Design of Energy Management Strategy for Integrated Energy System Including Multi-Component Electric–Thermal–Hydrogen Energy Storage

Abstract

To address the challenges of multi-energy coupling decision-making caused by the complex interactions and significant conflicts of interest among multiple entities in integrated energy systems, an energy management strategy for integrated energy systems with electricity, heat, and hydrogen multi-energy storage is proposed. First, based on the coupling relationship of electricity, heat, and hydrogen multi-energy flows, the architecture of the integrated energy system is designed, and the mathematical model of the main components of the system is established. Second, evaluation indexes in three dimensions, including energy storage device life, load satisfaction rate, and new energy utilization rate, are designed to fully characterize the economy, stability, and environmental protection of the system during operation. Then, an improved radar chart model considering multi-evaluation index comprehensive optimization is established, and an adaptability function is constructed based on the sector area and perimeter. Combined with the operation requirements of the electric–thermal–hydrogen integrated energy system, constraint conditions are determined. Finally, the effectiveness and adaptability of the strategy are verified by examples. The proposed strategy can obtain the optimal decision instructions under different operation objectives by changing the weight of evaluation indexes, while avoiding the huge decision space and secondary optimization problems caused by multiple non-inferior solutions in conventional optimization, and has multi-scenario adaptability.

1. Introduction

Against the background of energy structure optimization and transformation, the utilization ratio of renewable energy such as wind power and photovoltaic continues to increase, and China’s energy structure begins to change from centralized to distributed [1]. The traditional energy structure is single in form and lacks coordination, resulting in low energy utilization ratio. The introduction of integrated energy systems (IESs) provides a new method for optimizing energy supply, improving energy efficiency and the ecological environment [2]. Integrated energy systems (IESs) can effectively improve the utilization ratio of energy through the cooperative scheduling of various forms of energy such as hydrogen energy, heat energy, and electric energy, and become an important trend of future development [3].

The research of integrated energy systems mainly focuses on the construction of a multi-component energy network model and its collaborative management method. Past research on integrated energy systems has mainly focused on discussing the local energy combinations and collaborative relationships such as “electricity-heat” and “electricity-hydrogen”. Reference [4] conducts research on electricity–heat integrated energy systems and designs a two-stage robust optimization scheduling model. Reference [5], considering the instability of new energy and uncertain demand, proposes a day-ahead scheduling framework for energy centers that include electricity and heat, models uncertainty using the Monte Carlo method, and analyzes risk using Conditional Value at Risk (CVaR) methodology. Building on this foundation, this paper comprehensively covers the synergy between electricity, heat, and hydrogen, achieving deep coupling and collaborative complementarity among three types of energy in the entire process of production, conversion, storage, and consumption.

In the study of optimization management strategies for integrated energy systems, reference [6] focuses on day-ahead energy scheduling for interconnected smart homes with shared energy storage systems. It addresses energy scheduling under secondary cost functions and contract constraints through a special optimization scheme to reduce the total energy costs for users. Reference [7] takes solar thermal power station as the main energy supply equipment, and constructs an economic scheduling model of electric–thermal–gas interconnected integrated energy system. This model considers generalized energy storage, and uses CVaR theory to evaluate and select operation risk coefficient, which can effectively reduce system operation costs. The optimal scheduling strategy for comprehensive electric–thermal–gas energy systems established in the literature [8] fully considers the load demand response on the demand side, and designs a carbon trading mechanism by applying the life cycle assessment approach, which realizes the improvement of economy and the reduction of carbon emission. The above cases can make use of the characteristic differences in different energy sources to achieve the optimal management of specific goals. At present, most of the research on electric–thermal–hydrogen integrated energy systems has relatively singular optimization objectives and is applicable to relatively fixed scenarios. Based on this, this paper will take into account the environmental protection, stability, and economy of the system. The radar chart will be used to index various key elements related to the electricity–heat–hydrogen system and incorporate them into its framework, with different emphases on achieving different optimization objectives as required.

Concerning multi-objective optimization scheduling strategies, reference [9] employs cost minimization, CO₂ emission reduction, and maximization of overall energy utilization as comprehensive objectives for fuzzy optimization scheduling in integrated energy systems. The analytic hierarchy process is utilized to determine the comprehensive weights and transform the multi-objective problem into a single-objective problem solved by satisfaction index. Reference [10] applies the analytic hierarchy process to assign weights to different objectives with the aim of enhancing economic and environmental performance of combined heat and power systems. However, while the analytic hierarchy process can rank indicators and determine their importance level to some extent, it fails to demonstrate dynamic graphical changes that depict interrelationships between indicators. To address this limitation, this paper proposes an improved radar chart method that vividly presents both the importance levels of these indicators in integrated energy systems and their interactions through dynamic graphical changes.

