Enhanced Management of Unified Energy Systems Using Hydrogen Fuel Cell Combined Heat and Power with a Carbon Trading Scheme Incentivizing Emissions Reduction

Abstract

In the quest to achieve “double carbon” goals, the urgency to develop an efficient Integrated Energy System (IES) is paramount. This study introduces a novel approach to IES by refining the conventional Power-to-Gas (P2G) system. The inability of current P2G systems to operate independently has led to the incorporation of hydrogen fuel cells and the detailed investigation of P2G’s dual-phase operation, enhancing the integration of renewable energy sources. Additionally, this paper introduces a carbon trading mechanism with a refined penalty–reward scale and a detailed pricing tier for carbon emissions, compelling energy suppliers to reduce their carbon footprint, thereby accelerating the reduction in system-wide emissions. Furthermore, this research proposes a flexible adjustment mechanism for the heat-to-power ratio in cogeneration, significantly enhancing energy utilization efficiency and further promoting conservation and emission reductions. The proposed optimization model in this study focuses on minimizing the total costs, including those associated with carbon trading and renewable energy integration, within the combined P2G-Hydrogen Fuel Cell (HFC) cogeneration system. Employing a bacterial foraging optimization algorithm tailored to this model’s characteristics, the study establishes six operational modes for comparative analysis and validation. The results demonstrate a 19.1% reduction in total operating costs and a 22.2% decrease in carbon emissions, confirming the system’s efficacy, low carbon footprint, and economic viability.

1. Introduction

Across the globe, nations have recognized the importance of diminishing carbon emissions as an essential metric. At its 75th session, the United Nations General Assembly heard China’s commitment to peak carbon emissions by 2030 and achieve carbon neutrality by 2060 [1,2]. In the realm of carbon emissions, the electricity sector, predominantly powered by fossil fuels, contributes approximately 40% [3,4]. With the intrinsic potential for emission reductions, the electricity sector leads in China’s national unified carbon emission trading market, hastening the transition of Chinese electrical companies towards low-carbon operations. This transition facilitates the progression towards a sustainable energy supply that is both cleaner and lower in carbon emissions [5,6]. The advent of the Integrated Electricity–Heat Energy System (IEHS) has heralded a new era in energy optimization. This system efficiently harnesses both electric and thermal energy, thereby enhancing the overall energy efficiency and fostering a low-carbon economy through the synergistic interaction of these energy forms [7,8].

Wind and solar power exhibit considerable fluctuations and unpredictability. These energy sources, without sufficient grid management strategies, might lead to underutilization. Power-to-gas (P2G) technology emerges as an innovative approach to enhance the utilization of these renewable energies. Research in [9] established a low-carbon economic dispatch model incorporating P2G storage, showing its effectiveness in augmenting the grid’s capacity to integrate energy from wind and solar sources. Further studies in [10,11] explore how P2G can convert excess wind energy into hydrogen through electrolysis using an electrolier (EL), and subsequently produce synthetic natural gas by combining this hydrogen with CO₂, which markedly improves wind energy absorption and serves as a model for low-carbon operations. According to [12], the conversion efficiency from hydrogen to synthetic natural gas stands at 55%, with an electrolysis efficiency of 80%, and the combustion process emits zero carbon while offering superior efficiency compared to natural gas. However, [13] indicates that current research on the energy conversion cycle between EL, hydrogen fuel cells, and methane reactors (MRs) does not account for the potential heat recovery from fuel cells. This suggests significant opportunities to further explore the emission reduction potential of dual-stage P2G processes, making it crucial to delve deeper into this area.

