Carbon Emission Optimization of the Integrated Energy System in Industrial Parks with Hydrogen Production from Complementary Wind and Solar Systems

Abstract

With the increasing utilization of renewable energy sources, hydrogen production from complementary wind and solar (HPCWS) systems has become a part of the construction of the integrated energy system (IES). However, renewable energy generation faces uncertainty; in addition, the IES lacks model representation. To solve this problem, this study proposes a carbon day-ahead optimal dispatch model for an integrated energy system with HPCWS and establishes carbon equations for conventional power generation and natural gas. The demand-side response of the IES is considered in conjunction with the objective functions of low-carbon operation and hydrogen storage gain maximization; furthermore, constraints are established to keep the dispatch results of the equipment within reasonable limits. Secondly, the scheduling model requires a faster and more accurate solution algorithm, so an improved particle swarm algorithm is proposed to solve the minimum of the objective function, and the superior convergence speed and accuracy of the algorithm are verified. The comparison of the IES before and after the introduction of HPCWS yields the changes in carbon emission values and hydrogen production before and after the optimization for the respective seasons and scenarios. In addition, the article also discusses the effect of season on the optimization results.

1. Introduction

In 2021, with the increasing global focus on “peak carbon” and “carbon neutrality”, China proposed the development of a new power system primarily based on new energy sources, with the aim of advancing the new energy industry and accelerating the adoption of energy harvesting technologies [1]. Hydrogen energy, which is recognized as an ideal clean energy, has become a key research focus, particularly its production using clean energy sources [2,3,4]. At present, China’s renewable energy generation, which is dominated by wind and solar power, faces challenges, such as intermittency and stochasticity, which hinder the large-scale adoption and efficient utilization of clean energy [5,6,7]. Integrated energy systems, which combine multiple energy sources to meet diverse demands—such as electricity, heating, and cooling—can ensure stable and efficient operation, particularly in building applications in complex scenarios [8].

In the field of research on integrated energy supply systems and hydrogen production systems, domestic and international scholars have primarily explored these topics from the perspectives of economic viability and energy consumption. Specifically, Chen constructed a mixed energy system comprising wind power generation, electrolyzers, fuel cells, and batteries; the study proposed a mixed-integer optimization model aimed at system capacity to enhance energy efficiency and economic performance [8]. Chen designed an optimization scheduling model for an integrated energy system tailored for a specific agricultural industrial park [9]. This model integrates biomass energy and power-to-gas technology and employs the ε-constraint method to optimize direct and indirect carbon emissions, thereby achieving a reduction in overall carbon emissions. Furthermore, Dai investigated combined heat and power systems, establishing comprehensive energy supply models and demand-side optimization models using various supply strategies; the study provided a detailed discussion of energy scheduling strategies based on different priorities [10]. Ma analyzed the coupling characteristics of various energy sources in the integrated energy system (IES) from the demand side and proposed an optimization scheme aimed at minimizing the system operating costs associated with diverse energy storage devices, thereby effectively promoting the widespread adoption of renewable energy sources [11]. In [12], energy efficiency and economic viability were prioritized, and a weighted average method was utilized to optimize and validate the model’s applicability in different scenarios.

Regarding renewable energy storage, Sun considered energy prices in the IES and applied the principle of iso-incrementality to develop an equipment control methodology to minimize economic costs [13]. Dong explored the coordinated control strategies among renewable energy storage stations, renewable energy aggregation stations, and shared battery storage; the study significantly reduced the issues of curtailed wind and solar energy while saving on storage costs [14]. Nan implemented a dynamic scheduling policy that addresses the problem of uncertain loads and multiple operating scenarios [15].

In the domain of green hydrogen production, Xu provided a detailed account of large-scale water electrolysis hydrogen production systems and demonstrated the efficiency of hydrogen production technology through a model design based on photovoltaic generation in direct current microgrids [16]. Cheng discussed the policies and technological developments of the hydrogen energy industry within the context of the “14th Five-Year Plan”, emphasizing the necessity of water electrolysis for hydrogen production [17]. Yuan proposed a hydrogen load coordination control strategy based on model predictive control and validated the effectiveness and robustness of this model through case studies [18]. Sun compared the performance differences between traditional thyristors and pulse width modulation hydrogen production power supplies [19]. Finally, Guo proposes a day-ahead optimization framework for IESs, aiming to achieve effective integration gain of wind energy and overall efficiency improvement of the integrated system, forming an efficient and scalable approach [20]. However, the modeling of the above studies is exclusively based on economics as the metric, while modeling and optimal scheduling with carbon emissions as the optimization metric are still not considered.

Collectively, the aforementioned literature reflects the research advancements in integrated energy systems concerning the enhancement of energy efficiency, the reduction in costs, and the minimization of environmental impacts; it also highlights the need for further investigation into environmental costs. This study focuses on IESs and integrated energy hydrogen production systems and aims to investigate the day-ahead scheduling scheme for minimum carbon emission and maximum hydrogen production for IESs equipped with hydrogen production from complementary wind and solar (HPCWS). Although scholars at home and abroad have conducted extensive discussions on economic and energy consumption aspects, much of the literature still mainly focuses on energy and economic efficiency and lacks in-depth research on the environmental impacts. With the increasing global attention to sustainable development and carbon neutrality goals, reducing carbon emissions has become an important direction in energy system research. Therefore, the goal of this study is to design an IES optimization scheduling model combined with a HPCWS system to reduce carbon emissions and improve the overall efficiency of the system. At the same time, this study also introduces the workflow of the improved particle swarm algorithm, and test functions are used to verify the feasibility of the optimization algorithm and summarize the advantages of the algorithm. The mathematical model of the integrated energy system is verified by introducing numerical examples. Finally, the future application prospects of the system are summarized. Therefore, the contributions of this study are as follows:

