Low-Carbon Control of Integrated Energy by Combining Cuckoo Search Algorithm and Particle Swarm Optimization Algorithm

Abstract

With the increasing severity of global climate change, low-carbon development has become a key issue in the energy industry. As an effective way to optimize energy utilization and reduce carbon emissions, integrated energy system is receiving increasing attention. However, existing low-carbon control methods still face many challenges in improving system efficiency and reducing carbon emissions, and the ability of multi-energy cooperative scheduling and optimal control is insufficient. Therefore, a hybrid algorithm combining the particle swarm optimization and cuckoo search algorithms is designed to adjust the integrated energy low-carbon control capability. The proposed algorithm required fewer iterations than the genetic cuckoo algorithm, which only went through 43 iterations. The convergence speed was improved by 34.8% compared with a single cuckoo algorithm. Among the four scenarios, scenario 4 and scenario 3 had the highest utilization rates of 99.75%, while scenario 1 had the lowest utilization rate of 61.96%. This indicates that the integrated energy system controlled by the particle swarm optimization cuckoo algorithm, while considering carbon capture and storage as well as power-to-gas conversion, can effectively utilize solar energy resources for power generation and achieve energy-saving and emission reduction effects. In summary, this method can help the integrated energy system adapt to various optimization strategies, which promotes the development of low-carbon control technologies in the energy industry.

1. Introduction

With the continuous growth of global energy demand and increasingly severe environmental pollution, the low-carbon transformation of the energy industry has become a common concern of countries around the world [1]. In this context, the integrated energy system (IES), as a comprehensive and multi-energy complementary energy utilization mode, can improve energy utilization efficiency, reduce energy consumption, and decrease carbon emissions through the cooperative scheduling of various energy forms (such as electricity, heat, cold, and gas) [2]. Therefore, the IES has become a key technology for promoting energy structure optimization and sustainable development. However, the current low-carbon scheduling and optimization control of the IES still faces many challenges. First, the volatility and uncertainty of renewable energy are strong, making it difficult to match energy supply and demand, which reduces the stability of system operation [3]. Second, existing IES optimization scheduling methods mostly focus on optimizing a single energy source, without fully considering the deep integration of low-carbon technologies such as carbon capture and storage (CCS) and power to gas (P2G), resulting in insufficient potential for carbon reduction [4]. In addition, the current IES scheduling optimization mainly relies on traditional optimization algorithms, such as cuckoo search (CS) and particle swarm optimization (PSO), but single optimization algorithms have clear shortcomings, such as the slow convergence speed of the CS algorithm. It is easy to become stuck in local optimization. Although the PSO algorithm performs better in a local search, it is often difficult to find the optimal solution in complex energy system optimization problems [5]. Therefore, developing approaches to efficiently optimize IES low-carbon scheduling, improve the intelligence of energy scheduling, and balance renewable energy consumption and carbon emission control remains an urgent problem in the current research field.

In view of this, a low-carbon control method for developing an IES based on the PSO-CS hybrid optimization algorithm is proposed, which fully combines the global search ability of the CS algorithm and the local optimization ability of the PSO algorithm, and improves the convergence speed and accuracy of the optimization algorithm. The IES low-carbon scheduling optimization framework is constructed, focusing on CCS and P2G technologies. The process of carbon emission and energy conversion is quantified through mathematical modeling, and the PSO-CS hybrid algorithm is used to optimize system scheduling, so as to improve carbon emission reduction capacity and energy efficiency. The innovation of the research lies in the proposed PSO-CS hybrid optimization strategy, which compensates for the shortcomings of a single optimization method in IES low-carbon scheduling and improves the global optimization ability and computing efficiency. CCS and P2G are combined to optimize carbon emission control, enhance the absorption capacity of renewable energy, achieve low-carbon and efficient energy scheduling, and design an intelligent carbon trading mechanism. The synergistic optimization of carbon reduction and economy has been achieved, providing energy enterprises with more intelligent, economical, and sustainable low-carbon scheduling solutions. The research not only provides an efficient calculation method for low-carbon optimization of the IES but also provides a new theoretical support and technical path for future intelligent energy management, carbon emission control, and deep utilization of renewable energy.

2. Literature Review

In the current global focus on low-carbon development and energy transformation, the need to achieve low-carbon and efficient energy systems through technological innovation and policy guidance has become a key issue. Specifically, Zhang J et al. studied the improvement of urban green economy efficiency. Based on the sample data of 276 Chinese cities in 2021, they revealed that a single factor such as environmental regulation, environmental subsidies, green credit, green equity market, and enterprise intelligence level was not enough to determine urban green economy efficiency. On the contrary, it optimized the efficiency of the urban green economy through the coordinated configuration of multiple factors, providing beneficial insights for sustainable development [6]. In addition, He B et al. focused on the impact of the digital economy on carbon emissions. The digital economy significantly reduced carbon emissions by improving energy efficiency and technological innovation, and the effect was better after optimizing the industrial structure and resource allocation. The financial development was positively correlated with carbon emission reduction and there was a double threshold effect. Therefore, the government should seize the development opportunities of “new infrastructure” and “digital technology” to achieve the “dual carbon” goal [7].