In addition, to unleash the emission reduction potential of industrial park areas, the literature [14] indicates that applying a carbon trading mechanism to IEHS can effectively promote carbon emission reductions. Recent studies have introduced a carbon trading framework into IEHS, examining the influence of carbon trading prices [15]. Subsequent research developed a low-carbon economic model for IEHS that incorporates these mechanisms [16]. Further enhancements have been made to carbon emission estimation techniques, introducing a stepwise carbon trading approach that significantly cuts emissions [17,18]. An optimized version of this model refines the carbon trading calculation methodologies, improving both the low-carbon efficiency and economic performance of the system [19]. Another approach introduces a penalty-tiered carbon trading system derived from a stepwise model but it lacks detailed carbon emission-price ranges, leaving the impact on carbon reduction ambiguous [20]. An analysis of these studies reveals a gap in the detailed consideration of dual-stage P2G operations and the effect of carbon emission-price ranges on carbon trading mechanisms, which results in vague outcomes regarding carbon reductions. Addressing these issues, this paper utilizes the penalty-tiered carbon trading system to coordinate the dual-stage operations of P2G, refines the emission-price ranges, and evaluates the effectiveness of various reward factors.

In addition, the predominant approach in IEHS research has focused on Combined Heat and Power (CHP) units with fixed thermal–electric ratios [21,22,23]. Recent proposals advocate for a “heat dictates power” strategy, which leads to significant electricity losses, increased wind curtailment, and diminished system regulation capabilities, thereby reducing economic efficiency [24,25]. Although there is research exploring the adjustability of thermal-electric ratios within CHP units to enhance system operations, it overlooks the potential heat utilization from High-Temperature Fuel Cells (HFCs) and the flexibility of thermal–electric ratios, thus not fully capitalizing on possible energy savings and emission reductions [26]. Therefore, it is imperative to consider the utilization of heat from HFCs and conduct in-depth research on the roles of adjustable thermal–electric ratios of both HFCs and CHP in IEHS to further enhance energy-saving and emission reduction efforts.

To achieve the dual-carbon goals, this study introduces an advanced energy system optimization approach using a dynamic reward–penalty carbon trading framework for P2G systems integrated with HFCs, aimed at optimizing both the carbon footprint and economic performance. Initially, the model incorporates a sophisticated two-phase P2G process within an IEHS framework, utilizing a tiered carbon trading mechanism. This model also takes into account the flexible thermal–electric ratio of HFCs and CHP configurations to minimize the total operational costs, expenses associated with carbon trading, and utilization costs of renewable energies. Subsequently, the optimization challenges are tackled using the versatile Bacterial Foraging Optimization Algorithm, ensuring a thorough global search capability. Comparative evaluations of various operational strategies validate the efficiency of the tailored IEHS, underlining its effectiveness.

2. The Award and Punishment Step-by-Step Carbon Trading Mechanism and the IEHS Model

In this study, we explore the refined operation of P2G technologies within an IEHS, focusing on a two-stage process. This is examined under a dynamic reward–punishment carbon trading mechanism. The paper delves into the optimization of an adjustable energy system incorporating combined CHP. A comprehensive analysis is provided on the structure of the IEHS model, which is tailored to operate under the dynamic reward–punishment carbon trading mechanism. Additionally, the operational strategy for HFC in this framework is elaborated.

2.1. The Structure of IEHS

Figure 1 illustrates the conceptual architecture of the IEHS. Within the established framework of energy and power systems, sources such as wind turbines, solar photovoltaic arrays, and Combined CHP units deliver electrical energy primarily to various electrical loads and P2G systems. Subsequently, the electricity is transformed into hydrogen via EL units, which are then utilized directly by HFC to generate both electricity and heat. Excess hydrogen is transformed into natural gas by MR equipment to supply gas loads, further achieving cascaded consumption of energy for efficient utilization. In the thermal network, HFCs, CHP, and gas boilers (GBs) provide heat to thermal loads. In the gas network, the demand for gas loads mainly involves purchasing higher-level gases and a joint supply of methane-synthesized natural gases. In IEHS, apart from the complementary coordinated use of electrical and thermal energies, it also includes storage devices for gases, thermal energies, and hydrogen energies to achieve energy storage and time shifting. These storage devices can transfer energy between high-demand peak periods and low-demand off-peak periods to balance and optimize energy supply. Meanwhile, CO₂ generated or absorbed within the system is ultimately traded through carbon trading markets to achieve dual benefits in terms of the economy and the environment.

