Economic, Low-Carbon Dispatch of Seasonal Park Integrated Energy System Based on Adjustable Cooling–Heating–Power Ratio

Abstract

With the application and continuous development of green energy within the park integrated energy systems (PIESs), environmental pollution and resource depletion caused by traditional energy sources have been effectively mitigated. However, the existing research primarily focuses on fixed operating conditions, leading to significant wastage of renewable energy. To enhance the integration of renewable energy and improve overall energy efficiency, in this paper, a seasonal park integrated energy system (SPIES) based on an adjustable cooling–heating–power ratio (SPIESchpr) strategy is proposed to maximize the energy utilization efficiency and system operational economy. In SPIESchpr, to achieve additional carbon emission reductions, a novel seasonal laddered carbon trading mechanism (SLCTM) is proposed. Compared to traditional carbon trading methods, the SLCTM significantly improves the low-carbon performance of PIES. Finally, the effectiveness of the proposed SPIESchpr is validated through three scenario analyses and a detailed case study of typical daily operations. The experimental results demonstrate that, compared to fixed heat-to-cool ratios and conventional carbon trading mechanisms, the proposed SPIESchpr significantly reduces both total operational costs and carbon emissions during both heating and cooling seasons. Consequently, the proposed SPIESchpr not only enhances the energy efficiency, economic benefits, and carbon reduction potential of PIES but also provides a valuable reference for year-round operational dispatching strategies.

1. Introduction

The escalating global demand for electricity has accelerated the depletion of finite fossil fuel reserves and exacerbated environmental degradation [1,2,3], necessitating urgent exploration of sustainable energy alternatives. Advances in generation technologies have driven the widespread adoption of renewable energy systems worldwide, particularly wind and solar photovoltaic power, owing to their environmental benefits and wide availability. However, traditional power systems are generally designed to supply only a single type of energy load, making it difficult to leverage the complementary characteristics of different energy sources. Integrated energy systems (IESs) have been widely used due to their advantages of coupling multiple energy sources, such as power, heat, natural gas, and achieving interaction between different energy systems [4,5,6]. Meanwhile, IESs are typically categorized by scale into urban, park, and end-user systems. Park integrated energy systems (PIESs) are specifically designed for micro-energy networks in high-energy-density applications such as industrial parks, data centers, and residential communities. The effective coordination and optimal dispatch of multi-energy systems within parks can significantly enhance the operational efficiency, economic performance, and environmental sustainability of PIESs. Given these benefits, research on PIES optimization has become a crucial focus in energy management, with important implications for developing intelligent, low-carbon, and high-efficiency energy systems [7,8,9].

With the growth of IESs, the patterns of energy supply and demand have undergone significant changes, revealing distinct operational features. Therefore, the coupling between different energy sources and the inherent uncertainty of renewable energy are important guarantees for the safe and steady functioning of IES. Wang et al. in [10] developed a new IES multi-objective optimization model integrating electricity, heating, and cooling, and the NSGA-II was adopted to obtain the best operational strategy for IESs. However, the limited number of devices included in their IESs may restrict compatibility with broader energy technologies. Existing research has explored various optimization approaches for IES. Jiang et al. in [11] formulated a coordinated gas–electric distribution system model employing a two-stage optimization framework to solve the associated mixed-integer nonlinear programming problem. Li et al. in [12] proposed a combined cooling, heating, and power (CCHP) system integrated with hydrogen storage, simultaneously minimizing operational costs and carbon emissions while enhancing wind power integration. In [13], Wang et al. developed an IES framework incorporating power-to-gas (P2G) and combined heat and power (CHP) technologies, and the alternating direction method of multipliers was used to obtain the optimal results. In [14], Perrone et al. proposed a model for a biomass-based renewable energy CCHP mode to minimize the cost, which did not involve carbon emissions. In [15], Su et al. introduced a reliability analysis approach for power supplies in complex industrial automation systems to enhance safety and efficiency. However, this technique only addressed thermoelectric coupling without modeling the thermal–electrical conversion process. In [16], Jia et al. proposed a tri-objective optimization framework for regional IES incorporating economic, environmental, and reliability considerations. To address uncertainties in energy supply and demand, Chen et al. [17] developed a low-carbon economic dispatch model for IES, integrating P2G, CHP, and carbon capture and storage (CCS) technologies. In [18], Liu et al. explored the economic, environmental, and thermal comfort implications of sizing a multi-energy IES considering uncertainties. Most existing studies use CHP or CCHP equipment in a simple way and only consider fixed heat-to-power and cold-to-power ratios, which limit the flexibility and efficiency of operation.

The inherent energy coupling in IES presents both opportunities and challenges. Improper coordination may result in significant efficiency losses and increased operational costs, underscoring the critical importance of developing accurate multi-energy coupling models for IES optimization [19]. Addressing this challenge, Yan et al. in [20] developed a renewable-dominant multi-energy coupling framework incorporating gas boilers (GB), electric boilers (EB), P2G, and dual energy storage systems (electrical and thermal), demonstrating enhanced renewable energy utilization rates. Huang et al. in [21] designed a reduced-order transfer function model combined with electric-driven compressors for precise and efficient analysis of integrated electricity–gas systems. Zhang et al. in [22] investigated the water–electricity–gas coupling process in P2G and proposed a multi-energy coupled regional IES incorporating P2G. Ma et al. in [23] proposed an optimal dispatching model for IES that integrates CHP, P2G, and CCS, analyzing the coupling characteristics among electricity, heat, natural gas, and carbon. Zhu et al. in [24] proposed a hybrid energy system coupling solar, wind, and hydrogen and optimized the system using NSGA-II and MOPSO. Li et al. in [25] proposed a CCHP-containing IES for wind energy integration that achieved low operating costs. Chen et al. in [26] employed a biomass energy combined heat and power system to modify the heat-to-electricity ratio, thus lowering the operational expenses of the rural IES and enhancing the clean energy utilization rate. Wang et al. in [27] developed a system that integrates CCHP with ground source heat pumps. The adjustment of the ratios of cooling, heating, and electricity greatly diminished primary energy usage in the integrated energy system. The aforementioned research confirmed the substantial impact of CCHP and the strategy of adjusting the ratio of heat, cold, and electricity in decreasing the operational expenses of the IES and enhancing the utilization rate of renewable energy. Nevertheless, there exists a limited number of studies examining their contribution to the reduction in carbon emissions.