Meanwhile, faced with global climate change, countries began to implement low-carbon regulation and control policies and put forward many regulatory measures. Hu Wei et al. found that there are few studies on how climate policies affect the investment and financing behaviors of energy-intensive enterprises. Therefore, an evaluation method for low-carbon city pilot projects was proposed, which combined differential analysis of microdata to optimize energy-intensive industries [8]. Caglar A.E. et al. found that energy resources play a crucial role in achieving decarbonization goals in the economy. The study demonstrated the transition between nuclear energy research and the development budget and low-carbon economy and used the nonlinear autoregressive distributed lag method to control the development trend of the low-carbon energy economy. The results indicated that shifting from nuclear research and development to a low-carbon economy could improve the environment and subsequently enhance quality [9]. Zhou X et al. proposed a renewable energy-integrated energy production unit utilization rate, which provided various energy products and flexible adjustment functions for non-hydropower renewable energy power systems with high penetration and improved the flexibility of power system operation [10]. Gao et al. used the multivariate difference analysis method to analyze the potential mechanism of energy emission reduction policies on urban green total factor energy efficiency. The results showed that this method could optimize energy emission reduction to a certain extent [11]. Huang W et al. found that multi-energy systems can use the coupling between multi-energy sectors to realize the flexibility of the energy system. On this basis, the steady-state and dynamic network model of electricity, heat, and natural gas in cross-regional energy networks was established to calculate carbon dioxide (CO₂) emissions. This method could effectively improve the operating efficiency of multi-energy systems [12].

At present, the control strategy of an IES cannot be separated from algorithm solving. CS, the genetic algorithm (GA), PSO, and other algorithms have appeared successively, and these algorithms have been widely used to solve power scheduling and allocation problems. Imran M. et al. found that intrusion detection systems based on artificial intelligence technology are gaining interest in the research community. To solve this problem, an anomaly detection method based on CS was designed. The results showed that this method could accurately detect network intrusion behavior, and its accuracy was higher than that of similar algorithms [13]. Aiming at the problem that traditional CS algorithms are easily fall into local optimality, Abed-alguni B.H. et al. constructed an optimized exploratory CS algorithm and combined it with the refraction learning method to overcome a sub-optimal capability. The results showed that the improved CS algorithm had stronger practical competitiveness compared with other swarm optimization algorithms [14]. Shishavan S.T. et al. improved the CS search using the GA for community discovery. The results showed that the improved CS algorithm had high advantages in modularity and normalization of mutual information [15]. Singh N. et al. found that the Salp Swarm algorithm could not optimally explore and utilize every function. Therefore, an optimized PSO was proposed to avoid ignoring local minima. The results showed that the proposed method achieved better search results than the existing relevant methods [16]. To solve the poor convergence of a single PSO algorithm, Zeng N. et al. proposed a PSO algorithm based on dynamic neighborhood switching. This algorithm designed a new speed update mechanism, which was superior to some existing PSO algorithms in solving accuracy and convergence problems [17].

In summary, the current global focus on low-carbon development and energy transition has promoted research on the IES, but there are still many shortcomings in existing research. Although there have been some explorations of the urban green economy, digital economy, and low-carbon policies, there are few systematic studies on IES low-carbon scheduling and optimization and relatively weak studies on CCS and P2G technology collaborative optimization. Although existing optimization algorithms such as CS and PSO are used for energy scheduling, single algorithms often suffer from problems such as local optima and slow convergence, making it difficult to meet the optimization requirements of complex systems. Therefore, a PSO-CS hybrid optimization method is proposed in this paper. By combining the global search capability of CS with the local optimization advantage of PSO, the computational efficiency and optimization accuracy of IES low-carbon scheduling are improved, providing a more efficient and intelligent optimization solution for low-carbon energy systems.

3. Methods and Materials

This study introduces the main technologies of the IES, including CCS and P2G, and elaborates on their working principles. Subsequently, an IES framework is established. The advantages of CS, GA-CS, and PSO-CS are proposed. Finally, the control process of PSO-CS is emphasized.

3.1. Integrated Energy System Framework

The IES is a system that integrates multiple forms of energy, such as gas, thermal energy, electricity, cold energy, etc., through advanced technology and management models to optimize energy utilization efficiency and satisfy various energy demands [18]. The IES generally includes energy generation, energy transmission and distribution, energy conversion, energy storage, terminal energy consumption, and energy storage technologies [19]. At present, the main technologies for addressing climate change and reducing energy emissions globally include renewable energy technology, energy storage technology, hydrogen energy technology, and CCS technology [20,21]. CCS technology is a technique that obtains CO₂ from industrial or energy sources and transports it to specific locations for long-term storage to reduce greenhouse gas concentrations in the atmosphere. The principle of CCS technology for capturing, decomposing, and compressing CO₂ is shown in Figure 1.

The investment and operation costs of CCS technology are relatively high, and there is also a risk of gas leakage during transportation, as well as potential impacts on underground ecosystems. Many researchers have proposed P2G technology to address energy waste and cost control. P2G is a technology that converts electrical energy into gas fuel, mainly including two forms: power to hydrogen and power to methane conversion. The carbon consumption calculation during the operation of P2G is displayed in Equation (1).

$$T_{P2G,t}=\beta P_{P2G,t}$$

(1)

In Equation (1), $T_{P2G,t}$ signifies the amount of CO₂ consumed by P2G at time $t$. $\beta$ represents the unit consumption CO₂ conversion coefficient generated by P2G. The CO₂ captured and stored by CCS can serve as the carbon source required for the P2G technology reaction process. Therefore, this study combines technologies to build an IES via an electric–heat–gas coupling system that integrates wind, solar, gas turbine, P2G, and CCS technologies, involving multi-energy conversion and collaborative optimization of electricity, heat, and gas. The IES framework constructed is displayed in Figure 2.