• This study establishes a linear regression model of carbon emissions; this model can be used to calculate the carbon emissions generated per megawatt hour of electrical energy under the dispatch of thermal power plants. At the same time, the carbon emissions generated by burning a unit of natural gas are calculated using the calorific value of methane, thereby providing an important basis for quantitative analysis;
• A day-ahead optimization scheduling model combined with hydrogen production from complementary wind and solar systems is proposed and integrated into the IES to form a complete optimization scheduling framework, thereby improving the flexibility and efficiency of scheduling;
• Although the traditional particle swarm optimization algorithm has good performance in many optimization problems, it often faces problems such as slow convergence speed, and it easily falls into a local optimum in complex problems. Therefore, this study combines the characteristics of the simulated annealing algorithm to improve it, and the advantage of the improved algorithm is verified in terms of convergence speed;
• The examples of small-scale industrial parks operating in different seasons in Hebei Province are combined with the demand-side response to ensure optimal scheduling results and to improve the practicality of the model.

Section 2 introduces the IES topology of the target industrial park. Section 3 introduces the energy flow model of the IES and the mathematical model of the balance equation. Section 4 proposes the carbon emission regression model for the thermal power plant and the natural gas carbon balance equation. Section 5 establishes the constraint equations of the IES and the optimization of the objective function. Section 6 introduces the principles of the proposed solution algorithms and proves their superiority. Section 7 optimizes a set of examples using the solution algorithms and draws the relevant conclusions. Section 8 concludes the whole paper and prospects for the future.

2. IES Components

This study focuses on the optimal scheduling of a conventional IES to achieve minimum carbon emissions in an integrated energy system (IES) while ensuring a stable energy supply. A hydrogen production system consisting of photovoltaic power (PP) and wind power (WP) with intermittent power (IP) that supplies power to the electrolyzer is introduced to study the optimal scheduling of the IES; the aim of the system is to achieve the maximum amount of hydrogen production and the minimum carbon emissions [11]. In addition, the study proposes the addition of combined cooling, heating, and power (CCHP) to this IES to realize the combined supply of electricity and heat and cold energy. Finally, in order to ensure the maximum use of IP energy, the IES containing HPCWS is constructed, as shown in Figure 1. In this IES, the electrical energy loads include demand-side loads, electrolyzers, electric heaters, electric chillers, and lithium bromide absorption chillers; the power generation system includes thermal power generation (conventional power generation), intermittent power generation, and gas turbine power generation; the heating demand is met by a combination of gas-fired boilers, waste heat boilers, and electric heaters; and the cooling demand is met by electric chillers and lithium bromide absorption chillers [12].

The hydrogen produced will be transported outside the industrial park and used for specific production processes within that park. Hydrogen will be used as a feedstock or energy source to support energy-intensive industrial operations such as chemical, metallurgical, or other industries that require large amounts of heat and power.

3. IES Energy Flow and Balance

In this IES, electrical and chemical energy work together to realize an integrated energy supply for the industrial park. The process of conventional power generation is conducted through the consumption of fossil energy; in this process, chemical energy is finally converted into electrical energy, and fly ash, carbon dioxide, sulfur dioxide, and nitrogen oxides are produced. According to the Emission Standard for Air Pollutants from Thermal Power Plants GB 13223-2011 [21], China has strict regulations on harmful emissions from coal-fired boilers and gas turbine units. However, there are no strict regulations on carbon emissions; thus, the relationship between the generation of electricity and the emission of carbon dioxide can be deduced based on the power plant’s power generation capacity and the rate of carbon dioxide emissions [22]. Similarly, in a power generation system consisting of gas turbines, it is possible to calculate the carbon emissions and power generation from the gas consumption and the combustion efficiency of the gas [23].

3.1. IES Energy Flow

Figure 2 shows a schematic diagram of the direction of the flow of electricity/heat in the integrated energy system; the system includes a supply grid consisting of conventional power generation, intermittent power generation, gas turbines in the electrical energy section, and the power supply from the park’s electricity, refrigeration appliances, and heating appliances on the demand side. Conventional power generation uses coal-fired boiler units to generate electricity, with the unit’s capacity recorded as S_tri (unit kW) and the carbon emissions as M_tri (unit kg); intermittent generators are categorized into photovoltaic power generation and wind power generation, with the capacity connected to the grid recorded as S_cle and the power supplied to electrolysis tanks as S_hyd; the capacity of the gas turbine generator unit connected to the grid is recorded as Stur. In the system, the refrigeration appliances are central air conditioning systems and inhalation chillers; the installed capacities of these appliances are S_cool and S_LiBr, respectively. The heating appliances are mainly electric heating rods, which are used to supplement the production and transmission of heat energy, and their installed capacity is recorded as Shot. The electrolyzer’s function is to consume electrical energy to electrolyze water in an aqueous solution and convert it into hydrogen and oxygen, which is then collected in the hydrogen storage tanks.

The volume of natural gas is used as input in the heat part and is delivered to the gas turbine and gas boiler, respectively. The gas turbine is used as a supplement to the grid for power generation, and the gas boiler is used as a heat source for heating in winter; the volume of natural gas consumed per unit of time is denoted as V_tur and V_boi (unit: m³); the carbon emissions produced are M_tur and M_boi (unit: kg), respectively; the amount of heat produced per unit of time is denoted as E_tur and E_boi (in kW). The operation of the gas turbine generates a large amount of high-temperature exhaust gas, and the heat carried by the exhaust gas is collected by the waste heat boiler. The waste heat boiler delivers the heat to the heating network or absorption chiller according to the seasonal conditions; the heat energy per unit time delivered to the heating network is denoted as E_rem, and the heat energy per unit time delivered to the absorption chiller is denoted as E_LiBr. In addition, the heat energy per unit time delivered from the electric heater to the heating network is denoted as E_hot, respectively.