With the continuous improvement of the carbon trading market, carbon emissions trading (CET) and green certificate trading (GCT) are two trading mechanisms that are widely employed in PIES. Liu et al. in [28] developed a multi-region IES dispatch model that considered the CET and GCT mechanisms to reduce the IES operating cost. Yuan et al. in [29] formulated a low-carbon economic dispatch model for PIES that integrates carbon capture technology and a laddered carbon trading mechanism (LCTM), demonstrating significant reductions in both operational costs and emissions. Building upon this framework, Wei et al. in [30] introduced a three-stage investment planning model for PIES equipment under LCTM, revealing that system emissions are highly sensitive to baseline carbon prices but show limited variation with changes in price interval duration. Further advancing this research direction, Zhang et al. in [31] implemented a two-stage optimization approach for hybrid renewable systems utilizing a reward–penalty LCT strategy. Complementing these works, Wang et al. in [32] proposed a robust planning methodology for regional IES that accounts for carbon price uncertainty to improve emission reduction potential. Zhao et al. in [33] developed a PIES model incorporating P2G and CCS, as well as using an optimization strategy with scenario analysis, but they did not consider renewable energy and load uncertainties. Sun et al. in [34] proposed an ideal PIES dispatching model that takes into account variable loads and P2G using the seasonal LCTM (SLCTM), which improved both system flexibility and overall efficiency. While the studies above successfully implemented LCTM, they offered limited consideration of the impact of seasonal conditions on operational dispatching outcomes. In addition, the integration of CCHP equipment with LCTM remains underexplored.

To improve the economics of PIES, Li et al. in [35] developed an IES model integrating CHP, CCS, and P2G and proposed a multi-objective optimization method based on compromise planning to obtain the optimal solution in terms of environment and economy. Alizad et al. in [36] used a stochastic dynamic programing approach to optimize the design of a P2G integrated energy system, the investment costs and operating costs of the system were reduced. Guo et al. in [37] developed a nonlinear co-optimization model for regional IES with multi-regional energy sharing and storage. They proposed a two-level co-optimization method to obtain a more economical solution. Li et al. in [38] proposed a Stackelberg game optimization framework and methodology for balancing the interests of energy operators and consumers to reduce the cost for energy consumers. Meng et al. in [39] developed a two-level game optimal dispatching model based on the demand response model and the LCTM model of user experience, and the user satisfaction, the economy, and the low carbon of IES operation were improved. Tan et al. in [40] proposed a coordinated operation strategy for multi-regional IES that considered market participation. This strategy favors the economy and environmental friendliness of multi-regional IES. To reduce cost and carbon emission, Lyu et al. in [41] proposed a price-based integrated model for low-carbon economic dispatch of thermoelectric demand response and vehicle grid integration. Li et al. in [42] proposed a bi-level closed-loop framework integrating consumer and market interactions, employing NSGA-II to optimize system economics. These studies have demonstrated the significant effectiveness of LCTM in improving the economic feasibility and environmental sustainability of PIES. However, existing methods mainly rely on LCTM and energy conversion equipment for low-carbon economic dispatch without fully integrating them with other operational dispatch strategies.

The ability of CHP and CCHP to adjust the thermoelectric ratio provides a new solution for the energy transition and contributes to the improvement of global energy efficiency. Hajabdollahi et al. in [43] investigated an IES with CCHP; the annual variable electric cooling ratio strategy and particle swarm algorithm were employed for optimization and solution. Wang et al. in [44] conducted a comparative energy flow analysis between CCHP and separated production systems, demonstrating that CCHP systems can adaptively track both electrical and thermal loads across multiple operational modes. In a complementary study targeting emission reduction, Su et al. in [45] employed a carbon footprint methodology to quantify emissions from diverse generation assets and developed an adjustable thermoelectric ratio CHP model to enhance the low-carbon performance of IES. Zhang et al. in [46] constructed a CHP system containing an absorption heat pump and concluded that operating at 100% turbine heat acceptance load with a thermoelectric ratio of 100% reduced the coal consumption rate while increasing the power output. The aforementioned literature predominantly considers either the thermal-to-electricity ratio or the cold-to-electricity ratio in isolation, with relatively few studies simultaneously examining the adjustable cool–heat–power ratio strategy while accounting for both thermal and electrical energy.

In IES, the use of P2G and CCS can reduce carbon emissions and enhance the efficiency of renewable energy. The implementation of the variable electric cooling ratio strategy and adjustable thermoelectric ratio strategy is effective, but it has not addressed the relationship between thermal, cool, and electrical energy. To overcome these limitations, in this work, a seasonal PIES based on the adjustable cool–heat–power ratio (SPIESchpr) is proposed. This strategy facilitates dynamic multi-energy coordination, significantly improving energy utilization in PIES compared to conventional approaches. In SPIESchpr, equipment models containing photovoltaic (PV), wind turbine (WT), CCHP, and P2G are developed. The equipment output constraints, the unique charging and discharging state constraints of the energy storage, the constraints of equal initial and end capacities of the energy storage, and the constraints of the overall system’s electric, heat, cold, and natural gas balances are set. The energy purchase cost (EPC), energy abandonment cost (EAC), and CTC are also taken as objective functions. A novel adjustable cool–heat–power ratio (Achpr) strategy is introduced to enhance natural gas utilization efficiency through optimal waste heat allocation between heating and cooling demands. Comparative analysis against conventional constant ratio (Cchpr) approaches confirms its superior performance. The synergistic integration of P2G with CCHP enables effective conversion and storage of surplus renewable generation, simultaneously improving energy utilization efficiency and economic performance. Furthermore, the implementation of an SLCTM demonstrates considerable emission reduction potential, validated through three comparative scenarios. The LCTM, the proposed strategy, significantly enhances the low-carbon operational performance of PIES and supports flexible seasonal adaptation throughout the year. By dynamically allocating waste heat between heating and cooling applications, the strategy maximizes natural gas utilization efficiency.

The rest of the work is organized as follows. Section 2 describes the overall framework of the SPIESchpr, developing the mathematical model of the SPIESchpr, the Achpr strategy, and the SLCTM. Section 3 develops the SPIESchpr low-carbon economic dispatch model and sets constraints. Section 4 discusses the impact of different carbon trading mechanisms and different strategies on the system through a case study. Finally, in Section 5, the conclusions of this study are described.

2. Description of the SPIESchpr

In the proposed SPIESchpr, the deep coupling of electric, heat, cold, hydrogen, and natural gas energy sources is included. The mathematical model of the SPIESchpr, the Achpr strategy, and the SLCTM are described in detail in this section.

2.1. The SPIESchpr Framework

In this paper, the SPIESchpr utilizes multiple energy sources, including electricity, heat, cooling, natural gas, and hydrogen, as shown in Figure 1. From Figure 1, the power demand of PIES is met by a combination of PV, WT, power grid purchasing electricity, CCHP, and electricity storage (ES). To maximize the use of renewable energy, the EB, EC, and energy storage prioritize electricity generated from PV and WT. When renewable generation is high, excess power from PV and WT is converted to hydrogen and stored using a P2G system. This hydrogen can subsequently be converted into natural gas to meet demand when the natural gas supply is insufficient. During periods of low renewable energy generation, the P2G system is inactive, and the system relies on CCHP, grid electricity purchases, and discharges from energy storage to meet demand.