In Figure 2, the IES structure consists of four core modules: energy input, energy conversion, energy storage, and energy output. At the energy input level, the system integrates renewable energy sources such as wind and solar, which are connected to the external grid and natural gas network. The energy conversion process uses gas turbine, P2G, and CCS technologies to achieve various forms of energy conversion such as electrical energy, thermal energy, and chemical energy. The energy storage module stores excess renewable energy through hydrogen energy storage (combined with P2G) and battery energy storage, improves the system’s ability to absorb fluctuating energy, and provides stable power support for P2G and CCS. Finally, the energy output stage ensures that the electricity and heat demands are effectively met. The mathematical calculation of a gas turbine is displayed in Equation (2).

$$P_{MT}\left(\begin{array}{c}t\end{array}\right)={\displaystyle \frac{H_{MT}\left(\begin{array}{c}t\end{array}\right){\eta }_{MT}}{\left(\begin{array}{c}1-{\eta }_{MT}\end{array}\right){\eta }_{res}^{MT}{K}_{h0}}}$$

(2)

In Equation (2), $P_{MT}\left(\begin{array}{c}t\end{array}\right)$ signifies the electrical power output of the gas turbine at $t$. $H_{MT}\left(\begin{array}{c}t\end{array}\right)$ signifies the thermal power output of the gas turbine at $t$. ${\eta }_{MT}$ represents the conversion ratio of the gas turbine. ${\eta }_{res}^{MT}$ represents the proportion of waste heat recovery in gas turbines. $K_{h0}$ represents the heating coefficient of the gas turbine. The waste heat recovery ratio of a gas turbine is shown in Equation (5).

$${\eta }_{res}^{MT}={\displaystyle \frac{T_1-T_2}{T_1-T_0}}$$

(3)

In Equation (3), $T_0$ represents the real-time ambient temperature value of the unit. $T_1$ and $T_2$ represent the intake air temperature and exhaust air temperature, respectively, which are used as environmental factors to reflect the potential impact of temperature changes on the proportion of waste heat recovery. In a gas turbine system, the assumption that the intake temperature ($T_1$) and exhaust temperature ($T_2$) affect the heat recovery efficiency through the heat exchange process is reasonable in engineering modeling. However, to optimize the PSO-CS algorithm, the model is simplified, and the impacts of other factors such as gas quality or operating load are not considered on the recovery rate and gas consumption. Gas consumption is derived based on Equation (3), with gas consumption as the main variable, as shown in Equation (4).

$$Q_{MT}\left(t\right)={\displaystyle \frac{\sum H_{MT}{\left(t\right)}_{\mathsf{\Delta }t}}{\left(1-{\eta }_{MT}\right){\eta }_{res}^{MT}{K}_{h0}H}}$$

(4)

In Equation (4), $Q_{MT}\left(t\right)$ is the gas consumption of the gas turbine at time $t$, which represents the total gas consumed by the gas turbine in a specific time period. $\sum H_{MT}{\left(t\right)}_{\mathsf{\Delta }t}$ represents the total energy output or heat output of the gas turbine at time $t$. ${\eta }_{MT}$ represents the thermal efficiency of the gas turbine (without units, ranging from 0 to 1). $K_{h0}$ represents the reference gas consumption coefficient or unit energy consumption rate of the gas turbine. $H$ represents the low calorific value of the gas. In the IES mathematical model, the energy conversion efficiency and its influence on system optimization are characterized by Equations (3) and (4).

Based on the integration of CCS and P2G technologies, an innovative carbon emissions trading model is proposed. The operation mechanism of this model is to divide carbon emission quotas into multiple levels and set differentiated trading pricing for each level [22,23]. In this tiered carbon emissions trading model, the carbon emission follows Equation (5).

$$\left\{\begin{array}{c}{T}_{C{O}_2,t}=T_{G,t}+T_{MR,t}-T_{CCS,t}\\ T_{G,t}={\epsilon }_G{P}_{G,t}\\ T_{MR,t}={\epsilon }_{MT}^e{T}_{MT,t}^e+{\epsilon }_{MT}^h{T}_{MT,t}^h\end{array}\right.$$

(5)