2.2. The Principle and Model of Adjustable Thermal–Electric Ratio

(1) The principle of the adjustable thermal–electric ratio.

The CHP system utilizes the waste heat generated by fuel combustion in gas turbines to improve energy efficiency. The system can achieve real-time adjustment of electricity generation by controlling the intake of the gas turbine. At the same time, by controlling the absorption of waste heat by the heat recovery boiler, the system can change the amount of heat supplied. Through this method, the system can achieve a real-time adjustable thermal–electric ratio while adjusting the thermal–electric capacity. Specifically, when the load demand is high, the system can increase the intake of the gas turbine and burn more fuel to increase electricity generation. Meanwhile, the heat recovery boiler can fully absorb the heat in the waste gas to meet the higher heat demand. Thus, the system can achieve a higher thermal–electric ratio under high load. Based on this, this paper proposes an adjustable thermal–electric ratio model.

(2) The adjustable thermal–electric ratio model.

Reference [27] provides the range of the adjustable thermal–electric ratio. The working model is as follows:

$$\left\{\begin{array}{l}{P}_e^{\mathrm{CHP}}\left(t\right)=\left(1-k_h\right){\eta }_e^{\mathrm{CHP}}{L}_{NG}{P}_g^{\mathrm{CHP}}\left(t\right)\\ P_h^{\mathrm{CHP}}\left(t\right)=k_h\left(1-k_{\mathrm{loss}}\right){\eta }_h^{\mathrm{CHP}}{L}_{\mathrm{NG}}{P}_g^{\mathrm{CHP}}\left(t\right)\\ P_{g,\min }^{\mathrm{CHP}}\le P_h^{\mathrm{CHP}}\left(t\right)\le P_{g,\max }^{\mathrm{CHP}}\\ \mathsf{\Delta }{P}_{g,\min }^{\mathrm{CHP}}\le P_g^{\mathrm{CHP}}\left(t+1\right)-P_g^{\mathrm{CHP}}\left(t\right)\le \mathsf{\Delta }{P}_{g,\max }^{\mathrm{CHP}}\\ {\kappa }^{\mathrm{CHP}}=P_h^{\mathrm{CHP}}\left(t\right)/P_e^{\mathrm{CHP}}\left(t\right)=k_h\left(1-k_{\mathrm{loss}}\right){\eta }_h^{\mathrm{CHP}}/\left(1-k_h\right){\eta }_e^{\mathrm{CHP}}\\ {\mathit{\kappa }}_{\min }^{\mathrm{CHP}}\le P_h^{\mathrm{CHP}}\left(t\right)/P_e^{\mathrm{CHP}}\left(t\right)\le {\mathit{\kappa }}_{\max }^{\mathrm{CHP}}\end{array}\right.$$

(1)

where $P_g^{\mathrm{CHP}}(t)$ represents the input power of natural gas for a CHP unit during a specific time period t; concurrently, $P_e^{\mathrm{CHP}}(t)$ denotes the electrical power output; $P_h^{\mathrm{CHP}}(t)$ symbolizes the thermal power output of the CHP unit during the same interval; $L_{\mathrm{NG}}$ is defined as the low calorific value of natural gas and is consistently set at 9.7 kW/m³; the conversion efficiencies for electricity and thermal energy within the CHP system are represented by ${\eta }_e^{\mathrm{CHP}}$ and ${\eta }_h^{\mathrm{CHP}}$, respectively; $k_h$ and $k_{loss}$ quantify the rates of heat loss and the ratio of heat utilized for heating by the CHP unit; constraints on the natural gas power input are defined by $P_{g,\max }^{\mathrm{CHP}}$ and $P_{g,\min }^{\mathrm{CHP}}$, which delineate the maximum and minimum allowable values; $\mathsf{\Delta }{P}_{g,\max }^{\mathrm{CHP}}$ and $\mathsf{\Delta }{P}_{g,\min }^{\mathrm{CHP}}$ describe the maximum and minimum permissible rates of change in gas power input; the thermoelectric ratio of the CHP, along with its maximum and minimum allowable values, are designated as ${\kappa }^{\mathrm{CHP}}$, ${\mathit{\kappa }}_{\max }^{\mathrm{CHP}}$, and ${\mathit{\kappa }}_{\min }^{\mathrm{CHP}}$.