The proposed SPIESchpr system integrates multiple energy sources and storage devices to ensure a reliable natural gas supply. The natural gas is sourced from both the external grid and the P2G system. Within this framework, the design of GB, CCHP unit, and gas storage (GS) systems prioritizes natural gas generated from P2G. When P2G production is insufficient, supplementary natural gas is procured from the grid, while the GS discharges stored energy to meet demand.

The heating subsystem consists of GB, CCHP, EB, and HS units, which operate in synergy to balance supply and demand. During periods of heat surplus, excess thermal energy is stored in the HS. Conversely, the HS discharges heat to compensate for shortages. The system dynamically adjusts heat production based on renewable energy availability. When solar and wind generation are high, the EB serves as the primary heat source, supplemented by the GB and CCHP. When the amount of renewable energy generation is low, the GB and CCHP become the main heat sources, and the EB offers auxiliary support.

The cooling subsystem employs the EC, CCHP, and cool storage (CS) to meet cold requirements. The EC and CCHP collectively supply the required cooling load, with surplus cooling energy stored in the CS. When the cooling supply is insufficient, the CS discharges to compensate for the deficit. Owing to its higher coefficient of performance, the EC operates as the primary cooling provider, while the CCHP and charge/discharge cycles of the CS provide supplementary support.

2.2. The SPIESchpr Modeling

2.2.1. EC Modeling

The EC units utilize electric power to drive compressors within a refrigeration cycle, Using the phase transition process, the refrigerant absorbs heat in the evaporator and releases heat in the condenser to create a low-temperature environment. This method not only avoids the pollution issues associated with traditional coal-fired refrigeration but also supports the transition to low carbon by integrating with renewable energy. The cooling power output P_EC,c of the EC is defined as follows.

$$\left\{\begin{array}{l}{P}_{\mathrm{EC},\mathrm{c}}={\eta }_{\mathrm{EC}}{P}_{\mathrm{EC},\mathrm{e}}\\ 0\le P_{\mathrm{EC},\mathrm{e}}\le P_{\mathrm{EC},\mathrm{e},\max }\end{array}\right.$$

(1)

where P_EC,e is the power consumed; ${\eta }_{\mathrm{EC}}$ is the electric chiller coefficient of performance, indicating the energy conversion efficiency of the EC; and P_EC,e,max is the maximum input power of the EC.

2.2.2. EB Modeling

The EB units convert electrical energy directly into thermal energy through electrically driven heating elements, utilizing water or other media to absorb and distribute the heat. Their core operation relies on efficient and precise thermal output by clean energy sources, significantly reducing carbon emissions and particulate pollution. EB offers a flexible and reliable heat supply due to its rapid response and intelligent temperature control capabilities. When wind and solar generation are abundant, they absorb renewable energy, thereby minimizing wind and solar power curtailment. The heat power output P_EB,h of the EB is defined as follows.

$$\left\{\begin{array}{l}{P}_{\mathrm{EB},\mathrm{h}}={\eta }_{\mathrm{EB}}{P}_{\mathrm{EB},\mathrm{e}}\\ 0\le P_{\mathrm{EB},\mathrm{e}}\le P_{\mathrm{EB},\mathrm{e},\max }\end{array}\right.$$

(2)

where P_EB,e and ${\eta }_{\mathrm{EB}}$ are the power consumed and heating efficiency, respectively, and P_EB,e,max is the maximum input power of the EB.

2.2.3. P2G Modeling

In the PIES, the P2G system consists of an electrolytic cell (EL) and a methane reactor (MR). The EL uses electrical energy to split water into hydrogen and oxygen. Then, hydrogen and carbon dioxide react in the MR to produce natural gas. Due to the variability of renewable energy, such as solar and wind, the P2G helps maximize their utilization while minimizing carbon emissions in the PIES. The chemical equation is described by (3).

$$\left\{\begin{array}{l}{2\mathrm{H}}_2\mathrm{O}\to {2\mathrm{H}}_2{+\mathrm{O}}_2\\ {4\mathrm{H}}_2{+\mathrm{CO}}_2\to {\mathrm{CH}}_4{+2\mathrm{H}}_2\mathrm{O}\end{array}\right.$$

(3)

When wind and solar energy are abundant, the EL uses excess power from wind and photovoltaic to break down water into hydrogen and oxygen, which is stored in a hydrogen storage facility. Consequently, the hydrogen power output P_EL,H of the EL is defined as follows.

$$\left\{\begin{array}{l}{P}_{\mathrm{EL},\mathrm{H}}={\eta }_{\mathrm{EL}}{P}_{\mathrm{EL},\mathrm{e}}\\ 0\le P_{\mathrm{EL},\mathrm{e}}\le P_{\mathrm{EL},\mathrm{e},\max }\end{array}\right.$$

(4)

where P_EL,e and ${\eta }_{\mathrm{EL}}$ are the power of consuming power and conversion efficiency of EL, respectively, and P_EL,e,max is the maximum input power of the EL.

The MR uses a chemical reaction between carbon dioxide and hydrogen to produce natural gas and water, which can either be stored or supplied directly to natural gas-consuming equipment. When natural gas is insufficient, the hydrogen storage facility releases hydrogen and outputs natural gas through the MR facility, reducing the cost of purchasing natural gas for the system. The model of the MR is shown in (5).

$$\left\{\begin{array}{l}{P}_{\mathrm{MR},\mathrm{g}}={\eta }_{\mathrm{MR}}{P}_{\mathrm{MR},\mathrm{H}}\\ 0\le P_{\mathrm{MR},\mathrm{H}}\le P_{\mathrm{MR},\mathrm{H},\max }\end{array}\right.$$

(5)

where P_MR,g, P_MR,H, and ${\eta }_{\mathrm{MR}}$ are the output of natural gas power, the power of consuming hydrogen, and conversion efficiency of MR, respectively, and P_MR,H,max is the maximum input power of the MR.

2.2.4. GB Modeling

The GB uses natural gas as a fuel for heating. Natural gas is combusted in the boiler’s combustion chamber, and the heat generated is transferred from the hot gases and flames to the boiler’s heat exchanger. The heat exchanger transfers the heat to water to form hot water or steam to provide heat. Assuming the GB as an idealized model, considering only input gas power and output thermal power, P_GB,h of the GB is defined as follows.

$$\left\{\begin{array}{l}{P}_{\mathrm{GB},\mathrm{h}}={\eta }_{\mathrm{GB}}{P}_{\mathrm{GB},\mathrm{g}}\\ 0\le P_{\mathrm{GB},\mathrm{g}}\le P_{\mathrm{GB},\mathrm{g},\max }\end{array}\right.$$

(6)

where P_GB,g and ${\eta }_{\mathrm{GB}}$ are the input natural gas power and thermal efficiency, respectively, and P_GB,g,max is the maximum input power of the GB.