In Equation (5), $T_{C{O}_2,t}$ is the total carbon emissions of the system at moment $t$, which represents the net carbon emissions of the IES at a specific time, taking into account power purchase from the grid, emissions from gas turbine operation, and the emission reduction effect of CCS. $T_{G,t}$ is the carbon emissions caused by electricity purchase from the external grid, indicating the indirect carbon emissions generated by the system through purchasing electricity from the grid. The carbon emissions of grid electricity depend on its carbon intensity and are usually related to the energy mix of the grid (such as the proportion of thermal power). $T_{MR,t}$ is the carbon emissions generated by gas turbine operation, indicating the direct carbon emissions generated by burning gas when the gas turbine is running at time $t$, which is divided into two parts: power supply and heating. $T_{CCS,t}$ is the amount of CO₂ captured by CCS technology at time $t$, which represents the amount of CO₂ captured by the CCS system from gas turbines or other emission sources. It is deducted from the total emission as emission reduction. ${\epsilon }_G$ is the carbon emission factor for purchasing electricity from the grid, reflecting the amount of carbon emissions generated per unit of electricity (purchased from the grid). It is usually based on the average carbon intensity of the power grid, which may vary over time. ${\epsilon }_{MT}^e$ is the carbon emission coefficient of gas turbine power supply, which reflects the carbon emission per unit power output of gas turbine in power generation mode. It is related to the carbon content and combustion efficiency of gas. $T_{MT,t}^h$ is the electric power output of the gas turbine at time $t$, indicating the energy output of the gas turbine for power supply. $T_{MT,t}^h$ is the thermal power output of the gas turbine at time $t$, indicating the energy output of the gas turbine for heating. ${\epsilon }_{MT}^h$ is the carbon emission coefficient of gas turbine heating, which reflects the carbon emission per unit heat output of the gas turbine in heating mode. It is related to the carbon content and thermal efficiency of gas. This study includes ${\epsilon }_{MT}^h$ in the calculation to ensure emission integrity and provide basic data for future cogeneration or waste heat utilization schemes, although current simplified models assume that heat is not fully utilized.

In summary, this study has mastered the calculation method of CO₂ emissions in the IES, laying the foundation for subsequent research on controlling carbon emissions.

3.2. Selection of Optimization Methods for CS Algorithm Based on Evolutionary Algorithm

The research analyzes CCS, P2G, and other technologies, constructs a simplified mathematical model, and designs an innovative carbon emission trading model. However, traditional carbon trading mechanisms can still be optimized in terms of market equilibrium, quota allocation, and trading efficiency. Therefore, CS is introduced, which is a swarm intelligence optimization strategy that simulates the breeding behavior of cuckoo birds. In the CS algorithm, each solution is regarded as a “bird nest”, and the quality of the solution is analogous to the fitness of the “bird nest” [24]. The CS algorithm is widely used in data clustering, image processing, and solving power problems [25]. The solution of the CS algorithm is shown in (6).

$$x_i^{(k)},i\in \left\{\begin{array}{c}1,2,\cdots ,NP\end{array}\right\}$$

(6)

In Equation (6), $x_i^{(k)}$ represents the $i$-th nest at the $k$-th hatching nest position. $NP$ signifies the bird nest. $k$ signifies the iteration. The global search form calculation in the CS algorithm is shown in Equation (7).

$$x_i^{(k+1)}=x_i^{(k)}+\alpha \oplus Levy(\lambda )$$

(7)

In Equation (7), $\alpha$ represents the step size control variable applied to control the random search range. $\oplus$ represents dot product operation. The form of local search is shown in Equation (8).

$$\alpha ={\alpha }_0\times \left(x_i^{(k)}-x_{best}^{(k)}\right)\times randn$$

(8)

In Equation (8), ${\alpha }_0$ represents the scaling factor, with a conventional value of 0.01. $x_{best}^{(k)}$ refers to the optimal solution for the location point of the hatching nest in the $k$-th generation. $randn$ signifies a random number that adheres to a standard normal distribution. The CS process is displayed in Figure 3.

Figure 3 shows the operation steps of the CS. First, the initial parameters are set and the optimal nest position is recorded. Then, the remaining nest position is updated continuously, and compared with the best position, and replaced with a better solution. The best position is selected, and the final output is the optimal solution [26,27]. Although CS has a strong global search ability and convergence speed, it is easy to fall into the local optimal, especially in high-dimensional space. To predict energy supply and demand and the price trend more accurately, the PSO algorithm is introduced in this study. By simulating the process of birds searching for food, the position and speed of particles are updated, and the global optimal solution is sought [28]. To improve the performance of the search, specific constraints are applied to the velocity and position, and the constraint calculation is shown in Equation (9).

$$V_{id}^{k+1}=\omega V_{id}^k+c_1{r}_1\left(P_{id}^k-X_{id}^k\right)+c_2{r}_2\left(P_{gd}^k-X_{gd}^k\right)$$

(9)

In Equation (9), $X_{id}^k$ signifies the particle position. $V_{id}$ represents the particle velocity. $\omega$ signifies the inertia weight. $c_1$ signifies the individual learning factor. $c_2$ signifies the population learning factor. $k$ represents the current iteration count. $r$ signifies a random number. $c_2$ signifies the optimal solution of the $i$-th particle in the $d$-th dimensional space. $P_{gd}^k$ signifies the optimal solution of the entire particle swarm in $d$-dimensional space. The global value calculation of the PSO population is shown in Equation (10).

$$P_g={\left[P_{g1},P_{g2},L,P_{gD}\right]}^T$$

(10)

In Equation (10), $P_g$ signifies the global value of the population. The running process of PSO is displayed in Figure 4.

This study introduces the PSO combined with the CS, which can maximize the global search ability and convergence speed of the CS. Moreover, the particle optimization of the PSO can leave the CS less likely to fall into the global optimal solution, ultimately forming the PSO-CS.