In the refrigeration part of the input of electric energy and heat input from the waste heat boiler, the inhalation chiller absorbs the heat energy collected by the waste heat boiler through a series of physical changes after the output of cold water. The cold power generated by this process is recorded as Q_LiBr (unit: kW). The electric chiller produces cold power by consuming electric energy for heat exchange, and the cold power produced is denoted as Q_cool. Line loss, heat dissipation per unit time, and cold dissipation per unit hour are introduced in the three components, which are denoted as S_obs, E_obs, and Q_obs, respectively. The amount of loss is calculated as a proportion of the load; thus, the proportionality coefficients σ_S, σ_E, and σ_Q are introduced, i.e.:

$$S_{obs}={\sigma }_s\cdot S_{output}$$

(1)

$$E_{obs}={\sigma }_E\cdot E_{output}$$

(2)

$$Q_{obs}={\sigma }_Q\cdot Q_{output}$$

(3)

In this study, the internal energy of a medium is measured as a variable of the difference between the thermodynamic temperature of the medium and the thermodynamic temperature of the outside world of that medium at the usual conditions (25 °C, 1 standard atmospheric pressure).

3.2. IES Energy Balance

In the electrical energy component, the energy currents conform to a constant equation:

$$S_{tri}+S_{cle}+S_{tur}-S_{obs}=S_{hot}+S_{cool}+S_{LiBr}+S_{output}$$

(4)

The units in Equation (1) are converted to kilowatts (kW). The electrolysis of water is the reverse of the hydrogen–oxygen combustion reaction, and the electrolytic cell takes advantage of this by converting electrical energy into chemical energy. Assuming that the complete combustion of hydrogen and oxygen to produce water has a calorific value per unit volume of $H_h^V$ (in kJ∙m⁻³) in standard conditions and that the volume of hydrogen produced per unit hour is V_hyd, a portion of the electrical energy consumed will be involved in the thermo-chemical reaction; therefore, the energy utilization of the electrolysis cell is defined as follows:

$${\xi }_{hyd}={\displaystyle \frac{V_{hyd}\cdot H_h^V}{3600\cdot {\displaystyle {\int }_{t_0}^t{S}_{hyd}(t)}dt}}$$

(5)

In this study, it is assumed that the hydrogen generated from the electrolyzer is fully transferred to the hydrogen storage tanks and that no hydrogen leakage, for example, is involved. The hydrogen in the storage tanks will be transported to hydrogen loads outside the industrial park, so possible hydrogen losses during transfer are not considered. It is also assumed that no energy from the hydrogen loads will be transferred to this industrial park.

In the CCHP heating network, the natural gas input conforms to the constant equation:

$$V_{GAS}=V_{tur}+V_{boi}$$

(6)

A gas turbine is a turbine in which compressed air and gas are injected into a combustion chamber; the gas rapidly burns and expands to drive the impeller to rotate, the impeller transmits the torque to a generator, and the exhaust gas carries the heat into a waste heat boiler [23]. In the standard case, it is assumed that the calorific value per unit volume of natural gas and compressed air entering the combustion chamber with complete chemical reaction is $H_{tur}^V$. The energy is allocated to electrical and thermal energy according to different weights, denoted as w_St and w_Et. The coefficient of performance of the gas turbine is as follows:

$${\xi }_{tur}={\displaystyle \frac{3600\cdot {\displaystyle {\int }_{t_0}^t{w}_{St}\cdot S_{tur}(t)+w_{Et}\cdot E_{tur}(t)}dt}{V_{tur}\cdot H_{tur}^V}}$$

(7)

Therefore, the energy balance equation of the gas turbine can be derived. In the winter in the northern region of China, the heating company supplies heat to the park. The gas boiler has high thermal efficiency, a simple structure, and other advantages. Through the combustion of natural gas, the heat energy produced by the chemical reaction is transferred to the heating water [24]. Similarly, assuming the standard case in which the natural gas and compressed air entering the boiler combustion chamber to fully carry out the chemical reaction have a calorific value per unit volume of $H_{boi}^V$, it is possible to derive the coefficient of performance of the gas boiler as follows:

$${\xi }_{boi}={\displaystyle \frac{3600\cdot {\displaystyle {\int }_{t_0}^t{E}_{boi}(t)}dt}{V_{boi}\cdot H_{boi}^V}}$$

(8)

As the exhaust gas of the gas turbine carries high-temperature gasses that escape, a waste heat boiler is set up to collect the energy carried by the exhaust gas of the gas turbine, and the high-temperature exhaust gas is turned into low-temperature exhaust gas and discharged into the atmosphere. Therefore, the heat transfer efficiency of the waste heat boiler is recorded as η_rem, and the energy conservation equation for the waste heat boiler is as follows:

$${\eta }_{rem}\cdot E_{tur}=E_{LiBr}+E_{rem}$$

(9)

The thermal efficiency and power factor of the electric heater are very high; thus, most of the electric energy consumed by the electric heater is converted into thermal energy, and its thermal efficiency is η_hot. At the same time, the corresponding power line can be considered to have no reactive power. Therefore, the heat conversion equation of the electric heater is as follows:

$${\eta }_{hot}\cdot S_{hot}=E_{hot}$$

(10)

Finally, the balance equation of the heat supply network is as follows:

$$E_{boi}+E_{rem}+E_{hot}-E_{obs}=E_{outvut}$$

(11)

The CCHP cold transmission pipe network is similar to the heating network, and most of the electric chillers in buildings are central air conditioners. Unlike electric heaters, central air conditioners have a certain energy conversion efficiency and power factor as a power load; therefore, the coefficient of performance of central air conditioners is as follows:

$${\xi }_{cool}={\displaystyle \frac{{\displaystyle {\int }_{t_0}^t{Q}_{cool}(t)}dt}{{\displaystyle {\int }_{t_0}^t{S}_{cool}(t)}dt}}$$