In view of the above problems, this study uses a multi-objective optimization strategy based on radar charts to achieve the optimized management of a comprehensive energy system with electricity, heat, and hydrogen energy storage. This paper first designs a general architecture of an integrated energy system including power grid, heat network, and hydrogen network, and then an optimization model for energy management of an integrated energy system including multiple energy storage is developed. Secondly, considering the stability, economy, and environmental protection of the system, the energy management strategy for the electric–thermal–hydrogen integrated energy system based on improved radar chart is proposed. Finally, a case study simulation is carried out to verify the superiority of the energy management strategy proposed in this paper in improving system performance by comparing with the result of SPEA2 algorithm.

2. Integrated Energy System Model

2.1. Electric–Thermal–Hydrogen Integrated Energy System

The architecture of the electric–thermal–hydrogen integrated energy system with multiple energy storage proposed in this paper is shown in Figure 1. The system uses wind power and photovoltaic as inputs, and the load side includes electricity, heat, and hydrogen loads. The energy conversion unit includes an electric boiler, an electrolyzer, and a fuel cell; the energy storage unit includes a battery, a heat storage tank, and a hydrogen storage tank.

2.2. Mathematical Model

2.2.1. Wind Turbine

The components of wind turbine include a blade, a rotary body, a wind turbine, a nose, and a tail. To conduct mathematical modeling of a wind turbine [11]

$${\mathrm{P}}_{\mathrm{m}}={\displaystyle \frac{1}{2}}\mathrm{\pi }{\mathrm{R}}^2{\mathrm{v}}^3\rho {\mathrm{C}}_{\mathrm{p}}$$

(1)

The above formula represents the conversion relationship between wind speed and the output power of a wind turbine. Where R is the radius of the wind blade, with a value of 68 m; v is the input wind speed; ρ is the air density, with an ideal value of 1.205 kg/m³; and C_p is the wind energy utilization coefficient, which is determined by the blade pitch angle and the tip speed ratio of the wind turbine. C_p is calculated by the following formula:

$$\left\{\begin{array}{c}{\mathrm{C}}_{\mathrm{p}}(\theta ,\lambda )=0.0068\lambda +0.5176(\frac{116}{{\lambda }_{\mathrm{i}}}-0.4\theta -5){\mathrm{e}}^{-{\displaystyle \frac{21}{{\lambda }_{\mathrm{i}}}}}\\ {\lambda }_{\mathrm{i}}={\displaystyle \frac{1}{\frac{1}{\lambda +0.08\theta }-\frac{0.035}{{\theta }^3+1}}}\end{array}\right.$$

(2)

where θ is the blade moment Angle and λ represents the tip speed ratio of the blade, with a value of 5.

2.2.2. Photovoltaic Array

The energy conversion expression of photovoltaic array is as follows [12]:

$$\mathrm{I}={\mathrm{N}}_{\mathrm{P}}{\mathrm{I}}_{\mathrm{ph}}-{\mathrm{N}}_{\mathrm{P}}{\mathrm{I}}_{\mathrm{S}}\left[{\mathrm{e}}^{{\displaystyle \frac{\theta }{\mathrm{A}\mathrm{K}\mathrm{T}}}\left({\displaystyle \frac{\mathrm{V}}{{\mathrm{N}}_{\mathrm{S}}}}+{\displaystyle \frac{\mathrm{I}{\mathrm{R}}_{\mathrm{S}}}{{\mathrm{N}}_{\mathrm{P}}}}\right)}-1\right]-{\displaystyle \frac{{\mathrm{N}}_{\mathrm{P}}}{{\mathrm{R}}_{\mathrm{sh}}}}\left({\displaystyle \frac{\mathrm{V}}{{\mathrm{N}}_{\mathrm{S}}}}+{\displaystyle \frac{\mathrm{I}{\mathrm{R}}_{\mathrm{S}}}{{\mathrm{N}}_{\mathrm{P}}}}\right)$$

(3)

$$\mathrm{P}=\mathrm{V}\mathrm{I}$$

(4)

where ${\mathrm{N}}_{\mathrm{p}}$ and ${\mathrm{N}}_{\mathrm{s}}$ are the number of photovoltaic cells in series and parallel, respectively; ${\mathrm{I}}_{\mathrm{p}\mathrm{h}}$ and ${\mathrm{I}}_{\mathrm{s}}$ are photogenerated current and diode saturation current, respectively; ${\mathrm{R}}_{\mathrm{s}}$ and ${\mathrm{R}}_{\mathrm{s}\mathrm{h}}$ are series and parallel equivalent resistance, respectively; and V is the terminal voltage.