3.3. Application of PSO-CS Algorithm in Low-Carbon Control of Integrated Energy

Hybrid algorithms can improve the search efficiency and accuracy while maintaining broad exploration capabilities. The CS algorithm mainly undertakes global search tasks, while the PSO algorithm focuses on conducting detailed local searches in promising solution regions discovered during the CS. The iterative calculation of PSO-CS search speed is shown in Equation (11).

$$V_{id}^{k+1}=\omega V_{id}^k+k_{i,1}{r}_1\left(P_{id}^k-X_{id}^k\right)+k_{i,2}{r}_2\left(P_{gd}^k-X_{gd}^k\right)$$

(11)

The position iteration of the PSO-CS is displayed in Equation (12).

$$X_{id}^{k+1}=X_{id}^k+V_{id}^{k+1}+r_3\left(X_{id}^k-X_{id}^{k-1}\right)\oplus L(r_3(P_{gd}^k-X_{id}^k),\lambda )$$

(12)

In Equation (12), $r_3$ represents the randomness parameter that increases the initial population position. From the above calculation, in the PSO-CS, the particle position update aims to optimize the performance of the local search. The parameters will be dynamically adjusted based on the distance between each particle and the optimal solution, which helps to refine the search and prevent premature sinking into local optimal solutions. The execution of the PSO-CS is detailed in Figure 5.

From Figure 5, the PSO-CS is roughly divided into four steps. Firstly, the fitness values of individuals are superimposed to obtain a total fitness. The second step is to divide the fitness of an individual by the total fitness value to derive the probability of the individual being taken. The third is to accumulate the probabilities of each individual within the group. The final step is to generate a random number as the discovery probability. If the probability of an individual being selected is less than the probability of the bird nest being preserved for the next generation, the individual has been discovered and needs to update the population position before re-comparing. Therefore, the PSO-CS can obtain the optimal or near optimal solution in complex power systems by leveraging its inherent advantages and utilizing a reasonably defined fitness evaluation mechanism. The purpose is to combine power generation equipment to minimize power generation costs or maximize power generation efficiency. In this way, the PSO-CS algorithm can effectively solve energy scheduling problems by concretizing the energy scheduling problem through digital models and operational frameworks, enabling the energy control framework to adapt to changes in demand and supply.

Finally, a low-carbon energy control framework is built by the combined PSO-CS algorithm. The framework is centered on an IES that integrates multiple energy input and conversion technologies. First, at the energy input level, the system uses wind and solar energy as renewable energy sources, while connecting the external grid and natural gas network to supplement energy demand. At the energy conversion level, gas turbines are responsible for converting gas into electricity and heat. P2G technology generates hydrogen gas by electrolyzing water and further reacts with CO₂ to produce methane. CCS technology captures CO₂ generated by the system and stores it to reduce emissions. At the energy storage level, the system uses hydrogen energy storage and battery energy storage to store excess renewable energy, improve the absorption capacity of fluctuating energy, and provide stable power support for P2G and CCS. At the energy output level, the system ensures that electricity and heat demand are met, while the methane generated by P2G is output through the gas network. The PSO-CS algorithm plays a core optimization role in the framework. Through the hybrid strategy simulating CS and particle swarm behavior, the electric power and thermal power output of the gas turbine, the power consumption and methane output of P2G, and the power purchase ratio of the grid are dynamically adjusted to minimize the power generation cost and minimize the carbon emission. The framework also introduces a tiered carbon emission trading model as an economic control means and reduces emissions through the tiered pricing incentive system, so as to ultimately achieve efficient energy conversion, storage, and output, meet diverse needs, and improve low-carbon economic benefits.

To assess the performance, firstly, the CS is implemented through Matlab programming, and the algorithm equation is input to calculate the total cost of a low-carbon energy system on a certain day. During this process, the parameters of the CS are set. The population size is 60, the maximum iteration is 500, and the probability of discovering a bird’s nest is set at 0.25. For the convenience of subsequent experiments, four basic scenarios are defined for the integrated energy control system, each corresponding to different assumptions. Scenario 1 is an IES without considering the role of CCS and P2G. Scenario 2 is an IES that does not consider CCS and P2G. Scenario 3 is an IES that does not consider PG and CCS. Scenario 4 is a comprehensive energy system that considers both CCS and P2G. Scenario 1 does not consider the functionality of CCS and P2G, but rather serves as a baseline scenario for comparison with other scenarios to understand system performance without these two technologies. Scenario 2 and scenario 3, respectively, consider introducing CCS or P2G technology, with the aim of analyzing the independent impact of each technology on system performance and evaluating its effectiveness. Finally, scenario 4 considers both CCS and P2G technologies to test how they can be used together to optimize an IES, particularly in terms of carbon emissions reduction, cost optimization, and energy efficiency. The parameter settings involved in the four basic scenarios are displayed in

Table 1. Calculation parameters for four basic scenarios.

Parameter	Numerical Value	Parameter	Numerical Value
Gas turbine power (MW) *	[5, 30]	Gas turbine climbing	[−20, 20]
P2G electrolytic cell power (MW)	[0, 15]	P2G electrolytic cell climbing	[−5, 5]
Hydrogen power input to methane generator (MW)	[0, 25]	Climbing of methane generator	[−5, 5]
Hydrogen power input of hydrogen fuel cell (MW)	[0, 25]	Climbing of hydrogen fuel cells	[−5, 5]
P2G operation and maintenance coefficient (RMB/MW) *	22.98	CCS operation and maintenance coefficient (RMB/MW)	22.98
Abandoned wind cost coefficient (RMB/MW)	313.82	Abandoned light cost coefficient (RMB/MW)	313.82
Cost coefficient for CO2 consumption (RMB/MW)	52.36	Cost coefficient for CO2 sequestration (RMB/MW)	31.42

* In “Gas turbine power (MW)”, the “MW” stands for Megawatt, which is a unit of power. “RMB/MW” means the cost in Chinese currency per megawatt of installed or generated power.