(12)

LiBr absorption chillers use a high-temperature water vapor refrigerant, with a concentrated solution of lithium bromide as the absorber, to reduce the temperature via physical changes in the reaction chamber [25]. The coefficient of performance of the LiBr absorption chiller is defined as follows:

$${\xi }_{LiBr}={\displaystyle \frac{{\displaystyle {\int }_{t_0}^t{Q}_{LiBr}(t)}dt}{{\displaystyle {\int }_{t_0}^t[S_{LiBr}(t)+E_{LiBr}(t)]}dt}}$$

(13)

The equilibrium equation for the cold transfer pipe network is as follows:

$$Q_{cool}+Q_{LiBr}-Q_{obs}=Q_{output}$$

(14)

4. Carbon Emission Calculations for IES

Commercial natural gas in China contains more than 90% methane, along with other components such as nitrogen, ethane, and propane, and its average density is about 0.7 times the average density of air. The average density of air under standard conditions (0 °C, 1 standard atmosphere) is ρ₀ = 1.29 kg∙m⁻³; therefore, the average density of natural gas under standard conditions is ρ_GAS = 0.8255 kg∙m⁻³. The periodic table shows that the relative atomic mass of carbon is 12.011, that of hydrogen is 1.008, and that of oxygen is 15.9994; therefore, the element carbon occupies 74.914% of the mass fraction of methane.

By the chemical reaction formula:

$$C{H}_4(\mathrm{g})+2O_2(\mathrm{g})\to C{O}_2(\mathrm{g})+2H_{2}O(g)$$

In the case of complete methane combustion, all of the carbon in methane is converted to carbon dioxide. Considering only natural gas, which is composed exclusively of methane, the carbon emissions from gas turbines and gas boilers are as follows:

$$M_{tur}=V_{tur}\cdot {\rho }_{C{H}_4}\cdot 74.914\%$$

(15)

$$M_{boi}=V_{boi}\cdot {\rho }_{C{H}_4}\cdot 74.914\%$$

(16)

The hourly rate of CO₂ emissions from the 660 MW generating unit of the power plant at different generating capacities is given in [14]. The relationship between the amount of electricity generated and the amount of carbon dioxide emitted in one hour, using the calculation based on the relative atomic mass of carbon and oxygen to obtain the carbon emissions, is shown in

Table 1. Carbon emissions of 660MW generators.

Generation Capacity (MW∙h)	CO2 Emissions (kg)	Carbon Emissions (kg)
362	381,623.24	104,125.61
497	539,028.39	147,111.63
559	453,117.32	123,664.78
614	564,526.62	154,070.61
659	589,483.89	160,881.94

.

Based on the information in the table, it is possible to obtain the slope of the linear regression between electricity generation and carbon emissions as b_tri = 253.4. Therefore, it can be assumed that conventional electricity generation emits 253.4 kg of carbon mass per 1 MW∙h of electricity generated.

5. Optimizing the Objective Function

5.1. IES Constraints

The IES is optimized in terms of electrical, thermal, and cooling power per unit hour, with minimum carbon emissions and maximum hydrogen production as the objective function; at the same time, the normal supply of electrical, thermal, and cooling loads is ensured [10]. The balance model of the power and energy of the system is presented in Section 2. In practice, the equipment operates differently depending on the season and load. Adding system constraints can control the starting and stopping of the equipment in different seasons and different scenarios, and the optimization is performed during the simulation of the program for the cases where the power is negative or exceeds the maximum allowable overload power of the equipment. The gas turbine thermal power constraints are as follows:

$$x_{tur}\cdot E_{tur}^{min}\le E_{tur}(t)\le x_{tur}\cdot E_{tur}^{max}$$

(17)

$$w_{St}+w_{Et}=1$$

(18)

where x_tur describes the operating state of the gas turbine and takes the value of {0,1}, $E_{tur}^{\min }$ describes the lower limit of heat production per unit time of the gas turbine, and $E_{tur}^{\max }$ describes the upper limit of heat production per unit time of the gas turbine.

(1) Gas boiler thermal power constraints:

$$x_{boi}\cdot E_{boi}^{min}\le E_{boi}(t)\le x_{boi}\cdot E_{boi}^{max}$$

(19)

where x_boi describes the operating state of the gas boiler and takes the value of {0,1}, $E_{boi}^{\min }$ describes the lower limit of heat production per unit time of the gas boiler, and $E_{boi}^{\max }$ describes the upper limit of heat production per unit time of the gas turbine.

(2) Electrical heater thermal power constraints:

$$0\le E_{hot}(t)\le x_{hot}\cdot E_{hot}^{max}$$

(20)

where x_hot describes the operating state of the gas turbine and takes the value of {0,1} (as the electric heater can realize smooth power regulation, the lower limit of the thermal power of the electric heater can be considered to be zero), and $E_{hot}^{\max }$ describes the upper limit of the heat production per unit time of the gas turbine.

(3) Thermal power input constraints for absorption chillers:

$$x_{LiBr}\cdot E_{LiBr}^{min}\le E_{LiBr}(t)\le x_{LiBr}\cdot E_{LiBr}^{max}$$

(21)

$$S_{LiBr}=\left\{\begin{array}{l}{S}_{LiBr}^{max}\hspace{1em}\hspace{1em}\hspace{1em},Q_{LiBr}(t)>200\\ 0.5\cdot Q_{LiBr}(t),Q_{LiBr}(t)\le 200\end{array}\right.$$

(22)

where x_LiBr describes the working state of the absorption chiller and takes the value of {0,1}, $E_{LiBr}^{\min }$ describes the lower limit of absorbed heat per unit time of the absorption chiller, and $E_{LiBr}^{\max }$ describes the upper limit of absorbed heat per unit time of the absorption chiller.