2.2.3. Hydrogen Production Device

The formula for calculating the relationship between the power input to the electrolytic cell and the volume of hydrogen gas produced is as follows [13]:

$${\mathrm{V}}_{\mathrm{h}}={\displaystyle \frac{3600{\mathrm{V}}_{\mathrm{m}}{\mathrm{C}}_0\mathrm{P}}{2\mathrm{U}{\mathrm{N}}_{\mathrm{A}}}}$$

(5)

where ${\mathrm{V}}_{\mathrm{h}}$ is the volume of hydrogen generated (unit is L); P is the electrolytic power input to the electrolytic cell; ${\mathrm{V}}_{\mathrm{m}}$ is the molar volume of the gas in the standard state; C₀ is the number of unit coulomb electrons; U is the voltage of the direct current access (unit is V); and ${\mathrm{N}}_{\mathrm{A}}$ is Avogadro’s constant.

2.2.4. Energy Storage Battery

State of Charge (SOC) of the energy storage battery refers to the ratio of the remaining capacity of the battery to the rated capacity, which can reflect the operating status of the battery. In this paper, ampere-hour integral method is used to estimate SOC status, and the charge and discharge capacity can be determined by integrating the charging and discharging currents at each time point, so as to update the SOC value of this moment accordingly [14]. The expression is as follows:

$${\mathrm{q}}_{\mathrm{SOC},\mathrm{k}}={\mathrm{q}}_{\mathrm{SOC},\mathrm{k}-1}-{\displaystyle \frac{1}{{\mathrm{C}}_{\mathrm{e}}}}{\displaystyle \int {\mathrm{I}}_{\mathrm{bat},\mathrm{i}}}\mathrm{d}\mathrm{t}$$

(6)

The ampere-hour integral method is appropriately simplified as follows:

$${\mathrm{q}}_{\mathrm{SOC},\mathrm{k}+1}={\mathrm{q}}_{\mathrm{SOC},\mathrm{k}}+{\displaystyle \frac{{\mathrm{P}}_{\mathrm{bt}}}{{\mathrm{C}}_{\mathrm{bt}}{\mathrm{V}}_{\mathrm{bt}}}}$$

(7)

where ${\mathrm{P}}_{\mathrm{b}\mathrm{t}}$ represents the charging and discharging power; ${\mathrm{C}}_{\mathrm{b}\mathrm{t}}$ represents the capacity of energy storage batteries; and ${\mathrm{V}}_{\mathrm{b}\mathrm{t}}$ represents the charging and discharging voltage.

2.2.5. Thermal Storage Device

Heat storage ratio (SOT) refers to the ratio of the remaining heat of the heat storage device to the rated capacity, which can reflect the charging and releasing state of the device. Overcharge and overdischarge will affect the service life of the device. Take the overcharge state as SOT greater than 0.8, and the overdischarge state as SOT less than 0.2. The SOT is calculated as follows:

$${\mathrm{q}}_{\mathrm{SOT},\mathrm{k}+1}={\mathrm{q}}_{\mathrm{SOT},\mathrm{k}}+{\displaystyle \frac{{\mathrm{P}}_{\mathrm{tst}}}{{\mathrm{C}}_{\mathrm{tst}}}}$$

(8)

The above formula represents the relationship between the thermal storage ratio of a thermal storage device and the charging and discharging thermal power. Where ${\mathrm{P}}_{\mathrm{t}\mathrm{s}\mathrm{t}}$ represents the actual charge and release heat power, ${\mathrm{C}}_{\mathrm{t}\mathrm{s}\mathrm{t}}$ represents the heat storage capacity.

2.2.6. Hydrogen Storage Device

Hydrogen storage ratio (SOH) of the hydrogen storage device refers to the ratio of the remaining hydrogen of the hydrogen storage device to the rated capacity, which can reflect the state of hydrogen charging and discharging of the device. Overcharge and overdischarge will affect the service life of the device. In this paper, the SOH health state is taken as 0–0.9, and the SOH calculation formula is as follows:

$${\mathrm{q}}_{\mathrm{SOH},\mathrm{k}+1}={\mathrm{q}}_{\mathrm{SOH},\mathrm{k}}+{\displaystyle \frac{{\mathrm{P}}_{\mathrm{hst}}}{{\mathrm{C}}_{\mathrm{hst}}}}$$

(9)

where ${\mathrm{P}}_{\mathrm{h}\mathrm{s}\mathrm{t}}$ represents the actual hydrogen charging and discharging power, and ${\mathrm{C}}_{\mathrm{h}\mathrm{s}\mathrm{t}}$ represents the hydrogen storage capacity.