[29,30].

4. Results

This section presents an application analysis on the proposed algorithm. Firstly, the operating component loads of the IES are predicted. Secondly, the algorithm effectiveness in low-carbon control is validated. Finally, the simulation analysis is carried out to comprehensively assess the method.

4.1. Algorithm Validation Analysis

The experiment first validates the performance of the improved CS and selects the daily electricity load, gas load, heat load, wind turbine output, and photovoltaic output in a certain region for analysis. In the IES, the unit price of natural gas is set at 2.96 RMB per cubic meter. This billing model can more accurately reflect the cost changes in electricity supply, which helps optimize energy consumption and grid load management. The PSO-CS algorithm predicts the electricity load, gas load, heat load, wind turbine output, and photovoltaic output of a certain region, as shown in Figure 6.

In Figure 6, the PSO-CS accurately predicted the changes in relevant data at different time periods. The heat load power was generally higher than the other items, and the curve was relatively stable. The maximum power value appeared at 10 h, with a value of 119.3 kW, and the minimum value appeared after 25 h, with a value of 90.12 kW. The output power of photovoltaic power was 0 kW at 0–5 h and 21–25 h. The maximum power of the electrical load occurred at 13 h, at 121.86 kW. The power curves of the five indicators showed a downward trend after 20 h, with peaks occurring between 5 and 20 h. The above data indicate that the algorithm can accurately predict the power consumption of various indicator parameters through the IES, which can help the system in energy control. In the PSO-CS algorithm, the population size is set to 60 and the discovery probability is set to 0.25. These parameters are determined based on the common settings and preliminary experimental adjustments of the CS algorithm and PSO algorithm. A population size of 60 can balance the global search ability and computational efficiency, and a discovery probability of 0.25 ensures a reasonable nested update frequency in the CS algorithm. To verify the robustness of parameter selection, sensitivity analysis is performed on the population size (40, 60, and 80) and discovery probability (0.15, 0.25, and 0.35), and the results are shown in

Table 2. Sensitivity analysis of parameters.

Population Size	Discovery Probability	Convergence Iteration Number	Fitness Value
40	0.15	130	0.87
	0.25	140	0.88
	0.35	135	0.91
60	0.15	115	0.90
	0.25	100	0.95
	0.35	120	0.91
80	0.15	125	0.89
	0.25	110	0.90
	0.35	130	0.92

.

According to the results in Table 2, when the population size was set to 60, the discovery probability was set to 0.25, the convergence iteration was the lowest, which was 100, and the fitness value was the highest, which was 0.95. Subsequently, the PSO-CS was tested in the experiment. The single CS was compared with the GA-CS. The performance results are shown in Figure 7.

From Figure 7a, it can be seen that the convergence iterations of the three algorithms varied greatly. The single CS algorithm had the most convergence iterations, at 66. In contrast, the GA-CS algorithm converged after 56 iterations, and the convergence speed was 15.2% higher than that of the single CS algorithm. The PSO-CS algorithm had the fewest convergence iterations, at only 43, and the convergence speed was 34.8% higher than that of the single CS algorithm. This shows that the proposed PSO-CS algorithm can find the optimal solution in a shorter time, significantly improving the computational efficiency and scalability of the system. Figure 7b showed that the total cost of the three algorithms varied greatly. The highest cost of the single CS algorithm was 594,800 RMB, while the highest cost of the GA-CS algorithm was 274,200 RMB. The maximum cost of the PSO-CS algorithm was similar to that of the GA-CS, which was 273,700 RMB. There was also a clear gap in carbon emissions, shown in Figure 7c. The carbon emission controlled by the single CS algorithm was the highest, reaching 27,322 t. The carbon emissions under the control of the GA-CS algorithm amounted to 26,150 t. The carbon emission of the PSO-CS algorithm was the lowest, at only 22,455 t, which was 4867 t less than the single CS algorithm. This shows that the proposed PSO-CS algorithm performs better in reducing carbon emissions and has more advantages in cost control, and its overall performance is better than the other two algorithms. The final experiment shows that when the PSO-CS algorithm is combined with CCS and P2G technologies, it can more efficiently optimize power and thermal power scheduling in scenario 4, further verifying the effectiveness and practicality of this method in IESs. The power and thermal power situations in scenario 4 are compared, as displayed in Figure 8.

In Figure 8a, the gas turbine, hydrogen fuel cell, wind power, and photovoltaic power generation equipment together meet the power supply demand of the electric load. During periods of high renewable energy production, especially when wind and photovoltaic power operated efficiently, these systems could provide the majority of electricity to power users, which significantly reduced the system’s purchasing cost. Meanwhile, P2G technology provides additional on-grid capacity for the consumption of renewable energy, helping to balance supply and demand on the grid and reducing energy waste. By converting excess electricity into hydrogen, the P2G system can store it when there is a surplus of renewable energy supply and release it, further enhancing the flexibility and stability of the system. During periods of low renewable energy production, such as when wind and PV were insufficient, hydrogen fuel cells and gas turbines significantly increased their power output as electricity demand increased to ensure that the power load was satisfied. Meanwhile, the demand for purchasing electricity in the system also increased to make up for the power gap. Between 8:00 and 21:00, the probability of purchasing electricity was relatively low, indicating that the proposed algorithm could effectively regulate power output and reduce dependence on the external power grid during this period. The sharp decline in wind power generation from 8 to 10 h may be caused by one of the following reasons. First, wind energy resources may have undergone changes, such as reduced wind speed or an unfavorable wind direction. Second, wind power generation may be restricted by the grid to balance the load on the grid or to cope with fluctuations in other energy sources.