2.3. P2G Two-Stage Operational Process

P2G technology facilitates the transformation of electrical power into a gas form, predominantly hydrogen or methane. In order to describe the operation of P2G systems more accurately, this paper introduces EL, MR, and HFC models to refine the P2G process into two steps: electric hydrogen production and methanation. The refined P2G two-phase operation is shown in Figure 2.

In the EL model, electrical energy is initially converted into hydrogen. Subsequently, this hydrogen serves a dual purpose: it is either directly utilized in the HFC model to generate both electricity and heat or it is transferred to the MR where it reacts with carbon dioxide to produce synthetic natural gas, thereby fulfilling the demands of the gas load, GBs, and CHP systems. Direct utilization of hydrogen in HFCs offers several advantages compared to its conversion to natural gas for subsequent combustion in GBs or CHP. Primarily, it streamlines the energy transformation process by reducing the steps involved, thus curtailing the cascading loss of energy. Moreover, hydrogen demonstrates superior energy efficiency relative to natural gas and emits no CO₂ during consumption. Therefore, a direct supply of HFCs can achieve higher energy efficiency and environmental friendliness.

The above model of energy conversion can be described as follows [28].

2.3.1. EL Equipment

P2G can convert electrical energy into chemical energy in the gas to realize the conversion of energy in time and space, and its core component is the EL equipment. The EL is divided into three types: the proton exchange membrane EL, alkaline EL, and high-temperature solid oxide EL, of which the more widely used is the proton exchange membrane EL. The high-temperature solid oxide EL’s efficiency can reach approximately 85%, which is higher than the remaining two types, but its operating temperature is high, which is not ideal, and it is not currently promoted on a large scale. This paper does not elaborate on the specific types and working principles of the EL, as s more detailed description can be found in reference [29]. This paper selects the more widely used alkaline EL, the structure and principle of which are shown in Figure 3.

The EL model constructed in this paper is as follows:

$$\left\{\begin{array}{l}{P}_{\mathrm{EL},{\mathrm{H}}_2}(t)={\eta }_{\mathrm{EL}}{P}_{\mathrm{e},\mathrm{EL}}(t)\\ P_{\mathrm{e},\mathrm{EL}}^{\min }⩽P_{\mathrm{e},\mathrm{EL}}(t)⩽P_{\mathrm{e},\mathrm{EL}}^{\max }\\ \mathsf{\Delta }{P}_{\mathrm{e},\mathrm{EL}}^{\min }⩽P_{\mathrm{e},\mathrm{EL}}(t+1)-P_{\mathrm{e},\mathrm{EL}}(t)⩽\mathsf{\Delta }{P}_{\mathrm{e},\mathrm{EL}}^{\max }\end{array}\right.$$

(2)

where at time period t, the EL generates hydrogen energy output, designated as $P_{\mathrm{EL},{\mathrm{H}}_2}(t)$, while the electrical energy input to the EL is indicated by $P_{\mathrm{e},\mathrm{EL}}$; the efficiency of converting hydrogen energy in the EL is captured by the metric ${\eta }_{\mathrm{EL}}$; the operational parameters for the EL include a defined range for power input, with $P_{\mathrm{e},\mathrm{EL}}^{\min }$ representing the minimum threshold and $P_{\mathrm{e},\mathrm{EL}}^{\max }$ serving as the maximum permissible value; the rate of increase in the EL’s operation is bounded by $\mathsf{\Delta }{P}_{\mathrm{e},\mathrm{EL}}^{\max }$ as the upper limit and $\mathsf{\Delta }{P}_{\mathrm{e},\mathrm{EL}}^{\min }$ as the lower limit.