2.2.5. Energy Storage Modeling

Energy storage devices can store energy when the system has sufficient energy and release energy to replenish it when the energy is insufficient. Therefore, the energy storage device can balance the peaks and valleys of the energy consumed by the system and improve the reliability of the system [47]. The calculation of the energy storage system is defined as follows.

$$\left\{\begin{array}{l}{P}_i(t)={\eta }_{i,\mathrm{cha}}{P}_{i,\mathrm{cha}}(t)-P_{i,\mathrm{dis}}(t)/{\eta }_{i,\mathrm{dis}}\\ E_i(t+1)=E_i(t)+P_i(t)\end{array}\right.$$

(7)

where P_i,cha(t) and η_i,cha are the charging power and the charging efficiency of energy storage device i at moment t; P_i,dis(t) and η_i,dis are the discharging power and the discharging efficiency of energy storage device i at moment t; E_i(t) and E_i(t + 1) are the capacities of energy storage device i at moments t and t + 1; a positive value of P_i(t) indicates that energy storage device i is charging at moment t; and a negative value of P_i(t) indicates that energy storage device i is in a discharged state at moment t. Among them, i contains ES, HS, CS, GS, and hydrogen storage tank.

2.3. The Achpr Strategy

The Achpr strategy is designed to maximize energy efficiency by adjusting the proportion of waste heat generated by the CCHP. During the heating season, the majority of waste heat is directed toward heating to meet heat load demand and, at this time, the heat-to-power ratio is usually at its maximum. Conversely, during the cooling season, most waste heat is allocated for cooling to supply the cool load, with the cool-to-power ratio reaching its maximum. Compared to the constant cool–heat–power ratio strategy used in existing studies, the proposed Achpr demonstrates greater improved adaptability to seasonal variations and enables dynamic adjustment of waste heat utilization. This significantly enhances the energy utilization efficiency of PIES while reducing carbon emissions.

The CCHP system implemented in PIES integrates three core components, a gas turbine (GT), a waste heat boiler (WHB), and an absorption chiller (AC), forming a comprehensive solution that simultaneously generates power, heating, and cooling. The thermodynamic process initiates with GT combustion, where high-temperature, high-pressure gases drive turbine rotation, converting the chemical energy of natural gas into mechanical energy, which is then transformed into electricity. Waste heat recovered from the exhaust gases is utilized by the WHB to provide space heating and is also supplied to the AC to produce cooling energy. The complete system modeling framework incorporates these energy conversion processes as follows.

$$\left\{\begin{array}{l}{P}_{\mathrm{CCHP},\mathrm{e}}={\eta }_{\mathrm{CCHP},\mathrm{e}}{P}_{\mathrm{CCHP},\mathrm{g}}\\ 0\le \epsilon \le P_{\mathrm{CCHP},\mathrm{h}}/P_{\mathrm{CCHP},\mathrm{e}}\\ 0\le \delta \le P_{\mathrm{CCHP},\mathrm{c}}/P_{\mathrm{CCHP},\mathrm{e}}\\ 0\le P_{\mathrm{CCHP},\mathrm{g}}\le P_{\mathrm{CCHP},\mathrm{g},\max }\end{array}\right.$$

(8)

where P_CCHP,g is the power of natural gas consumed; P_CCHP,g,max is the maximum input natural gas of the CCHP; ${\eta }_{\mathrm{CCHP},\mathrm{e}}$ is the power generation efficiency; P_CCHP,e, P_CCHP,h, and P_CCHP,c are power, heat, and cool energy output from CCHP, respectively; and ε and δ are the heat-to-power ratio and the cool-to-power ratio. The heat-to-power ratio is the ratio of heat to electrical energy output from the CCHP and the cool-to-power ratio is the ratio of cool to electrical energy output from the CCHP.

2.4. The SLCTM

In the PIES, the carbon trading mechanism plays a crucial role in addressing climate change and reducing greenhouse gas emissions. Carbon quotas can be traded by the park in the carbon trading market. When the park has surplus quotas, it can sell them and, if the quota is insufficient to meet carbon emission needs, it must purchase additional quotas. This mechanism, which includes free carbon quotas, actual carbon emissions, and carbon transaction costs, helps drive energy conservation and emissions reduction efforts within enterprises.

2.4.1. Seasonal Free Carbon Allowance Model

Unlike conventional carbon trading approaches, the SLCTM represents a climate-adaptive policy instrument designed to address seasonal variations in energy demand. By dynamically adjusting carbon allowances across different seasons, the SLCTM promotes the optimization of the energy structure, reduces dependence on conventional fossil fuels, and accelerates the transition toward sustainable energy systems. To enhance the low-carbon performance of PIES, in this paper, the SLCTM framework is adopted to allocate annual carbon quotas every quarter. The seasonal free carbon emission allowance for trading is mathematically formulated as follows.

$$E_{\mathrm{fr},s}={\alpha }_s{E}_{\mathrm{fr}}$$

(9)

where E_fr,s is the total free carbon allowances of the seasonal total of the park S; E_fr is the annual carbon allowances; and α_s is the scale factor for different seasons.

2.4.2. Seasonal Actual Carbon Emissions Model

For the IES considered in this work, carbon emissions primarily originate from thermal power purchased from the external grid, as well as from the CCHP and GB. While the CCHP simultaneously produces electricity, heat, and cooling, the GB generates only heat. The actual carbon emissions can be calculated from the carbon emission sources generated in the IES. Therefore, in this paper, the seasonal actual carbon emissions are calculated by (10).

$$\left\{\begin{array}{l}{E}_{\mathrm{tr},s}=E_{\mathrm{grid},s}+E_{\mathrm{g},s}-E_{\mathrm{P}2\mathrm{G},s}\\ E_{\mathrm{grid},s}={\omega }_{\mathrm{e}}{\displaystyle \sum _s^S{\displaystyle \sum _t^T{P}_{\mathrm{grid},s}(t)}}\\ E_{\mathrm{g},s}={\omega }_{\mathrm{g}}{\displaystyle \sum _s^S{\displaystyle \sum _t^T{P}_{\mathrm{total},s}(t)}}\\ P_{\mathrm{total},s,t}(t)=P_{\mathrm{CCHP},\mathrm{e},s}(t)+P_{\mathrm{CCHP},\mathrm{h},s}(t)+P_{\mathrm{CCHP},\mathrm{c},s}(t)+P_{\mathrm{GB},\mathrm{h},s}(t)\\ E_{\mathrm{P}2\mathrm{G},s}={\omega }_{\mathrm{P}2\mathrm{G}}{\displaystyle \sum _s^S{\displaystyle \sum _t^T{P}_{\mathrm{MR},\mathrm{g},s}(t)}}\end{array}\right.$$

(10)

where E_tr,s, E_grid,s, and E_g,s are the actual total carbon emissions of the park in the S quarter, the actual carbon emissions of the park in the S quarter of the park from the higher-level power grid, and the actual carbon emissions from natural gas-consuming equipment in season S of the park, respectively; E_P2G,s is the actual carbon dioxide consumption of the natural gas production of the P2G equipment in the park in the S quarter; ω_e, ω_g, and ω_P2G are the actual carbon emission intensity of thermal power units, the actual carbon emission intensity of the gas units, and the carbon dioxide absorption intensity of natural gas generated by the MR, respectively; P_CCHP,e,s, P_CCHP,h,s, and P_CCHP,c,s are the electricity, heat, and cool output from CCHP during the S quarter; P_GB,h,s is the GB output heat in S quarter; and P_MR,g,s is the natural gas produced by the MR during the S quarter.