3. Enhanced Radar Chart-Based Multi-Objective Optimization Strategy

3.1. Optimization Indicators

3.1.1. Establishment of Optimization Indicators

• Load satisfaction rate

The load satisfaction rate can reflect the balance of supply and demand of the integrated energy system and reflect the stability of the system.

$${\mathrm{Q}}_{\mathrm{mzl}}={\displaystyle \frac{{\mathrm{P}}_{\mathrm{el}}}{{\mathrm{P}}_{\mathrm{elmax}}}}+{\displaystyle \frac{{\mathrm{P}}_{\mathrm{tl}}}{{\mathrm{P}}_{\mathrm{tlmax}}}}+{\displaystyle \frac{{\mathrm{P}}_{\mathrm{hl}}}{{\mathrm{P}}_{\mathrm{hlmax}}}}$$

(10)

where ${\mathrm{P}}_{\mathrm{e}\mathrm{l}}$ is the power supplied to the electrical load, ${\mathrm{P}}_{\mathrm{t}\mathrm{l}}$ is the power supplied to the thermal load, and ${\mathrm{P}}_{\mathrm{h}\mathrm{l}}$ is the power supplied to the hydrogen load. ${\mathrm{P}}_{\mathrm{e}\mathrm{l}\mathrm{m}\mathrm{a}\mathrm{x}}$ is the electrical load demand, ${\mathrm{P}}_{\mathrm{t}\mathrm{l}\mathrm{m}\mathrm{a}\mathrm{x}}$ is the thermal load demand, and ${\mathrm{P}}_{\mathrm{h}\mathrm{l}\mathrm{m}\mathrm{a}\mathrm{x}}$ is the hydrogen load demand.

2.

Absorption rate

The absorption rate is the utilization rate of new energy, reflecting the environmental protection of the system. The expression is as follows:

$$\eta ={\displaystyle \frac{{\mathrm{p}}_{\mathrm{pv}}+{\mathrm{p}}_{\mathrm{wt}}}{{\mathrm{p}}_{\mathrm{pvmax}}+{\mathrm{p}}_{\mathrm{wtmax}}}}$$

(11)

Among them, ${\mathrm{P}}_{\mathrm{p}\mathrm{v}}$ and ${\mathrm{P}}_{\mathrm{w}\mathrm{t}}$, respectively, represent the actual output of wind power and photovoltaic, and ${\mathrm{P}}_{\mathrm{p}\mathrm{v}\mathrm{m}\mathrm{a}\mathrm{x}}$ and ${\mathrm{P}}_{\mathrm{w}\mathrm{t}\mathrm{m}\mathrm{a}\mathrm{x}}$, respectively, represent the maximum power generation of wind turbines and photovoltaic arrays under these specific conditions.

3.

Life of energy storage equipment

The more charge and discharge times of the energy storage device, the greater impact on the life of the energy storage device, which can indirectly reflect the economy of the system. The frequency of charge and discharge is defined as the frequency of each complete charge and complete discharge of the energy storage battery, and the depth of charge and discharge can be used to indirectly characterize the index. The calculation formula is as follows:

$${\mathrm{Q}}_{\mathrm{dc}}={\displaystyle \frac{{\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left|{\mathrm{P}}_{\mathrm{bes}}\right|}}{\mathrm{n}\cdot {\mathrm{P}}_{\mathrm{besmax}}}}$$

(12)

where Q_dc represents the depth of charge and discharge, P_bes represents the power of energy storage charge and discharge, and P_besmax represents the rated power of energy storage.

3.1.2. Standardization of Optimization Indicators

In order to unify the unit and magnitude of each optimization index, and ensure that each optimization objective is consistent with the expected results of the radar map model, it is necessary to standardize each index.

The specific steps of standardization processing are as follows:

• Load satisfaction rate (X₁)

$${\mathrm{X}}_1=\mathrm{average}({\displaystyle \frac{{\mathrm{P}}_{\mathrm{el}}}{{\mathrm{P}}_{\mathrm{elmax}}}}+{\displaystyle \frac{{\mathrm{P}}_{\mathrm{tl}}}{{\mathrm{P}}_{\mathrm{tlmax}}}}+{\displaystyle \frac{{\mathrm{P}}_{\mathrm{hl}}}{{\mathrm{P}}_{\mathrm{hlmax}}}})$$

(13)

2.

New energy consumption rate (X₂)

Since the new energy consumption rate is already unitized by definition, it is no longer necessary to unitize. However, due to the difference in wind speed, light, temperature, and other specific resource conditions, sometimes the wind speed exceeds the cut out wind speed or is lower than the cut in wind speed, and the light and temperature do not meet the minimum requirements of photovoltaic power generation, then the wind power and photovoltaic power are 0. At this time, the denominator of the absorption rate calculation formula is 0, which will cause calculation difficulties. Thus, this situation is defined as all absorption, that is, the absorption rate is 1.

3.