2.3.2. Methanation of MR Equipment

The methanation reaction is the reduction in carbon dioxide by hydrogen to synthesize methane and water under specific temperature conditions and catalysts, and this reaction is a volume reduction reaction usually accompanied by the release of energy, i.e., the thermal effect. The methanation reaction is the core reaction of coke oven gas to natural gas, especially in the adiabatic multi-stage cycle. In order to obtain industrialization research, this paper does not elaborate further on the working principle, as a more detailed description can be found in reference [30]. The structure and principle of MR is shown in Figure 4.

The model delineated in this study represents the operational dynamics of an MR.

$$\left\{\begin{array}{l}{P}_{\mathrm{MR},\mathrm{g}}(t)={\eta }_{\mathrm{MR}}{P}_{{\mathrm{H}}_2,\mathrm{MR}}(t)\\ P_{{\mathrm{H}}_2,\mathrm{MR}}^{\min }⩽P_{{\mathrm{H}}_2,\mathrm{MR}}(t)⩽P_{{\mathrm{H}}_2,\mathrm{MR}}^{\max }\\ \mathsf{\Delta }{P}_{{\mathrm{H}}_2,\mathrm{MR}}^{\min }⩽P_{{\mathrm{H}}_2,\mathrm{MR}}(t+1)-P_{{\mathrm{H}}_2,\mathrm{MR}}(t)⩽\mathsf{\Delta }{P}_{{\mathrm{H}}_2,\mathrm{MR}}^{\max }\end{array}\right.$$

(3)

where at any given time t, the natural gas output, denoted as $P_{\mathrm{MR},\mathrm{g}}(t)$, is generated from the MR, influenced by the hydrogen input, labeled $P_{{\mathrm{H}}_2,\mathrm{MR}}(t)$; the conversion efficiency of this process, represented by ${\eta }_{\mathrm{MR}}$, indicates the effectiveness of converting hydrogen into methane; operational constraints are defined by $P_{{\mathrm{H}}_2,\mathrm{MR}}^{\max }$ and $P_{{\mathrm{H}}_2,\mathrm{MR}}^{\min }$, which are the maximum and minimum thresholds for hydrogen energy inputs to the MR; the operational flexibility of MR, concerning its capability to adjust output levels, is bounded by $\mathsf{\Delta }{P}_{{\mathrm{H}}_2,\mathrm{MR}}^{\max }$ and $\mathsf{\Delta }{P}_{{\mathrm{H}}_2,\mathrm{MR}}^{\min }$, representing the upper and lower limits of the MR’s operational ram**.

2.3.3. Hydrogen Fuel Cell (HFC) Equipment

In HFCs, only hydrogen reacts with oxygen to form water, and the whole process is pollution-free, does not emit carbon, and does not follow the Carnot cycle. HFCs have a high energy conversion efficiency and have become an important direction for future battery research. The specific reaction principle is not elaborated on further in this paper, and for a detailed understanding, readers are directed to reference [31]. The structure and principle of HFCs are shown in Figure 5.