In Figure 8b, it can be seen that gas turbines and hydrogen fuel cells provided the thermal energy required for heating loads. During the period of 1–8 h, during the trough, the power grid purchased more electricity, wind power generation was large, electricity demand was low, and the gas turbine output decreased. P2G devices operated at the maximum power, while CCUS had a relatively high carbon capture rate. Its electricity could be provided by surplus wind power, and the energy storage device stored the excess wind power in the form of thermal energy and hydrogen energy and released it during the high electricity demand period of 9–20 h. Through peak shaving and valley filling, it also reduced operating costs. During this period, the output of the gas turbine increased, and the heat load was provided by the heat release of the gas turbine and the thermal storage device. At 21–24 h, wind power gradually increased, P2G energy consumption increased, and hydrogen fuel cell production increased.

4.2. Comparative Analysis of Low-Carbon Control Effects of Algorithms

To verify the low-carbon energy control effect of the proposed algorithm, carbon emission experiments were conducted in four different scenarios, and the results are shown in Figure 9.

As shown in Figure 9, due to the small randomness in each experiment, the results of each experiment may be different. Therefore, 50 experiments were conducted in this study to ensure the reliability and representativeness of the results. Figure 9a shows the total cost for four scenarios. Scenario 1 considered CCS and P2G to have the lowest total cost, at 594,800 RMB. The carbon emission consumption costs of scenario 1 and scenario 3 were 750,400 RMB and 759,200 RMB, respectively, which were much higher than the cost of scenario 4. As shown in Figure 9b, the actual carbon emissions controlled by the PSO-CS algorithm were highest in scenario 3, with a value of 14,773 t. The lowest carbon emission was in scenario 2, at 11,475 t, while scenario 4 had a carbon emission in the middle position, at 13,308 t. In Figure 9c, it can be seen that the wind energy utilization rate of scenario 4 was highest, at 99.08%, and it was lowest in scenario 1, at 64.68%. The wind energy utilization rate in scenario 3 was only lower than that in scenario 4, at 97.08%. This indicates that the IES under the control of the PSO-CS algorithm, which simultaneously considers the effects of CCS and P2G, can effectively utilize wind energy resources for power generation and carbon emission control. Figure 9d shows the light energy utilization efficiency for four different scenarios. Scenario 4 and scenario 3 had the highest utilization rates, both at 99.75%, while scenario 1 had the lowest utilization rate, at 61.96%. This indicates that the IES controlled by the PSO-CS algorithm, which simultaneously considers the effects of CCS and P2G, can effectively utilize solar energy resources for power generation and achieve energy-saving and emission reduction effects. Subsequently, experiments were conducted to calculate the carbon trading costs for different carbon emission ranges using the single CS algorithm, GA-CS algorithm, and PSO-CS algorithm based on a tiered carbon trading rule to test the impact of carbon price control, as displayed in Figure 10.

Figure 10a displays the total carbon emission trading cost control results of three algorithms for scenario 4. As the iteration increased, the total cost controlled by the three algorithms showed a downward trend. The PSO-CS showed a convergence effect in the cost curve at the 66th iteration, and the optimal solution for carbon price control was found. After 66 iterations, the cost remained constant at 594,812 RMB. The total cost of the GA-CS algorithm and single CS was higher than that of the PSO-CS algorithm, and the cost curve did not show a convergence trend. This indicates that PSO-CS can find the optimal solution with fewer iterations, saving costs. Figure 10b shows the total carbon emission trading cost control results of three algorithms for scenario 3. As the iteration increased, the total cost controlled by the three algorithms showed a downward trend. The cost curves of the PSO-CS algorithm and single CS algorithm converged after 181 iterations, and the optimal solution for carbon price control was found, with costs controlled at 594,942 RMB and 594,975 RMB, respectively. However, the cost curve of the GA-CS algorithm did not show a convergence trend, and its computational performance was poor. This indicates that the PSO-CS algorithm has a better overall performance and can achieve better low-carbon control effects.

4.3. Simulation Analysis of Integrated Energy Low-Carbon Control System

Finally, simulation experiments were carried out on the constructed control system. The equipment parameters are demonstrated in

Table 3. Experimental environment and equipment parameters.

Environment	Equipment and Parameters
Processor	Intel(R) Core(TM) i7-8565U CPU @1.80 GHz (Intel, Santa Clara, CA, USA)
GPU	NVIDIA GeForce RTX 2060 8 GB (NVIDIA, Santa Clara, CA, USA)
Memory	DDR 4 3200 MHz 8G2 (Crucial, Boise, Idaho)
Operating system	Windows 10 (64 bit)
Software	Matlab 2020
GPU parallel computing architecture	CUDA 10.1
Programming language	Java SE 17
Integrated development environment	(JDK 1.8 version, ×64)

. The simulation experiment selects the IEEE 30 node power system as the experimental object, which has 7 generators and 41 transmission lines. Two nodes are equipped with gas turbines, one of which contains a CCS device. The input end of the P2G equipment is connected to the power network node. The output end is linked to the natural gas network node.