(4) Electric chiller cooling capacity constraints:

$$x_{cool}\cdot Q_{cool}^{min}\le Q_{cool}(t)\le x_{cool}\cdot Q_{cool}^{max}$$

(23)

where x_cool describes the working state of the electric cooler and takes the value of {0,1}, $E_{cool}^{\min }$ describes the lower limit of the cooling capacity per unit time of the electric cooler, and $E_{cool}^{\max }$ describes the upper limit of the heat absorbed per unit time of the electric cooler.

(5) Electrolytic cell input electric power constraints:

$$x_{hyd}\cdot S_{hyd}^{min}\le S_{hyd}(t)\le x_{hyd}\cdot S_{hyd}^{max}$$

(24)

$$0\le S_{hyd}(t)\le S_{cle}^{max}(t)$$

(25)

$$S_{hyd}(t)+S_{cle}(t)=S_{cle}^{max}(t)$$

(26)

where x_hyd describes the working state of the electrolyzer and takes the value of {0,1}, $S_{hyd}^{\min }$ describes the lower limit of active power for stable operation of the electrolyzer, $S_{hyd}^{\max }$ describes the upper limit of active power for stable operation of the electrolyzer, and $S_{cle}^{\max }$ (t) describes the maximal output of the intermittent power supply at the moment t. In addition, we need to consider the capacity of the electrolyzer to select the volume of the hydrogen storage tank. The principle of selection is based on twice the maximum daily hydrogen production in the electrolyzer. However, HPCWS does not make the electrolyzer work at the maximum power point at all times. Therefore, we do not need to define the volume constraint of the hydrogen storage tank.

5.2. IES Objective Function

The optimization objective of the integrated energy system includes the demand-side response; the output and the demand-side load demand of the integrated energy system are defined as τ_out and τ_l, respectively, and the first objective function is defined as the minimum of the 2-parameter of the difference between τ_out and τ_l, i.e.:

$${\mathit{\tau }}_{out}={\left(S_{output},E_{output},Q_{output}\right)}^T$$

(27)

$${\tau }_l={\left(L_S,L_E,L_Q\right)}^T$$

(28)

$$\min \left\{F_1\right\}=\parallel {\tau }_l-{\tau }_{out}{\parallel }_2$$

(29)

where L_S represents the active power requirement of the demand-side load, L_E represents the heat load requirement of the demand-side load, and L_Q represents the cold load requirement of the demand-side load.

The second objective function is defined as the minimum value of the ratio of carbon emissions to the amount of hydrogen stored in the IES, i.e.:

$$\min \{F_2\}={\displaystyle \frac{b_{tri}\cdot {\displaystyle {\int }_{t_0}^t{S}_{tri}}dt+M_{tur}+M_{boi}}{v_{hyd}}}$$

(30)

The optimization model with F₁ and F₂ is designed to be bi-objective and to use the improved particle swarm optimization algorithm to find the best solution.

6. Numerical Case Analysis

6.1. PSO Improved Based on SA

Particle swarm optimization (PSO) is essentially a stochastic search algorithm, which can effectively optimize various functions, and it is widely used in the fields of constraint optimization, function optimization, robot control, power system optimization, parameter estimation in biomedicine, and so on. PSO algorithms originated from the simulation of a simple social system, and they have a strong global search capability for nonlinear functions. PSO initialization is the process of updating the speed and position of a group of random “particles” in the metric space, where the objective function is located after a certain number of iterations [26]. After a certain number of iterations, the “particles” gradually converge to the vicinity of a point and increasing the number of “particles” can effectively avoid the generation of local optimal solutions.

Simulated annealing (SA) is a stochastic optimization algorithm based on the annealing process in statistical mechanics that is usually used to solve combinatorial optimization problems. It is inspired by the process of crystal structure change during the annealing of metals and involves the simulation of the actions of crystals jumping out of the local energy minimum state during annealing; the aim is to find a globally optimal solution. In the search process, the SA algorithm can effectively avoid the search into the local optimal solution; combined with the PSO algorithm, it can greatly increase the search speed and stability. The basic idea of the improved PSO algorithm based on the SA algorithm is to make the SA algorithm participate in the position and velocity update of the “particle” during the iteration process of the basic PSO algorithm. As shown in Figure 3, the flow chart of the improved PSO algorithm based on the SA algorithm evaluates the adaptability of each particle after initializing the position, velocity, and initial temperature of the particle and selects the particle with the optimal adaptation value. Then, the adaptation value of each “particle” at the current temperature is determined as follows:

$$TF(p_i)=e^{-{\displaystyle \frac{F(p_i)-F(p_g)}{T}}}/\sum _{j=1}^N{e}^{-{\displaystyle \frac{F(p_j)-F(p_g)}{T}}}$$

(31)

where F(x) represents the objective function with x as the independent variable, p_i represents the position of the ith particle, p_g represents the position of the current optimal “particle”, N represents the total number of “particles”, and T represents the current temperature.