In this study, the model for HFC energy dynamics is delineated as:

$$\left\{\begin{array}{l}{P}_{\mathrm{HFC},\mathrm{e}}(t)={\eta }_{\mathrm{HFC}}^{\mathrm{e}}{P}_{{\mathrm{H}}_2,\mathrm{HFC}}(t)\\ P_{\mathrm{HFC},\mathrm{h}}(t)={\eta }_{\mathrm{HFC}}^{\mathrm{h}}{P}_{{\mathrm{H}}_2,\mathrm{HFC}}(t)\\ P_{{\mathrm{H}}_2,\mathrm{HFC}}^{\min }⩽P_{{\mathrm{H}}_2,\mathrm{HFC}}(t)⩽P_{{\mathrm{H}}_2,\mathrm{HFC}}^{\max }\\ \mathsf{\Delta }{P}_{{\mathrm{H}}_2,\mathrm{HFC}}^{\min }⩽P_{{\mathrm{H}}_2,\mathrm{HFC}}(t+1)-P_{{\mathrm{H}}_2,\mathrm{HFC}}(t)⩽\mathsf{\Delta }{P}_{{\mathrm{H}}_2,\mathrm{HFC}}^{\max }\\ {\kappa }_{\mathrm{HFC}}^{\min }⩽P_{\mathrm{HFC},\mathrm{h}}(t)/P_{\mathrm{HFC},\mathrm{e}}(t)⩽{\kappa }_{\mathrm{HFC}}^{\max }\end{array}\right.$$

(4)

where $P_{{\mathrm{H}}_2,\mathrm{HFC}}(t)$ represents the hydrogen energy required by the HFC at any given time t; ${\eta }_{\mathrm{HFC}}^{\mathrm{e}}$ and ${\eta }_{\mathrm{HFC}}^{\mathrm{h}}$ quantify the conversion efficiencies of the HFC for electricity and heat; the outputs in terms of electrical and thermal energies are denoted as $P_{\mathrm{HFC},\mathrm{e}}(t)$ and $P_{\mathrm{HFC},\mathrm{h}}(t)$ for time t, respectively; the model defines $P_{{\mathrm{H}}_2,\mathrm{HFC}}^{\max }$ and $P_{{\mathrm{H}}_2,\mathrm{HFC}}^{\min }$ as the upper and lower limits for the hydrogen energy input into the HFC, respectively; $\mathsf{\Delta }{P}_{{\mathrm{H}}_2,\mathrm{HFC}}^{\min }$ and $\mathsf{\Delta }{P}_{{\mathrm{H}}_2,\mathrm{HFC}}^{\max }$ serve as the creepage bounds, while ${\kappa }_{\mathrm{HFC}}^{\max }$ and ${\kappa }_{\mathrm{HFC}}^{\min }$ establish the constraints for the thermoelectric ratio of the HFC.

2.4. Reward and Penalty Laddering Carbon Trading Mechanism Modeling

The Incentive Laddering Mechanism for Carbon Trading, a market-oriented model predicated on carbon emissions, seeks to foster a reduction in these emissions through structured incentives. This mechanism employs a hierarchical system of carbon emission thresholds coupled with rewards for compliance and penalties for breaches. It introduces an incentive coefficient $\beta$ concept to further refine the categorization and handling of various carbon emission levels. Should the carbon emissions from an energy provider fall below the government-allocated free emission quota, a defined subsidy is granted to encourage continued adherence to low-carbon practices. The framework for this mechanism encompasses a model for actual carbon emissions, a tiered system for carbon trading rewards and penalties, and a model for managing carbon emission rights.

(1) Carbon Emission Allowance Model

In the IEHS, the primary contributors to carbon emissions include GBs, CHP systems, and power acquired from higher authorities. The prevalent allocation method in China currently utilizes a non-cost allocation system. This analysis posits that all power acquisitions from higher-level sources are attributable to coal-fired thermal power plants.