2.4.3. Seasonal Carbon Trading Cost Model

From the seasonal free carbon allowances and seasonal actual carbon emissions of the IES, the tradeable carbon emissions are defined as follows.

$$E_{\mathrm{M},s}=E_{\mathrm{tr},s}-E_{\mathrm{fr},s}$$

(11)

where E_M,s is the amount of carbon emissions traded in the seasons of PIES. If E_M,s > 0, it is E_tr,s greater than E_fr,s that needs to buy carbon allowances, and, if E_M,s < 0, it is E_tr,s less than E_fr,s that sells excess carbon allowances.

In order to further optimize the seasonal carbon trading mechanism, this paper introduces the stepped penalty coefficient. The carbon emission quotas to be purchased are divided into different regions. The more carbon emission quotas purchased, the higher the price in the corresponding region. The calculation of carbon trading cost is calculated by (12).

$$f_{\mathrm{c},s}=\left\{\begin{array}{l}\gamma (1+\alpha )(E_{\mathrm{M},s}+l)-\gamma l\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} E_{\mathrm{M},s}<-l\\ \gamma E_{\mathrm{M},s}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} -l\le E_{\mathrm{M},s}<l\\ \gamma (1+\alpha )(E_{\mathrm{M},s}-l)+\gamma l\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} l\le E_{\mathrm{M},s}<2l\\ \gamma (1+2\alpha )(E_{\mathrm{M},s}-2l)+\gamma (2+\alpha )l\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} 2l\le E_{\mathrm{M},s}<3l\\ \gamma (1+3\alpha )(E_{\mathrm{M},s}-3l)+\gamma (3+3\alpha )l\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}3l\le E_{\mathrm{M},s}<4l\\ \gamma (1+4\alpha )(E_{\mathrm{M},s}-4l)+\gamma (4+6\alpha )l\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}4l\le E_{\mathrm{M},s}\end{array}\right.$$

(12)

where f_c,s, γ, α, and l are the carbon trading cost of the park in the S quarter, the base price of carbon trading, the increase rate of carbon trading price at each tier, and the length of the carbon emission range, respectively; if f_c,s > 0, it is the cost of carbon trading; if f_c,s < 0, it is carbon trading income.

3. Optimal Dispatch SPIESchpr Model

3.1. Objective Function

In the proposed SPIESchpr model, the economic cost of the system is minimized as the objective function, which includes the E_PC (f_buy,s), energy E_AC (f_q,s), and C_TC (f_c,s). PIES typically procure electricity and gas from external sources such as the grid or natural gas networks. Energy procurement costs constitute a major economic factor, directly influencing the total operational expenditure. By optimizing purchasing strategies, such as selecting off-peak periods under time-of-use pricing, the overall system cost can be significantly reduced. Curtailment costs refer to economic losses arising from the forced abandonment of renewable energy or energy wastage due to insufficient absorption capacity or limited system regulation capabilities. However, by penalizing energy curtailment, the model promotes the deployment of solutions such as energy storage or demand response to enhance absorption capacity, thereby better reflecting real-world operational scenarios. Carbon trading costs are typically associated with fossil fuel consumption, converting carbon emissions into economic costs through carbon pricing. This mechanism inherently balances economic efficiency and environmental sustainability during the optimization process. Therefore, the objective function is defined as follows.

$$F=\min (f_{\mathrm{buy},s}+f_{\mathrm{c},s}+f_{\mathrm{q},s})$$

(13)

The term f_c,s has been described in Section 2.4.3.

In this paper, the term f_buy,s mainly comprises electricity purchase cost (C_PE) and gas purchase cost (C_PG), which are defined as follows.

$$f_{\mathrm{buy},s}={\displaystyle \sum _{s=1}^S({\delta }_{\mathrm{grid}}{P}_{\mathrm{buy},\mathrm{e},s}+{\delta }_{\mathrm{gas}}{P}_{\mathrm{buy},\mathrm{g},s})}$$

(14)

where δ_grid and δ_gas represent the unit prices of power and natural gas, respectively, P_buy,e,s denotes the thermal power purchased by the park from the higher-level power grid in the S quarter, while P_buy,g,s represents the natural gas purchased by the park from the natural gas grid in the S quarter.

The term f_q,s is mainly composed of penalty costs caused by wind and PV power abandonment, which are defined as follows.

$$f_{\mathrm{q},s}={\delta }_{\mathrm{q}}{\displaystyle \sum _s^S\left[\left(P_{\mathrm{WT},s,\max }-P_{\mathrm{WT},s}\right)+\left(P_{\mathrm{PV},s,max}-P_{\mathrm{PV},s}\right)\right]}$$

(15)

where δ_q represents the unit cost of energy abandonment for wind and PV; P_WT,s,max and P_PV,s,max are the maximum output of wind power and PV power in the park in the S quarter, respectively; and P_WT,s and P_PV,s are the actual wind power and PV power consumption in the park in the S quarter, respectively.

3.2. Constraints

In the proposed SPIESchpr mode, some constraints that can reflect the real operating state of the system, such as the electric, heat, cool, and natural gas balance constraints, the state and capacity constraints of the energy storage, and the hill climbing constraints, are considered in this subsection.

• Electric balance constraint

The power load is met by a combination of the power grid purchasing electricity, WT, PV, CCHP, and ES. Excess electricity is consumed by P2G, EB, and EC. This balance relationship is defined as follows.

$$P_{\mathrm{buy},\mathrm{e}}+P_{\mathrm{WT}}+P_{\mathrm{PV}}+P_{\mathrm{CCHP},\mathrm{e}}+P_{\mathrm{ES},\mathrm{dis}}=P_{\mathrm{e},\mathrm{load}}+P_{\mathrm{EC},\mathrm{e}}+P_{\mathrm{EB},\mathrm{e}}+P_{\mathrm{EL},\mathrm{e}}+P_{\mathrm{ES},\mathrm{cha}}$$

(16)

where P_buy,e is the power grid purchasing electricity; P_WT and P_PV are the WT and PV power output consumed; P_e,load is the power load; and P_ES,cha and P_ES,dis are the ES charging and discharging energy.

2.

Heat balance constraint

The heat load is satisfied by the EB, GB, CCHP, and HS. The waste heat distribution ratio of the CCHP is adjusted to deliver heat to the load with improved accuracy. The system heat balance is shown in (17).

$$P_{\mathrm{EB},\mathrm{h}}+P_{\mathrm{GB},\mathrm{h}}+P_{\mathrm{CCHP},\mathrm{h}}+P_{\mathrm{HS},\mathrm{dis}}=P_{\mathrm{h},\mathrm{load}}+P_{\mathrm{HS},\mathrm{cha}}$$

(17)

where P_h,load is the heat load; P_h,cha and P_h,dis are the HS charging and discharging energy.