After calculating the adaptation value, the position of the particle is updated according to Equations (32)–(34):

$$x_{i,j}(t+1)=x_{i,j}(t)+v_{i,j}(t+1)$$

(32)

$$\begin{array}{l}{v}_{i,j}(t+1)=\phi \cdot \{v_{i,j}(t)+c_1\cdot r_1\cdot [p_{i,j}-x_{i,j}(t)]+\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} c_2\cdot r_2\cdot [p_{g,j}-x_{i,j}(t)]\}\end{array}$$

(33)

$$\phi ={\displaystyle \frac{2}{2-(c_1+c_2)-\sqrt{{(c_1+c_2)}^2-4\cdot (c_1+c_2)}}}$$

(34)

where c₁ and c₂ represent learning factor 1 and learning factor 2, respectively, and r₁ and r₂ represent the values taken from a uniform distribution U(0,1), respectively. After the execution of the above steps, the optimal fitness value for this iteration and the global optimal fitness value are updated, and if the algorithm has searched all the “particles”, the program stops working. Otherwise, the “Particle” adaptation value is recalculated. After the search is complete, the de-tempering operation is carried out as follows:

$$T_{t+1}={\omega }_n{T}_t$$

(35)

$$T_0=F(p_g)/ln5$$

(36)

6.2. Algorithm Verification Analysis

In this study, to verify the performance of the improved PSO algorithm based on SA, an objective function is assumed for optimization, while the elementary particle swarm algorithm and the whale algorithm are used as a control group for comparison. A simple continuous function, F(x), is defined in the two-dimensional real plane with a control independent variable x ∈ {s: 0 ≤ s ≤ 100}. The optimization objective is to minimize the Euclidean distance from the curve of the function, F(x), at any point, P, in the two-dimensional plane G ∈ {(s,t): 0 ≤ s ≤ 100, 0 ≤ t ≤ 50}, and the objective function is denoted by the 2-parameter as follow:

$$\min \left\{F_3\right\}=\parallel P-P_f{}_2\parallel$$

(37)

where vector P is the vector pointing to the random point, P, from the coordinate origin; vector P_f is the vector pointing to the random point, P, from the coordinate origin at the point of minimum distance from the random point P on the function curve F(x). Figure 4 shows a comparison of the outputs of the traditional particle swarm, where the optimization algorithm and the improved particle swarm algorithm are based on the simulated annealing algorithm.

As can be seen in Figure 4, the traditional PSO algorithm requires more than 20 iterations for the result to converge to 0, and there is a probability that the program will “get lost” when it starts, resulting in more iterations for the output to reach stability. The improved particle swarm algorithm based on the simulated annealing algorithm stabilizes after about 15 iterations, and the discrete nature of the output value is weaker. After about 50 independent repeated experiments, it can be concluded that the convergence speed of SAPSO is improved by more than 20% compared to PSO. In summary, the improved PSO algorithm based on the simulated annealing algorithm has a more stable output and a faster response speed compared to the traditional PSO algorithm.

7. Analysis of Examples

7.1. Input Parameters

We use the integrated energy system of a small-scale industrial park in Hebei Province in summer and winter as an example. Its summer and winter demand-side electric load, heat load, and cooling load are shown in Figure 5, respectively; the wind power output, photovoltaic output, and intermittent energy output in summer and winter are shown in Figure 6. Constant parameters, such as the conversion rate and efficiency of the integrated energy system, are shown in

Table 2. Constant values of the IES.

Parameters	Value	Parameters	Value
${\xi }_{hyd}$	0.8	${\eta }_{hot}$	0.98
${\xi }_{fuel}$	0.43	$w_{St}$	0.15
${\xi }_{tur}$	0.6	$w_{Et}$	0.85
${\xi }_{boi}$	0.45	${\sigma }_S$	0.95
${\xi }_{LiBr}$	0.8	${\sigma }_E$	0.85
${\xi }_{cool}$	6.0	${\sigma }_Q$	0.85
${\eta }_{rem}$	0.75	${\sigma }_S$	0.85

; the system equipment parameters are shown in

Table 3. Equipment parameters of the IES.

Parameters	Value	Parameters	Value
$E_{tur}^{max}$	1500 kW	$Q_{cool}^{min}$	0 kW
$E_{tur}^{min}$	70 kW	$S_{hot}$	140 kW
$E_{boi}^{max}$	1500 kW	$S_{cool}$	200 kW
$E_{boi}^{min}$	0 kW	$S_{hyd}$	200 kW
$E_{LiBr}^{max}$	600 kW
$E_{LiBr}^{min}$	0 kW
$Q_{cool}^{max}$	80 kW

; and the physical parameters of hydrogen and methane are shown in

Table 4. Physical and chemical properties of methane and hydrogen.

Formula	Calorific Value per Unit Volume at Standard Conditions	Density in Standard Conditions
${CH}_4$	−35.9 $\mathrm{M}\mathrm{J}/{\mathrm{m}}^3$	0.716 $\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$
$H_2$	−12.7 $\mathrm{M}\mathrm{J}/{\mathrm{m}}^3$	0.089 $\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$

.

7.2. Setting the Scene

Three scenarios were set up for optimization, where Scenario A only considers minimizing carbon emissions without considering hydrogen production, and Scenario B further optimizes the system by introducing an electrolyzer and considering hydrogen production in addition to carbon emissions.

The introduction of hydrogen production may have some impact on the efficiency of the system, as the process of hydrogen production itself involves electricity consumption. However, by using hydrogen as an energy supply for the external industrial park, the system may bring gains in energy supply while achieving carbon reduction targets. The complex impact of hydrogen introduction on the operational efficiency of the system is further demonstrated by the large differences in equipment utilization and efficiency performance between the different scenarios, especially in summer and winter. Although hydrogen production itself may entail some energy losses, its application for hydrogen export in industrial parks can provide additional flexibility and energy supply capacity to the integrated energy system, thus, improving the overall efficiency and sustainability of the system.

In the summer and winter seasons, the use of the equipment varies from scenario to scenario, as shown in

Table 5. Equipment operating status.

Scenario	Summer A	Summer B	Winter A	Winter B
$x_{tur}$	1	1	1	1
$x_{boi}$	0	0	1	1
$x_{hot}$	0	0	1	1
$x_{LiBr}$	1	1	1	1
$x_{cool}$	1	1	0	0
$x_{hyd}$	0	1	0	1

.