$$\left\{\begin{array}{l}{E}_{ct}=E_{\mathrm{CHP}}+E_{\mathrm{GB}}+E_{\mathrm{e},\mathrm{buy}}+E_{\mathrm{g},\mathrm{load}}-E_{\mathrm{MR}}\\ E_{\mathrm{CHP}}={\lambda }_{\mathrm{h}}{\displaystyle {\displaystyle \sum }_{t=1}^T}\left({\lambda }_{e,\mathrm{h}}{P}_{\mathrm{CHP},\mathrm{e}}(t)+P_{\mathrm{CHP},\mathrm{h}}(t)\right)\\ E_{\mathrm{GB}}={\lambda }_{\mathrm{h}}{\displaystyle {\displaystyle \sum }_{t=1}^T}{P}_{\mathrm{GB},\mathrm{h}}(t)\\ E_{\mathrm{e},\mathrm{buy}}={\lambda }_{\mathrm{e}}{\displaystyle {\displaystyle \sum }_{t=1}^T}{P}_{\mathrm{e},\mathrm{buy}}(t)\\ E_{\mathrm{g},\mathrm{load}}={\lambda }_{\mathrm{g}}{\displaystyle {\displaystyle \sum }_{t=1}^T}{P}_{\mathrm{g},\mathrm{load}}(t)\end{array}\right.$$

(5)

where $E_{ct}$, $E_{\mathrm{CHP}}$, $E_{\mathrm{GB}}$, $E_{\mathrm{e},\mathrm{buy}}$, $E_{\mathrm{g},\mathrm{load}}$, and $E_{\mathrm{MR}}$ are the carbon credits required for IEHS, CHP, GB, upstream power purchase, gas load, and methanization, respectively. Carbon allowances for gas and coal-fired units are designated as ${\lambda }_{\mathrm{h}}$, ${\lambda }_{\mathrm{e}}$, and ${\lambda }_{\mathrm{g}}$ for thermal power production, electric power generation, and gas load management, respectively; upstream power purchases during time slot t are denoted as $P_{e,\mathrm{buy}}(t)$, while $P_{\mathrm{GB},\mathrm{h}}(t)$ represents the thermal energy produced by the GB within the same interval; $P_{\mathrm{g},\mathrm{load}}(t)$ indicates the gas load at any given time during the scheduling period t; ${\lambda }_{e,\mathrm{h}}$ refers to the conversion factor from electric to heat power in CHP unit.

(2) Real carbon emissions modeling

Within the MR protocol, it is essential to account for the absorption of a segment of CO₂ during the transformation of hydrogen into natural gas. The true carbon emissions are consequently formulated in the following manner:

$$\left\{\begin{array}{l}{E}_{{\mathrm{CO}}_2}=E_{\mathrm{e},\mathrm{buy},\mathrm{a}}+E_{\mathrm{total},\mathrm{a}}-E_{\mathrm{MR},\mathrm{a}}\\ E_{\mathrm{e},\mathrm{buy},\mathrm{a}}={\displaystyle {\displaystyle \sum }_{t=1}^T}\left(a_1+b_1{P}_{\mathrm{e},\mathrm{buy}}(t)+c_1{P}_{\mathrm{e},\mathrm{buy}}^2(t)\right)\\ E_{\mathrm{total},\mathrm{a}}={\displaystyle {\displaystyle \sum }_{t=1}^T}\left(a_2+b_2{P}_{\mathrm{total}}(t)+c_2{P}_{\mathrm{total}}^2(t)\right)\\ P_{\mathrm{total}}(t)=P_{\mathrm{CHP},\mathrm{e}}(t)+P_{\mathrm{CHP},\mathrm{h}}(t)+P_{\mathrm{GB},\mathrm{h}}(t)\\ E_{\mathrm{MR},\mathrm{a}}={\displaystyle {\displaystyle \sum }_{t=1}^T}\varpi P_{\mathrm{MR},\mathrm{g}}(t)\end{array}\right.$$

(6)

where for the IEHS, the actual carbon emissions, denoted as $E_{{\mathrm{CO}}_2}$, are recorded; when the IEHS sources electricity from a superior level, the emissions are represented by $E_{\mathrm{e},\mathrm{buy},\mathrm{a}}$; the MR process captures CO₂, quantified as $E_{\mathrm{MR},\mathrm{a}}$; the cumulative carbon emissions from the CHP unit, the MR facility, and the GB are calculated as $E_{\mathrm{total},\mathrm{a}}$, whereas $P_{\mathrm{total}}(t)$ indicates the equivalent power output of these units at any given time t. The parameter $\varpi$ represents the CO₂ absorption efficiency in the conversion of hydrogen to natural gas at the MR plant; parameters $a_1$, $b_1$, $c_1$, and $a_2$, $b_2$, and $c_2$ are employed to estimate emissions from coal-fired and gas-fired power systems, respectively.