3.

Cool balance constraint

The cool load is met by the EC, CCHP, and CS. The balanced relationship is shown in (18).

$$P_{\mathrm{EC},\mathrm{c}}+P_{\mathrm{CCHP},\mathrm{c}}+P_{\mathrm{CS},\mathrm{dis}}=P_{\mathrm{c},\mathrm{load}}+P_{\mathrm{CS},\mathrm{cha}}$$

(18)

where P_c,load is the cool load; P_CS,cha and P_CS,dis are the CS charging and discharging energy.

4.

Natural gas balance constraint

The natural gas load is met by a combination of the natural gas purchased from the gas grid, MR, and GS. The balanced relationship is defined as follows.

$$P_{\mathrm{buy},\mathrm{g}}+P_{\mathrm{CCHP},\mathrm{g}}+P_{\mathrm{MR},\mathrm{g}}+P_{\mathrm{GS},\mathrm{dis}}=P_{\mathrm{g},\mathrm{load}}+P_{\mathrm{CCHP},\mathrm{g}}+P_{\mathrm{GB},\mathrm{g}}+P_{\mathrm{GS},\mathrm{cha}}$$

(19)

where P_buy,g is the natural gas purchased from the gas grid; P_g,load is the natural gas load; and P_GS,cha and P_GS,dis are the GS charging and discharging energy.

5.

Ramp rate constraints

The ramp rate constraint refers to the maximum permissible rate of change in output power for energy conversion or power generation equipment within adjacent time intervals. This constraint reflects physical limitations of the equipment, resulting from mechanical inertia and thermal stress, which prevent abrupt and large adjustments in power output. It also helps avoid sharp fluctuations that could lead to grid frequency instability or equipment damage.

$$\Delta P_{c,\min }\le P_{c,t+1}-P_{c,t}\le \Delta P_{c,\max }$$

(20)

where P_c,t and P_c,t+1 are the power of equipment c at time t and t + 1; ΔP_c,min and ΔP_c,max are the climbing upper and lower limits of equipment c; and c includes all equipment in the system.

6.

Energy storage constraints

To prevent damage to the energy storage equipment due to overcharging and discharging and to ensure the stability and reliability of the system. The energy within the energy storage system must be within the upper and lower capacity limits. The remaining energy must be stored to ensure that the initial and ending capacities of the energy storage remain the same throughout the day.

$$\left\{\begin{array}{l}0\le P_i(t)\le B_{i,\mathrm{cha}}{P}_{i,\mathrm{cha},\max }\\ 0\le P_i(t)\le B_{i,\mathrm{dis}}{P}_{i,\mathrm{dis},\max }\\ B_{i,\mathrm{cha}}+B_{i,\mathrm{dis}}=1\\ E_{i,\min }\le E_i(t)\le E_{i,\max }\\ E_{i,\mathrm{t}0}=E_{i,\mathrm{T}}\end{array}\right.$$

(21)

where P_i,cha,max and P_i,dis,max are the maximum power for a single charge and discharge of i; B_i,cha and B_i,dis are the charging and discharging state of i; E_i,max and E_i,min are, respectively, the maximum and minimum values of the capacity of i; and E_i,t0 and E_i,T, respectively, indicate the initial capacity and termination capacity of i.

4. Case Studies and Discussion

Section 2 and Section 3 outline the strategies, mechanisms, and models proposed in this paper. To validate and verify the effectiveness of the proposed SPIESchpr model and strategy, two typical seasonal scenarios, heating season and cooling season, are considered. In addition, the dispatching period is set to 24 h. All experiments are conducted using CPLEX in MATLAB R2023a on a Windows 10 system.

The time-of-use electricity prices are shown in

Table 1. Time-of-use electricity prices.

Time	Power Price (CNY/kWh)
01: 00–07: 00 23: 00–24: 00	0.38
08: 00–11: 00 15: 00–18: 00	0.68
12: 00–14: 00 19: 00–22: 00	1.20

, and the natural gas price is set to 0.45 CNY/kWh. The operational parameters for various equipment are given in

Table 2. System coupling equipment parameters.

Facility	E (kW)	ηc
CCHP	600	ηCCHP,e: 0.3
		ε: 1.36
		δ: 1.03
EC	500	ηEC: 3.10
EB	100	ηEB: 0.98
EL	500	ηEL: 0.88
MR	250	ηMR: 0.60
GB	700	ηGB: 0.95

and

Table 3. Parameters of energy storage equipment.

Facility	E (kW)	ηi,cha/ηi,dis
ES	450	0.95/0.95
HS	500	0.95/0.95
CS	500	0.95/0.95
GS	150	0.95/0.95
H2S	200	0.95/0.95

. The maximum values of the WT and the PV output, as well as the demand for power, heat, cool, and natural gas loads in the park in each typical season, are shown in Figure 2. The parameters are derived from data of a real integrated energy system within a specific industrial park.

4.1. Analysis and Discussion of SPIESchpr

Two cases are set up to verify the validity of the proposed SPIESchpr. The results of the two cases are compared and analyzed in the heating and cooling seasons. Case 1 is defined as SPIESchpr without CCHP. Case 2 is represented as SPIESchpr with CCHP.

4.1.1. The SPIESchpr Model for the Heating Season

A comparative analysis of the two cases during the heating season is presented in

Table 4. Comparison of the two cases during the heating season.

	Case 1	Case 2
CTC (CNY)	−336.5014	−554.2501
Carbon emission (kg)	4891.2698	4047.3087
EAC (CNY)	63.1196	24.7802
CPE (CNY)	1061.8659	359.3434
CPG (CNY)	6698.2854	7302.3828
Total cost (CNY)	7486.7695	7132.2562

. The results demonstrate that Case 2 achieves a significant carbon emission reduction of 843.9611 kg compared to Case 1. This environmental benefit is attributed to the elimination of natural gas consumption for power generation in Case 2, as evidenced by the electrical balance depicted in Figure 3. While Case 1 exhibits lower CPG, Case 2 demonstrates superior overall performance, with reduced total costs. These findings validate the effectiveness of the SPIESchpr during the heating season and offer practical guidance for the dispatching of actual PIES, significantly enhancing their economic efficiency of PIES operations.

4.1.2. The SPIESchpr Model for the Cooling Season

Comparative results for the heating season scenarios are presented in

Table 5. Comparison of the two cases during the cooling season.