Number of charge and discharge of energy storage battery (X₃)

The depth of charge and discharge of the energy storage battery has been unitized when it is defined. However, the greater the depth of charge and discharge of the energy storage battery, the greater the damage to the life of the battery, that is, this index is also negatively correlated with the economy of the system. In order to make the optimization objective consistent with the expected results of the radar model, the depth of charge and discharge is treated as follows:

$${\mathrm{X}}_3=1-{\displaystyle \frac{{\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left|{\mathrm{P}}_{\mathrm{bes}}\right|}}{\mathrm{n}\cdot {\mathrm{P}}_{\mathrm{besmax}}}}$$

(14)

3.1.3. Determining the Weights of Optimization Indicators

In multi-objective optimization, for indicators of different importance, we need to give differentiated weights, usually using the subjective weight method, and using G1 method to calculate and determine the weights, the specific steps are as follows [15,16]:

Step (1): Arrange the optimization objectives in order of importance, with load satisfaction rate serving as a measure of the electric–thermal–hydrogen multi-energy storage system’s stability, new energy consumption rate evaluating its environmental performance, and energy storage charging and discharging frequency reflecting its economic efficiency. Prioritize these three optimization indicators based on subjective requirements.

$${\mathrm{X}}_1>{\mathrm{X}}_2>{\mathrm{X}}_3$$

(15)

Step (2): On the basis of ranking the importance of each indicator, determine the ratio of the importance of two adjacent indicators.

$$\left\{\begin{array}{c}{\mathrm{r}}_1={\mathrm{X}}_1/{\mathrm{X}}_2\\ {\mathrm{r}}_2={\mathrm{X}}_2/{\mathrm{X}}_3\end{array}\right.$$

(16)

where ${\mathrm{r}}_1$ and ${\mathrm{r}}_2$ are assigned according to the current design and requirements. The relative importance of ${\mathrm{X}}_{\mathrm{k}}$ and ${\mathrm{X}}_{\mathrm{k}+1}$ is proportional to the value of ${\mathrm{r}}_{\mathrm{k}}$, and ${\mathrm{r}}_{\mathrm{k}}$ takes 1 if it is equally important.

Step (3): Calculate the specific weight value of each optimization index according to Formula (17).

$$\left\{\begin{array}{c}{\omega }_1={\mathrm{r}}_1{\omega }_2\\ {\omega }_2={\mathrm{r}}_2{\omega }_3\\ {\omega }_3={(1+{\mathrm{r}}_1{\mathrm{r}}_2+{\mathrm{r}}_2)}^{-1}\end{array}\right.$$

(17)

where ${\omega }_{\mathrm{k}}$ is the specific weight of each optimization index.

3.2. Objective Function

In the process of utilizing the enhanced radar chart method to construct the objective function, initially, the weights of each indicator are sorted and based on this sorting outcome; the corresponding sector areas in the radar chart are arranged and allocated with angular degrees. Subsequently, employing the diagonals of each indicator’s respective sector area as axes enables every indicator to possess its own independent sector area, thereby addressing concerns related to shared sector areas and accurately reflecting indicator weights. Finally, connecting evaluation points successively along each axis completes the drawing of a comprehensive radar chart. By integrating half sectors from the respective indicator domains, this approach not only captures their influence on evaluation outcomes but also incorporates the interactions among indicators, thereby preventing fragmentation and illustrating their mutual influences. An objective function is designed based on parameters such as graph area and perimeter [17,18]. The specific steps are outlined as follows:

• Division of the unit circle: from the center of the circle O lead ray OA, cross the unit circle at point A, starting from OA, clockwise direction to do X₁, X₂, X₃ occupied by the sector, OB, OC line segment separate;
• Make the angular bisector of each region, respectively, marked as OX₁, OX₂, OX₃, that is, the corresponding line segment of the optimization index;
• Take the specific value of the optimized index after unitization as the length of the distance from the origin of each index, mark each length as X₁, X₂, X₃, and make three points a, b, and c, respectively, on the optimized index line segment;
• The three points are connected to obtain triangle ABC, which is the objective function image of the radar chart as shown in Figure 2.

Based on the improved radar chart image obtained in the figure above, its area S and perimeter L are calculated as follows:

$$\left\{\begin{array}{c}\mathrm{S}={\displaystyle \frac{1}{2}}\left({\displaystyle \sum _{\mathrm{i}=1}^2{\mathrm{X}}_{\mathrm{i}}{\mathrm{X}}_{\mathrm{i}+1}\sin \frac{{\theta }_{\mathrm{i}}+{\theta }_{\mathrm{i}+1}}{2}}+{\mathrm{X}}_1{\mathrm{X}}_3\sin {\displaystyle \frac{{\theta }_1+{\theta }_3}{2}}\right)\\ \mathrm{L}={\displaystyle \sum _{\mathrm{i}=1}^2\sqrt{{\mathrm{X}}_{\mathrm{i}}^2+{\mathrm{X}}_{\mathrm{i}+1}^2-2{\mathrm{X}}_{\mathrm{i}}{\mathrm{X}}_{\mathrm{i}+1}\cos \frac{{\theta }_{\mathrm{i}}+{\theta }_{\mathrm{i}+1}}{2}}+\sqrt{{\mathrm{X}}_1^2+{\mathrm{X}}_3^2-2{\mathrm{X}}_1{\mathrm{X}}_3\cos \frac{{\theta }_1+{\theta }_3}{2}}}\end{array}\right.$$

(18)

After calculating the area S and perimeter L, the system design adopts the area multiplied by perimeter as the objective function, and defines the objective function as follows:

$$\mathrm{F}=\mathrm{S}\times \mathrm{L}$$

(19)

The fitness objective function is jointly determined by the area and perimeter of the improved radar chart. The larger the fitness value, the better the overall performance of the system; conversely, if a certain indicator is too small, a larger fitness value still cannot be obtained. This method solves the problem of an uncertain area and perimeter caused by the sorting of indicators, and the impact of the sorting result on the evaluation result is in line with objective reality.