7.3. Optimization Results

The particle swarm optimization algorithm improved based on the simulated annealing algorithm updates a set of global best variables after each iteration, following substitution into the objective function to obtain the global minimum. In this study, the maximum number of iterations is set to 300, the number of particles is 50, the annealing constant is 0.8, and the search dimension is 24.

We need to define a key performance indicator: carbon emission reduction. The reference value for carbon emissions represents the emissions that would have been produced to meet the load requirements without the CCHP system. Carbon emission reduction is calculated as the percentage decrease in carbon emissions, comparing the optimized emissions value to the reference emissions value.

7.3.1. Optimal Scheduling in Summer Scenario A

In summer scenario A, the gas boiler, electric heater, and electrolyzer are off; at this time, all the PV and wind power generation is input into the grid; Figure 7 shows the histogram of carbon emissions in summer scenario A, where the horizontal coordinate represents the time, and the vertical coordinate represents the total carbon emissions of the IES after optimized scheduling. Figure 8, Figure 9, and Figure 10 show the optimal scheduling of electricity, heat, and cold in summer scenario A, respectively. Where the horizontal coordinate is time, and the vertical coordinate is the output power of each part of the IES after optimal scheduling.

This is shown in Figure 7, which illustrates the optimized hourly carbon emissions. Combined with the analysis in Figure 8, Figure 9 and Figure 10, we can see that the CCHP system’s operating configuration effectively minimizes carbon emissions. By regulating the energy allocation, the CCHP configuration achieves the optimal carbon emission performance in each hourly segment.

7.3.2. Optimal Scheduling for Summer Scenario B

Compared to summer scenario A, summer scenario B starts the operation of the electrolyzer; part of the PV and wind power contributes to the operation of the electrolyzer, and part of it is connected to the grid. Figure 11 shows the histograms of the carbon emissions and hydrogen gas production in summer scenario B. Where the horizontal coordinate indicates the time, the left vertical coordinate demonstrates the hydrogen production after optimized scheduling, and the right vertical coordinate shows the total carbon emissions of the IES after optimized scheduling. Figure 12 shows the optimal dispatch of electric power in summer scenario B, where the meaning of the coordinates is the same as in Figure 8.

This is shown in Figure 11, which illustrates the optimized hourly carbon emissions and hydrogen production. We can see that the operational configuration of the CCHP system is still effective in minimizing carbon emissions after the electrolyzer is operating. In addition, in summer scenario A and scenario B, the heat transfer power curves and cooling power curves are the same in both scenarios and are not shown in this paper as the heat released from the exhaust gas by the gas turbine is much larger than the heat load demand, while the heat absorbed by the inhalation chiller is entirely sufficient to supply the cooling load.

After the simulation of the example, it can be seen that in summer scenario A in this IES, the vertical carbon emission is 3556.6 kg/d before scheduling and the total carbon emission is 3193.2 kg/d after scheduling; the scheduling reduces the carbon emission by 10.2%. In summer scenario B, the total carbon emission is 3694.4 kg/d, which increases the carbon emission by 15.7% compared to the pre-introduction carbon emission. Therefore, the introduction of the hydrogen production equipment increases the carbon emissions when the total hydrogen production of the standard case is 878.29 m³.

7.3.3. Optimal Scheduling for Winter Scenario A

In winter scenario A, the electric cooler and electrolyzer are off, and all the PV and wind power is fed to the grid. A histogram of carbon emissions in winter scenario A is shown in Figure 13, and the optimal scheduling of the electricity, heat, and cooling in winter scenario A is shown in Figure 14, Figure 15, and Figure 16, respectively.

Figure 13 shows the optimized hourly carbon emissions. Same as the optimization results in summer, combined with the analysis in Figure 14, Figure 15 and Figure 16, we can see that the operational configuration of the CCHP system effectively reduces the carbon emissions.

7.3.4. Optimal Scheduling in Winter Scenario B

Compared to winter scenario A, winter scenario B starts the operation of the electrolyzer; part of the PV and wind power is discharged to the electrolyzer, and part of it is connected to the grid. Figure 17 shows the histograms of the carbon emission and hydrogen production in winter scenario B. Figure 18 and Figure 19 show the optimized scheduling of the electric power and heat transfer power in summer scenario B.

As shown in Figure 17, the graph shows the optimized hourly carbon emissions and hydrogen production. We can see that the operational configuration of the CCHP system is effective in minimizing carbon emissions even after the electrolyzer is running. In winter scenario A and scenario B, the heat absorbed by the inhalation chiller is entirely sufficient to supply the cold load; therefore, the cooling power transfer curves are the same in both scenarios and are not shown in this paper.

After the simulation of the example, it can be seen that, in this IES, the carbon emission before optimization is 5889.8 kg/d and that the total carbon emission is 3875.0 kg/d in winter scenario A. The optimization reduces the carbon emission by 34.2%. In winter scenario B, the total carbon emission is 4212.1 kg/d, and the carbon emission is increased by 8.7%. Therefore, the introduction of hydrogen production equipment increases the carbon emissions, at which point the amount of hydrogen produced in the standard case is 753.56 m³.

7.4. Evaluation of Algorithm Performance and Carbon Economics

7.4.1. Feasibility and Limitations of the Optimization Algorithm

We adopt a SAPSO-based optimization solution method, which aims to achieve the best energy allocation and hydrogen production scheme by finding the minimum value of the objective function. However, the computational complexity and time consumption of the algorithm may become a bottleneck for large-scale system applications in practice. Therefore, the computational efficiency of the SAPSO algorithm needs to be evaluated under different scale systems, especially its scalability in large-scale and real-time applications.