	Case 1	Case 2
CTC (CNY)	453.2054	311.0618
Carbon emission (kg)	5572.0797	5073.3087
EAC (CNY)	1.9742	2.1487
CPE (CNY)	3387.7520	2480.8309
CPG (CNY)	1498.3062	2105.1138
Total cost (CNY)	5341.2378	4899.1552

. The results reveals that Case 2 achieves a 31.36% reduction in carbon emissions compared to Case 1, though Case 1 demonstrates lower EAC. However, since Case 1 does not include CCHP, the CPE of Case 2 is smaller than that of Case 1, and the CPG of Case 1 is smaller than that of Case 2. The electric balance for Case 1 is shown in Figure 4. The total cost of Case 2 is lower than that of Case 1. Therefore, the model proposed in this paper is effective in the cooling season. The proposed SPIESchpr also demonstrates significant optimization effects during the cooling season of PIES. This indicates that the SPIESchpr can guide the operational dispatching of PIES throughout all typical seasons of the year.

4.2. Analysis and Discussion of Achpr

In this subsection, the Achpr and Cchpr strategies are applied to the heating and cooling seasons to evaluate the effectiveness of the proposed Achpr strategy. The C_TC, E_AC, C_PE, C_PG, total cost, and carbon emission are analyzed under the two strategies.

4.2.1. The Achpr for the Heating Season

A comparison of the results in the heating season using the Cchpr strategy and the Achpr strategy is shown in

Table 6. Comparison of the two strategies during the heating season.

	Cchpr	Achpr
CTC (CNY)	−524.8627	−554.2501
Carbon emission (kg)	4323.9869	4047.3087
EAC (CNY)	86.1003	24.7802
CPE (CNY)	477.9842	359.3434
CPG (CNY)	7343.6706	7302.3828
Total cost (CNY)	7382.8923	7132.2562

. It can be seen from Table 6 that the carbon emissions of the Achpr (4047.3087 kg) are less than the carbon emissions of the Cchpr strategy (4323.9869 kg). The Achpr strategy is 276.6781 kg less than the Cchpr, which is reduced by 6.40%. The C_TC, the C_PE, and the C_PG for the Achpr are smaller than those of the Cchpr. The total cost under Achpr (CNY 7132.2562) is 3.39% lower than the Cchpr (CNY 7382.8923).

In addition, since the heat load demand is higher than the power load during the heating season, the waste heat recovered from the CCHP system is mostly used for heat production, and the rest of the heat load is supplied by the EB, GB, and HS, while the GB provided a higher percentage of the heat load demand, as shown in Figure 5. This is verified by the fact that the heat-to-power ratio and cool-to-power ratio for Achpr during the heating season are shown in Figure 6, where the heat-to-power ratio of Achpr is higher than the cool-to-power ratio.

4.2.2. The Achpr for the Cooling Season

Table 7. Comparison of the two strategies under the cooling season.

	Cchpr	Achpr
CTC (CNY)	357.0432	311.0618
Carbon emission (kg)	5440.8739	5073.3087
EAC (CNY)	60.6191	2.1487
CPE (CNY)	2791.4466	2480.8309
CPG (CNY)	1984.6472	2105.1138
Total cost (CNY)	5193.7561	4899.1552

presents a comparative analysis of system performance under the Achpr and Cchpr strategies during cooling season operations. The results indicate distinct carbon emission profiles, with the Achpr and Cchpr yielding 5073.3087 kg and 5440.8739 kg of emissions, respectively, demonstrating Achpr’s superior environmental performance. The carbon emissions with the Achpr are 367.5652 kg lower than those of the Cchpr, which is a reduction of 6.76%. In terms of economic performance, the total costs of the Achpr and Cchpr are CNY 4899.1552 and CNY 5193.7561, respectively, and the total cost of the Achpr is 5.67% lower than the total cost of the Cchpr.

As shown in Table 7, the purchased natural gas cost under the Cchpr strategy is observed to be smaller than that under the Achpr strategy, whereas the purchased power cost under the Cchpr strategy is larger compared to Achpr. Power purchase and natural gas purchase under the Cchpr and Achpr under the cooling season are shown in Figure 7. From Figure 7, it is clear that the power purchase under the Achpr is significantly smaller than that of the Cchpr at t = 12, 16, 18, 21, and 22. Since the unit cost of power purchase is greater than that of natural gas during these periods, the total carbon emission under the Achpr is effectively reduced compared to the Cchpr.

In addition, since the cool load demand is higher than the power load during the cooling season, most of the waste heat recovered from the CCHP system is allocated for cooling production. The remaining cooling load is supplied by the EC and the CES, with the latter providing a higher percentage of the cool load demand, as shown in Figure 8. In addition, the changes in the heat-to-power ratio and cool-to-power ratio of Achpr during the cooling season are shown in Figure 9. It can be seen that the cooling power ratio is always at its maximum value, which further demonstrates that the proposed Achpr strategy is effective.

4.3. Analysis of the SLCTM

To validate the effectiveness of the SLCTM adopted in this work, the interval length l = 2t, the price growth rate α = 25%, and the carbon trading base price γ = 250 CNY/t. Three operation scenarios are set for comparative analysis. Scenario 1: under the SLCTM, the optimization objective function considers the E_PC and the E_AC and does not consider the C_TC; Scenario 2: under the traditional carbon trading mechanism, the optimization objective function considers the E_PC, the E_AC, and the C_TC; Scenario 3: under the SLCTM, the optimization objective function considers the E_PC, the E_AC, and the C_TC.

4.3.1. The SLCTM During the Heating Season

The dispatch results of the three operational scenarios in the heating season are shown in

Table 8. Comparison of three scenarios using the SLCTM in the heating season.

Name	Scenario 1	Scenario 2	Scenario 3
CTC (CNY)	−294.2166	−426.0831	−554.2501
Carbon emission (kg)	5010.8750	4249.6222	4047.3087
EAC (CNY)	77.6602	69.2760	24.7802
CPE (CNY)	933.0657	446.7419	359.3434
CPG (CNY)	6786.6721	7330.6493	7302.3828
Total cost (CNY)	7503.1813	7420.5841	7132.2562

. The carbon trading volume is positive, indicating that carbon quotas need to be purchased from outside; if the carbon trading volume is negative, the carbon quota can be sold externally.

As shown in Table 8, incorporating CTC into the optimization framework significantly reduces carbon emissions compared to scenarios without CTC. Specifically, Scenario 2 demonstrates a 15.19% emission reduction relative to Scenario 1, while Scenario 3 achieves an even greater reduction, with a 19.23% reduction compared to Scenario 1 and a 202.3135 kg reduction compared to Scenario 2. Therefore, the results indicate that integrating CTCs in the system can significantly reduce the environmental impact.

The electricity purchases and gas purchases for Scenario 1 for the heating season are shown in Figure 10. Combined with time-of-use electricity prices and natural gas prices, it can be seen that Scenario 1 does not consider the low-carbon objective and takes the economy as the operational objective. From Figure 10, with t in the periods from 1 to 7, 23, and 24, the price of purchased electricity is lower than that of natural gas, leading the system to purchase more electricity from the grid, which originates primarily from thermal power generation. In the rest of the period, natural gas is cheaper than electricity, resulting in increased natural gas purchases. Consequently, the system purchases more natural gas than purchased electricity. Therefore, the E_PC in Scenario 1 is lower than the E_PC in Scenario 2, but the actual carbon emissions from purchasing a large amount of thermal power are higher than those in Scenarios 2 and 3.