3.3. Constraints and Limitations

In order to ensure the safe and reliable operation of the multiple energy storage system, it is necessary to set some conditions and constraints for each unit and the whole system.

• System power balance

  $$\begin{array}{l}{\mathrm{P}}_{\mathrm{pv}}(\mathrm{t})+{\mathrm{P}}_{\mathrm{wt}}(\mathrm{t})=\\ {\mathrm{P}}_{\mathrm{bes}}(\mathrm{t})+{\mathrm{P}}_{\mathrm{ehi}}(\mathrm{t})+{\mathrm{P}}_{\mathrm{eci}}(\mathrm{t})-{\mathrm{P}}_{\mathrm{fco}}(\mathrm{t})+{\mathrm{P}}_{\mathrm{el}}(\mathrm{t})\end{array}$$

  (20)

  where ${\mathrm{P}}_{\mathrm{p}\mathrm{v}}\left(\mathrm{t}\right)$ represents the power generation of the photovoltaic unit at time t; ${\mathrm{P}}_{\mathrm{w}\mathrm{t}}\left(\mathrm{t}\right)$ represents the power generation of the wind unit; ${\mathrm{P}}_{\mathrm{b}\mathrm{e}\mathrm{s}}\left(\mathrm{t}\right)$ represents the charge and discharge power of the battery, positive for charging, negative for releasing ${\mathrm{P}}_{\mathrm{f}\mathrm{c}\mathrm{o}}\left(\mathrm{t}\right)$ electricity; ${\mathrm{P}}_{\mathrm{e}\mathrm{h}\mathrm{i}}\left(\mathrm{t}\right)$ represents the input power of the electric heating device; ${\mathrm{P}}_{\mathrm{e}\mathrm{c}\mathrm{i}}\left(\mathrm{t}\right)$ represents the input power of the electrolytic cell; ${\mathrm{P}}_{\mathrm{f}\mathrm{c}\mathrm{o}}\left(\mathrm{t}\right)$ represents the output power of the fuel cell; and ${\mathrm{P}}_{\mathrm{e}\mathrm{l}}\left(\mathrm{t}\right)$ is the power consumed by the electrical load. ${\mathrm{P}}_{\mathrm{b}\mathrm{e}\mathrm{s}}\left(\mathrm{t}\right)$ can be positive or negative, whereas the rest of the power values are positive.

Similarly, hydrogen network also satisfies the corresponding power balance equation:

$${\mathrm{V}}_{\mathrm{hsto}}(\mathrm{t})={\mathrm{V}}_{\mathrm{fci}}(\mathrm{t})+{\mathrm{V}}_{\mathrm{hl}}(\mathrm{t})$$

(21)

where ${\mathrm{V}}_{\mathrm{h}\mathrm{s}\mathrm{t}\mathrm{o}}\left(\mathrm{t}\right)$ represents the rate of hydrogen output from hydrogen storage tank at time t; ${\mathrm{V}}_{\mathrm{f}\mathrm{e}\mathrm{l}}\left(\mathrm{t}\right)$ represents the rate of hydrogen input by the fuel cell; and ${\mathrm{V}}_{\mathrm{h}\mathrm{l}}\left(\mathrm{t}\right)$ indicates the rate of hydrogen required for the hydrogen load.

2.

The power limit of wind and photovoltaic power generation units are as follows:

$$\left\{\begin{array}{c}0\le {\mathrm{P}}_{\mathrm{pv}}(\mathrm{t})\le {\mathrm{P}}_{\mathrm{pvmax}}(\mathrm{t})\\ 0\le {\mathrm{P}}_{\mathrm{wt}}(\mathrm{t})\le {\mathrm{P}}_{\mathrm{wtmax}}(\mathrm{t})\end{array}\right.$$

(22)

3.

The input power limit of energy conversion equipment is as follows:

$$\left\{\begin{array}{c}0\le {\mathrm{V}}_{\mathrm{fci}}(\mathrm{t})\le {\mathrm{V}}_{\mathrm{fcimax}}\\ 0\le {\mathrm{P}}_{\mathrm{eci}}(\mathrm{t})\le {\mathrm{P}}_{\mathrm{ecimax}}\\ 0\le {\mathrm{P}}_{\mathrm{ehi}}(\mathrm{t})\le {\mathrm{P}}_{\mathrm{ehimax}}\end{array}\right.$$

(23)

4.