The simulation experiment first uses Matlab software to solve the carbon emission effect and total cost and then compares it with the single CS algorithm. The comparison results are shown in Figure 11.

In Figure 11a, it can be seen that in the simulation results of the IEEE 30 node power system, the cost consumption of the three algorithms showed a convergence trend when the single CS algorithm reached 64 iterations, with a cost value of about 580,000 RMB. The cost curve of GA-CS was significantly lower than that of the single CS. When the experiment reached 50 iterations, it showed a convergence state, at 320,000 RMB. The cost curve of the PSO-CS algorithm was located at the bottom. When the experiment reached 47 iterations, it showed a convergence state, at 260,000 RMB. This indicates that the PSO-CS algorithm has stronger universality and also has good control effects when used in the IEEE 30 node power system. As shown in Figure 11b, when controlled by the PSO-CS algorithm, the CO₂ emissions of the experimental system were the lowest. When the experiment was iterated 48 times, the carbon emission was 22,355 t. The carbon emissions of the GA-CS and single CS were relatively close, far higher than those of the PSO-CS. The above data indicate that the PSO-CS can significantly reduce the number of iterations, improve the search efficiency, and accelerate the convergence speed. Finally, to verify the performance of the PSO-CS in controlling various components in the IES, ablation experiments were carried out, as displayed in

Table 4. Control results of various components in integrated energy systems based on PSO-CS.

Model	Mean Squared Error (MSE)	Root Mean Squared Error (RMSE)	Mean Absolute Error (MAE)
Electric load	0.41	0.002	0.0022
Gas load	0.55	0.003	0.0069
Heat load	0.50	0.007	0.0044
Photovoltaic energy	0.46	0.011	0.0010
Wind energy	0.32	0.023	0.0061
P2G power	0.21	0.024	0.0056
CCS power consumption	0.65	0.017	0.0048

.

The results in Table 4 clearly revealed that the MSE of P2G power consumption control calculated by the IES under PSO-CS algorithm control was the smallest, at 0.21, and the maximum MSE was CCS power consumption control, at 0.65. The RMSE of the PSO-CS for calculating the electrical load was 0.002, and the maximum RMSE was 0.024 for the P2G power consumption. The minimum MAE was photovoltaic energy, at 0.0010, and the maximum MAE was wind energy, at 0.0061. The PSO-CS can accurately grasp the carbon emissions of various components in integrated energy.

5. Discussion and Conclusions

The low-carbon development of the IES is an important way to achieve sustainable energy development and combat climate change. In this study, the PSO-CS hybrid algorithm was developed to optimize the low-carbon emission control strategy of the IES, and remarkable results were achieved. In theory, the PSO-CS algorithm combined the global search capability of the CS algorithm with the local fine search characteristics of the PSO algorithm, which significantly improved the optimization efficiency. The experimental results showed that the PSO-CS algorithm converged in only 43 iterations, and the convergence speed was increased by 34.8% compared with a single CS algorithm. This verified the theoretical advantages of the hybrid algorithm in solving complex nonlinear optimization problems (such as IES energy scheduling) and provided a new theoretical perspective on the application of swarm intelligence algorithms in multi-energy coupled systems. However, the improvement of the convergence speed may be affected by parameters such as the population size and discovery probability, so adaptive parameter adjustment should be further explored in the future to enhance the universality of the algorithm.

From a practical perspective, the maximum IES emission controlled by the PSO-CS algorithm was 22,455 t, which was 4867 t lower than the single CS algorithm. This indicates that the algorithm effectively reduces system carbon emissions by optimizing energy scheduling (such as prioritizing wind and solar energy and reducing the operating load of gas turbines). Meanwhile, the cost curve of the algorithm converged at the 66th iteration, and the operating cost was stable at 594,812 RMB, which was lower than the GA-CS algorithm, showing its balance ability between low-carbon operation and economic benefits. This result has important guiding significance for the actual IES operation. First, the algorithm can be used to schedule renewable energy in real time, improve the absorption ratio of wind and solar energy, and reduce the dependence on fossil energy. In addition, combined with the tiered carbon emission trading model, IES operators can achieve emission reduction targets at a lower cost in the carbon trading market, enhancing market competitiveness.

In summary, the proposed PSO-CS hybrid algorithm significantly improves the low-carbon operation efficiency and economic benefits of the IES, providing a new method for optimizing multi-energy coupling systems.

6. Limitations and Future Studies

This research has achieved good results, but there are some limitations to the study. Firstly, to focus on algorithm optimization, the IES is a simplified model constructed in this study, which only includes core modules such as energy input, conversion, storage, and output. Specific technologies for energy storage (e.g., battery capacity and hydrogen storage efficiency) and full-life cycle emissions from P2G and CCS operations (e.g., changes in grid carbon intensity during electrolysis and dynamic effects of CCS compression energy consumption) are not simulated in detail. This can lead to limited applicability of carbon emissions accounting and system efficiency assessment in real-world complex scenarios. Secondly, this study is based on curing parameters and assumptions and does not fully consider the impact of load fluctuations, weather conditions, and other realistic factors. Future studies can further integrate multi-scenario dynamic load data and full-life cycle emissions analysis based on more complex IES models to improve the authenticity and robustness, providing more comprehensive theoretical support for low-carbon optimization of actual energy systems.