The electricity purchases and gas purchases for Scenario 2 for the heating season are shown in Figure 11. While the optimization objective of Scenario 2 considers the C_TC. In the periods from 8 to 22, when the price of purchasing natural gas is lower than that of electricity, the system purchases as much natural gas as possible, as shown in Figure 11, to supply power through CCHP power generation and reduces the amount of purchased power to the higher grid. Therefore, compared with Scenario 1, Scenario 2 reduces the purchase of electricity while increasing the purchase of natural gas.

Figure 12 shows the electricity and natural gas purchases for Scenario 3 in the heating season. From Figure 12, in the periods 2 to 6, 23, and 24, electricity is purchased from the grid when its price is lower than that of natural gas. Conversely, in periods 8 to 22, natural gas is prioritized for purchase when it is more economical than electricity, and grid electricity procurement is minimized. Since Scenario 3 uses the SLCTM, where the price of carbon allowances increases in steps, further limiting carbon emissions from the system, and electricity purchases and natural gas purchases are further reduced, electricity purchases and natural gas purchases in Scenario 3 are again reduced compared to the other scenarios.

4.3.2. The SLCTM During the Cooling Season

Table 9. Comparison of three scenarios using the SLCTM in the cooling season.

Name	Scenario 1	Scenario 2	Scenario 3
CTC (CNY)	394.3157	314.9333	311.0618
Carbon emission (kg)	5439.6903	5138.5963	5073.3087
EAC (CNY)	11.2775	16.3601	2.1487
CPE (CNY)	2753.7367	2512.9162	2480.8309
CPG (CNY)	1830.0764	2123.4409	2105.1138
Total cost (CNY)	4989.4062	4967.6504	4899.1552

presents the operational dispatch outcomes for the three cooling season scenarios. The comparative analysis demonstrates that including CTC in the objective function results in significantly lower carbon emissions compared to the approach that excludes CTC. Specifically, Scenario 2 exhibits a 2.03% reduction in emissions relative to Scenario 1, while Scenario 3 achieves a more substantial decrease of 6.74% compared to Scenario 1. Furthermore, Scenario 3 shows an additional reduction of 65.2876 kg when contrasted with Scenario 2. These results confirm that the SLCTM effectively constrains carbon emissions while enhancing emission reduction performance.

Similarly, combining time-of-use electricity prices and natural gas prices, it can be seen that Scenario 1 does not consider the low-carbon objective and takes the economy as the operational objective. In the periods from 1 to 7, 23, and 24, the price of purchased electricity is lower than the price of purchased natural gas, and the system purchases as much electricity as possible from the higher grid. In the rest of the period, the price of purchased natural gas is lower than the price of purchased electricity, and the system purchases more natural gas than purchased electricity, as shown in Figure 13. Therefore, the EPC in Scenario 1 is lower than the EPC in Scenario 2 and Scenario 3, but the actual carbon emissions from purchasing a large amount of thermal power are higher than those in Scenario 2 and Scenario 3.

Figure 14 illustrates the electricity and natural gas procurement patterns for Scenario 2 during the cooling season, in which CTC is incorporated into the optimization objective. As depicted in Figure 14, during peak hours from 8 to 22, when electricity prices are typically higher, the system preferentially utilizes natural gas for CCHP power generation leveraging its cost advantage over grid electricity. This operational strategy results in maximized natural gas consumption for on-site generation while minimizing reliance on higher-priced grid electricity. Consequently, Scenario 2 demonstrates a distinct energy procurement profile compared to Scenario 1, characterized by reduced electricity purchases and increased natural gas utilization.

The electricity and natural gas purchases for Scenario 3 in the cooling season are shown in Figure 15. From Figure 15, in the periods from 1 to 5, 7, 23, and 24, the price of purchasing electricity is lower than the price of purchasing natural gas, and the system purchases more electricity than natural gas. Due to the high coefficient of performance of the EC, the power load and cool load are larger, and the renewable energy output is reduced, so the purchase of electricity is greater than the purchase of natural gas, in periods 6 and 15 to 18. It is in line with the lowest total cost and the smallest carbon emissions. Scenario 3 uses the SLCTM, where the price of carbon allowances increases in steps, further limiting the carbon emissions of the system.

Comparing the total costs of the three operating scenarios, Scenario 1 has the largest total cost, even though the E_PC is low because the C_TC is not taken into account in the optimization, which leads to a significant increase in the carbon emissions of the system and increases the C_TC of the system. Scenario 2 increases the E_PC, but the C_TC is reduced, and the C_TC is optimized using the traditional carbon trading mechanism, where the purchase price and selling price of carbon credits are only the base price, resulting in a low cost of carbon trading and a lower total cost. Scenario 3 adopts the SLCTM, which further reduces the carbon emissions of the system and lowers the C_TC of the system, while the system reduces the purchase of electricity and the purchase of natural gas, which reduces the E_PC of the system. Scenario 3 has the lowest total cost, which ensures that the system is low-carbon and, at the same time, can be operated economically. Therefore, the SLCTM has a significant effect on the low-carbon emissions of IES and is economically sound.

5. Conclusions

To improve the low-carbon economic operation of PIES, this work takes the minimum total cost of the system as the objective function. Considering the C_TC, E_PC, and E_AC, the low-carbon economy of SPIESchpr is developed to optimize the output of each device in the system. In this work, SLCTM is used to reduce the carbon emissions of the system effectively. The carbon emissions of Scenario 3 are lower than those of Scenario 1 and Scenario 2 in both heating and cooling seasons, and the proposed Achpr effectively improves the system economy. In contrast to the Cchpr strategy, which produces electrical, thermal, and cooling energy at a fixed efficiency, the proposed Achpr flexibly adjusts heating and cooling outputs in response to seasonal variations in energy demand. This reduces the carbon emissions of PIES and improves the economics of the system. However, there are still some shortcomings in the research content of this work, such as not considering the time-of-use natural gas prices. Fluctuations in energy prices may alter the trade-off between the economic and low-carbon performance of PIES, potentially leading to deviations in total operating costs from the present simulation results. Furthermore, while the simulation equipment employed in this paper comprises an idealized model consistent with system operation under normal conditions, actual operation requires consideration of the impact of power fluctuation. Consequently, future research may focus on bridging the gap between simulation models and real-world counterparts. Attempts to reduce this discrepancy will enhance the practical relevance of the results. Future research should also prioritize the synergistic optimization of time-of-use electricity pricing alongside other dynamic pricing mechanisms to address emerging challenges arising from high renewable energy integration, enhanced load flexibility, and electricity market reforms.