The energy storage device output power limit is as follows:

$$\left\{\begin{array}{c}-{\mathrm{P}}_{\mathrm{besmax}}\le {\mathrm{P}}_{\mathrm{bes}}(\mathrm{t})\le {\mathrm{P}}_{\mathrm{besmax}}\\ 0\le {\mathrm{P}}_{\mathrm{tst}}(\mathrm{t})\le {\mathrm{P}}_{\mathrm{tstmax}}\\ 0\le {\mathrm{P}}_{\mathrm{hst}}(\mathrm{t})\le {\mathrm{P}}_{\mathrm{hstmax}}\end{array}\right.$$

(24)

5.

The energy storage state limit of energy storage equipment is as follows:

$$\left\{\begin{array}{c}{\mathrm{q}}_{\mathrm{SOC},\min }<{\mathrm{q}}_{\mathrm{SOC},\mathrm{t}}<{\mathrm{q}}_{\mathrm{SOC},\max }\\ 0<{\mathrm{q}}_{\mathrm{SOH},\mathrm{t}}<{\mathrm{q}}_{\mathrm{SOH},\max }\\ 0<{\mathrm{q}}_{\mathrm{SOT},\mathrm{t}}<{\mathrm{q}}_{\mathrm{SOT},\max }\end{array}\right.$$

(25)

3.4. Solving Algorithm

Based on the above optimization objectives, fitness function and constraint conditions, and taking maximizing fitness function as the operation scheduling objective, particle swarm optimization algorithm is adopted to solve the optimal scheduling model of multi-component energy storage system. The implementation steps are as follows [19,20]:

• Define the population parameters

Define the parameters of the population, including population dimension, population number s, maximum number of iterations g, inertia weight w, self-learning factor ${\mathrm{c}}_1$, and group learning factor ${\mathrm{c}}_2$. Then, according to the design needs, define the position boundary and velocity boundary of the population.

2.

Population initialization

Randomly assign initial population locations.

3.

Calculate fitness

The position of the initial population is brought into the calculation, and whether the system power balance constraints are met is calculated first, and the individuals that do not meet the constraints are eliminated; the individuals meeting the constraint conditions are calculated after each unit optimization index, and then the objective function is calculated as the fitness.

4.

Compare the fitness

Compare the calculated value of the objective function calculated by the initial individual, and select the most suitable individual position as the best group position of the initial population.

5.

Update the population position and speed and do boundary processing.

6.

Replace the updated population into the calculation, and repeat steps 3 and 4.

7.

Repeat steps 4–6 until the number of iterations reaches the preset g.

8.

Output the optimal individual position.

The specific flow chart of particle swarm algorithm is as follows in Figure 3.

4. Case Analysis

In this section, the actual wind and solar data of a typical day in spring of a certain place are selected to do simulation examples with a time-scale of one hour before the day to verify the operation effect of the comprehensive energy system containing electric–thermal–hydrogen multiple energy storage. The parameters such as maximum working power, capacity, and conversion efficiency for each module in the system are set as follows in

Table 1. Parameters of the energy converter.

Fixtures	Maximum Input Power	Conversion Efficiency
Electrolyzer	24 kW	0.7
Electric boiler	24 kW	0.95
Fuel cell	1500 L/h	0.95

and

Table 2. Parameters of energy storage devices.

Energy Storage Devices		Numerical Value
Energy storage battery	Single energy storage battery capacity	12,000 Ah
	Number of batteries	8
	Maximum charge and discharge power	12 kW
Heat storage tank	Capacity	1,000,000,000 J
	Maximum charge and discharge power	12 kW
Hydrogen storage tank	Capacity	200,000 L
	Maximum charge and discharge power	1500 L/h

[21]:

The power predictions for wind turbine photovoltaic generation and load power are depicted in Figure 4, Figure 5 and Figure 6:

It can be seen that both wind power and photovoltaic output are volatile. The peak period of photovoltaic output is from 9:00 to 17:00 during the day, and the volatility of wind power output is relatively large. The demand for electricity and heat load has a mismatch: the demand for heat load is small at noon and large at night, and the demand for electricity and hydrogen load is large during the day, which can meet the actual new energy input and load demand.

In order to validate the effectiveness and applicability of the multi-objective optimization management strategy based on an enhanced radar chart proposed in this study, four scenarios were established for comparative analysis. Considering the impact of weight adjustments, where Scenario One, Two, and Three all employ the improved radar chart multi-objective optimization management strategy, only changing the optimization index weights, the weight radar charts for the three scenarios are as follows in Figure 7:

Scenario 1 has more balanced weight settings; in the first consideration of satisfying load satisfaction rate, the weight setting of Scenario 2 is more environmentally friendly, and that of Scenario 3 is more economical.

