity allocation are shown in

Table 7. Capacity configuration results.

Load Type	Configuration Capacity
WT (kw·h)	290
PV (kw·h)	290
ES (kw·h)	12
P2Gr (kw·h)	560
HT (m)3	1800
GB (kw·h)	430
GT (kw·h)	13
WHB (kw·h)	106
EB (kw·h)	257
HS (kw·h)	364
MET (kw·h)	440

.

Figure 20 shows the peak and valley load curves of the regional power system before and after optimization. The figure shows that the optimized dispatch scheme can reduce the peak–valley difference of the regional power system load to a certain extent. The peak–valley difference of the regional power system before optimization is 0.5952, and the peak–valley difference after optimization is 0.4142, which is reduced by 30.40%.

5. Conclusions

In this paper, a high-latitude multi-objective NSNGO algorithm is proposed, which combines the NSNGO algorithm with non-dominated sorting and introduces the CM metrics, and by comparing with other algorithms, the effectiveness of the NSNGO algorithm in terms of solving the model and the feasibility of the CM metrics are proved. The results show the effectiveness of the NSNGO algorithm in solving the model. In order to make sure that the multi-energy-coupled integrated energy station (IES) can meet the demand of load diversity under the low-carbon economy operation, an optimal configuration model of the capacity of the multi-energy-coupled integrated energy system (IES) of electricity–heat–hydrogen is proposed, and the energy storage priority strategy is introduced, in which a comparative experiment is designed through the configuration of the various installed capacities in the IES. The experimental results show that the total profit compared with the comparative model is higher by 5.91%, and the pollutant emission scalar function is reduced by 980.64 (g), which is 7.48% lower than the comparison model. The peak–valley difference of the regional power system before optimization is 0.5952, and the peak–valley difference of the regional power system after optimization is 0.4142, which is reduced by 30.40%, and the capacity configuration of the integrated energy station is achieved.

This paper presents a multi-energy-coupled integrated energy system model incorporating a storage prioritization strategy, yet it fails to comprehensively address the challenges related to its technical maturity and economic feasibility, including the following aspects:

(1)

Technical maturity: Despite significant advancements in energy storage technologies in recent years, some technologies (such as certain novel battery technologies) may still be in the research and development stage or limited to small-scale applications, and have not yet reached the maturity level required for large-scale commercialization. Immature technologies may lead to performance instability, high maintenance costs, and safety issues, all of which pose potential obstacles during implementation.

(2)

Economic feasibility: The cost of energy storage technologies remains one of the primary limiting factors for their widespread adoption. Although costs are gradually decreasing with technological advancements and scale production, in some regions or application scenarios, the return on investment may still be insufficient to attract sufficient private capital. Furthermore, the economic benefits of energy storage technologies are influenced by various factors, such as energy prices, policy subsidies, and tax incentives.

(3)

Technical and system integration challenges: The application of energy storage technologies in integrated energy systems also faces technical and system integration challenges. Differences in performance among various energy storage technologies, compatibility with other energy systems, and technical difficulties during system integration can all affect the effectiveness of technology implementation.

The actual operating conditions of the IES are often more complex than the model. Considering more actual operating conditions, the complexity of the model will be higher, and the model solution will be more difficult, so further improvement of the proposed model will be the main research work in the future. In future research, the multi-energy-coupled optimization model will be improved to consider the seasonal characteristics of the climate by dividing the four seasons into various typical day scenarios, taking into account the volatility of the three loads. The production and use of biofuels is now recognized as a viable way to reduce the use of fossil fuels and the pollution they cause, and the inclusion of biomass energy storage is considered for future integrated energy systems [34]. Finally, a neural network is introduced into the algorithm to improve the model’s solution efficiency, so as to solve the problem of real-time decision-making and realize the optimal capacity allocation and scheduling of the integrated energy system.