Although the SAPSO algorithm has achieved remarkable results in optimizing the performance of wind and light complementary hydrogen production systems, it still has some limitations in practical applications, mainly in terms of computational complexity and scalability of the algorithm. Specifically:

• As the scale of new energy generation systems continues to expand, the number of wind turbines and solar panels is also on a large-scale trend, leading to a sharp increase in the computational complexity of the SAPSO algorithm. In this case, the algorithm may require more computational resources and longer computation time, which has an impact on the application of minute-level optimal scheduling. Although this problem can be mitigated by sacrificing accuracy, it is still a significant challenge;
• The SAPSO algorithm may encounter performance bottlenecks when dealing with high-dimensional, large-scale problems. Although the algorithm has made a breakthrough in improving the convergence speed of traditional particle swarm optimization (PSO) algorithms, its convergence speed and accuracy may not be able to meet the demands of practical applications when facing complex multi-objective optimization problems. Therefore, we urgently need to further optimize the algorithm to improve its scalability and computational efficiency to adapt to the evolving practical application scenarios.

7.4.2. Carbon Economic Analysis

Our proposed optimized dispatch scheme needs to firstly satisfy the energy supply on the demand side and, on this basis, achieve the lowest carbon emission while improving the overall performance of the wind–solar hybrid hydrogen production system. However, the implementation of the optimization scheme needs to focus not only on the technical aspects of the optimization but also fully evaluate its economics. Economy is one of the key factors to achieve technical success in large-scale commercial applications, and how to balance costs and benefits directly determines the feasibility and promotion prospects of the system. Therefore, the optimal scheduling strategy in this paper focuses on carbon emissions while also analyzing its economics from a carbon economy perspective.

In this process, although the introduction of high percentage renewable energy (HPCWS) increases the output of conventional power generation to a certain extent, it also leads to a rise in carbon emissions. From a carbon economy perspective, this means that hydrogen production can be increased by appropriately sacrificing carbon emissions. It is by balancing carbon emissions with hydrogen production that the optimal dispatch scheme ensures that the overall efficiency of the system is maximized. Therefore, although the introduction of HPCWS in winter can reduce direct carbon emissions to a certain extent, some of the carbon emissions are still transferred to the hydrogen production process due to the nature of seasonal load fluctuations. This phenomenon reflects the distribution characteristics of carbon emissions and its impact on system scheduling under different seasonal energy demand fluctuations.

8. Conclusions and Future Perspectives

8.1. Conclusions of the Study

This study constructed an IES model and its corresponding mathematical model with the aim of reducing carbon emissions. Additionally, an HPCWS system was introduced. To enhance the convergence speed of the optimization algorithm, this study proposed and applied a PSO algorithm that was improved based on the simulated annealing optimization algorithm to solve the objective function. On one hand, the performance advantages of the improved particle swarm algorithm were verified. On the other hand, minimum carbon emission energy optimization scheduling for summer and winter before and after the introduction of hydrogen was conducted. This study not only verified the application value of the improved algorithm in terms of optimization scheduling, but it also provides a theoretical basis and practical guidance for realizing a low-carbon energy system. The main conclusions drawn from the research are as follows:

• After testing, the particle swarm optimization algorithm improved based on simulated annealing had a convergence speed approximately 20% higher than that of the traditional particle swarm optimization algorithm and exhibited stronger stability;
• Optimized scheduling significantly reduced carbon emissions, specifically by 10.2% for vehicles in the summer and 34.2% in the winter. Seasonal load distribution and availability of energy resources had a significant impact on these results. In the summer, energy resources are relatively abundant, especially solar and wind energy availability, so optimized scheduling can be more effective in reducing carbon emissions. However, during the winter months, the availability of energy resources is limited, especially the reduced availability of renewable energy sources, which results in relatively high carbon emissions from the IES. After the introduction of HPCWS, carbon emissions from the IES increased by 15.7% in the summer, while winter carbon emissions increased by 8.7% compared to the pre-introduction period. From a carbon economic perspective, although the introduction of HPCWS in winter reduced some carbon emissions, there is still a relatively large amount of carbon emissions transferred to the hydrogen production process, and this transfer is closely related to the seasonal load operation characteristics;
• In the analysis of carbon emissions in different seasons, the carbon emissions from the IES in winter increased by 21.35% compared to summer. In particular, before and after the introduction of hydrogen in winter, the carbon emissions of IES increased by 14.02% compared to summer. This reflects the seasonal fluctuations in the availability of energy resources and the higher load demand in winter, which further validates the effect of seasonal load operation on the changes in carbon emissions.

8.2. Future Perspectives

Future research will deeply explore and optimize the scheduling strategy to continuously reduce the carbon emissions of industrial parks and promote the construction of zero-carbon industrial parks by combining carbon capture technology. With the continuous optimization of scheduling strategies, the carbon emissions of industrial parks in the future will significantly move towards being low and zero carbon. The HPCWS system is also incorporated as a zero-carbon industrial raw material or energy storage method. The prospects are as follows:

• The collected carbon dioxide will support hydrogen preparation and can be used for methane synthesis, further contributing to the full realization of a carbon-neutral cycle. This development prospect provides an important technological support for the green energy transition and the achievement of carbon neutrality targets;
• The comprehensive consideration of hydrogen export will also face great challenges, as it involves the optimal scheduling of multiple industrial parks, and the computational scale will become even larger. Therefore, the optimal scheduling of hydrogen export will become one of the key hotspots for future research in this field;
• As an innovative clean energy technology, the HPCWS system not only effectively solves the problem of renewable energy volatility but also promotes the production of green hydrogen, which in turn makes an important contribution to the global carbon reduction strategy. In terms of promoting energy transition and developing low-carbon technologies, the HPCWS system can significantly reduce reliance on traditional fossil energy sources by utilizing renewable energy sources, such as wind and solar, to produce hydrogen, thereby reducing carbon emissions. In addition, HPCWS can also provide technical support for countries to achieve “carbon neutrality”, especially in energy-intensive industries and transportation.