The four sets of scenarios are:

Scenario 1: the weights of charge and discharge depth, absorption rate, and load satisfaction rate are set to 0.3, 0.3, and 0.4.

Scenario 2: the weight of depth of charge and discharge, absorption rate, and load satisfaction rate are set to 0.1, 0.4 and 0.5.

Scenario 3: the weight of depth of charge and discharge, absorption rate, and load satisfaction rate are set to 0.4, 0.1, and 0.5.

Scenario 4: SPEA2 algorithm is used to solve the electric–thermal–hydrogen integrated energy management model, and the solution with the best charge and discharge times is selected from the solution set.

Firstly, an analysis of the operational conditions of various modules within the system is conducted in Scenario 1. The subsequent diagram illustrates the dynamic trends of three distinct types of energy storage devices in this particular scenario.

As can be seen from Figure 8, the energy storage status of the energy storage battery and the heat storage tank is within the set range of 0.2–0.8, and the hydrogen storage status of the hydrogen storage tank is within the set range of 0–0.9, and the energy storage device can operate under normal conditions.

Figure 9 and Figure 10 show the energy conversion devices in the integrated energy system: the operating power curves of electrolytic cell, electric boiler, and fuel cell. It can be seen that the energy conversion devices can all operate normally under the constraint.

Figure 11 and Figure 12 illustrate the power, heat, and hydrogen supply situation within the integrated energy system. It is evident that the power supply curve for electricity, heat, and hydrogen aligns closely with the load demand curve, effectively meeting the load requirements.

The absorption rate variation curve for scenario one on that day is depicted in Figure 13. It can be observed that the absorption rate of renewable energy remains consistently high throughout most of the time period. However, a significant decline occurs between 14:00 and 16:00, which can be attributed to an abrupt surge in wind power output surpassing the system’s absorption capacity.

The optimization operating results for various types of scenarios were obtained through simulation examples in response to the four sets of scenarios, and a comparative analysis was conducted on the results for multiple scenario operations. The comparison of optimization indicator results is presented in

Table 3. Optimization results for four sets of scenarios.

	Scenario One	Scenario Two	Scenario Three	Scenario Four
Battery charging and discharging times	5.42	5.68	4.70	4.52
Reabsorption	0.913	0.916	0.898	0.906
Satisfy rate	0.932	0.928	0.921	0.915

:

The analysis of the optimization results of Scenarios One, Two, and Three is as follows: The load satisfaction rates under the three weight scenarios are all greater than 0.9, ensuring the stability of the system. Comparing Scenario Two and Scenario Three, both have the same demand for stability, but Scenario Two leans more towards environmental protection, while Scenario Three leans more towards economic considerations. After increasing the weight of the elimination rate in Scenario Two, the elimination rate indeed improved, but the number of battery charge and discharge cycles also increased, indicating that changes in the weight of the elimination rate index have a significant impact on indicators such as the number of battery charge and discharge cycles. The simulation results fully prove that by changing the weight of the multi-objective, the emphasis requirements of different performance can be met.

Compared with the simulation results of Scenario Three and Scenario Four, the battery charging and discharging times and absorption rate of Scenario Four are better, but its satisfaction rate is lower than that of Scenario Three. SPEA2 algorithm can find multiple excellent non-inferior solutions, providing a wider range of choices, and has a strong advantage in the case of providing multiple solution choices. The management strategy based on improved radar map proposed in this paper can quickly find solutions that meet the requirements of system energy efficiency and economy by using particle swarm optimization algorithm, and has its unique advantages in providing fast and single optimal solutions, which is suitable for scenarios with high real-time requirements.

5. Conclusions

Based on the construction of an integrated energy system architecture integrating electric–thermal–hydrogen multi-energy storage, this study presents a multi-objective optimization and scheduling strategy for electric–thermal–hydrogen multi-energy storage using an improved radar chart, considering system stability, environmental sustainability, and economic viability. Through comparative simulations in diverse scenarios, the following conclusions can be drawn:

• This strategy can effectively ensure the stability of load supply in integrated energy systems, and by changing the weights of multiple objectives, it can achieve result optimization under different performance requirements and attain various optimization effects.
• The proposed strategy demonstrates the ability to rapidly optimize based on predefined indicator weights. In comparison with the SPEA2 algorithm, which generates multiple solution sets, it possesses unique advantages in application scenarios that require a single optimal solution with high real-time performance.

In practical applications, integrated energy systems equipped with Energy Management Systems (EMS) are increasingly being widely adopted, providing an ideal application platform for the proposed optimization strategies. In various application scenarios such as new energy power plants and industrial parks, the optimization strategies based on radar charts can flexibly adjust the weights of each indicator on the radar chart according to their own key needs and objectives, thereby allowing the optimization strategies to better fit the characteristics of specific scenarios and achieve better optimization results.