(3) Reward and penalty laddering carbon emissions trading model

Calculation of both the carbon emission allowances and the real emissions from IEHS enables the precise quantification of carbon emission rights that are exchanged within the carbon trading market.

$$E_{{\mathrm{CO}}_2,\mathrm{t}}=E_{{\mathrm{CO}}_2}-E_{ct}$$

(7)

where $E_{{\mathrm{CO}}_2,\mathrm{t}}$ is the carbon credit trading amount of the IEHS.

This research proposes an enhanced carbon pricing model in carbon trading to further incentivize power companies towards emission reductions and boost the efficacy of the carbon trading scheme. The model introduces a tiered carbon trading structure that applies variable rewards and penalties based on how well companies meet their carbon quotas. Rewards are granted for emissions that fall below the allocated quota, encouraging the adoption of low-carbon technologies and further reducing carbon dioxide emission coefficients per kilowatt-hour to maximize revenue. Conversely, companies that exceed their carbon quotas by specific thresholds face escalating penalty costs. This tier-based approach to carbon pricing through linear segmentation aims to actively engage power enterprises in modifying their production strategies or adopting low-carbon technologies. Such adjustments are intended to control carbon emissions effectively, ensuring the precision and rationality of carbon trading and generating substantial economic benefits. The dynamics between the tiered pricing in this trading model and the segmented function reflecting the variance between actual emissions and the quota are depicted in Figure 6.

In Figure 6, the stepped structure in the carbon trading price function reflects the cost situation faced by energy supply companies when carbon emissions exceed the quota, and this structure is represented by the coordinates and shaded area in the first quadrant, symbolizing the role of the multi-energy complementary system. In scenarios where carbon emissions surpass allocated quotas, the financial burden of carbon credits on energy suppliers escalates. Conversely, when emissions remain below the allotted limits, delineated by coordinates in the third quadrant, these companies may accrue revenue through carbon trading. This potential revenue increases incrementally with further emission reductions, thereby encouraging power providers to adopt more stringent emission control strategies. This financial mechanism effectively motivates a reduction in emissions. A tiered pricing system for carbon emission credits, which differs from traditional methods, implements a graded approach. As companies acquire more carbon allowances, the cost associated with these increasing tiers escalates accordingly. Therefore, the cost of reward and punishment tiered carbon trading can be calculated in the following way:

$$C_{{\mathrm{CO}}_2}=\left\{\begin{array}{ll}{P}_{ct}\left(E_{{\mathrm{CO}}_2}-E_{ct}\right)+P_{ct}\beta \left(2E_{ct}-2E_{{\mathrm{CO}}_2}-e\right)& \hfill E_{C{O}_2}<E_{cl}-e^{\prime }\hfill \\ P_{c\mathrm{t}}\left(E_{{\mathrm{CO}}_2}-E_{ct}\right)+P_{cl}\beta \left(E_{ct}-E_{{\mathrm{CO}}_2}\right)& \hfill E_{ct}-e^{\prime }\le E_{C{O}_2}<E_{ct}\hfill \\ P_{ct}\left(E_{{\mathrm{CO}}_2}-E_{ct}\right)& \hfill E_{ct}\le E_{{\mathrm{CO}}_2}\le E_{ct}+E\hfill \\ P_{ct}\left(E_{{\mathrm{CO}}_2}-E_{ct}\right)+P_{ct}\alpha \left(E_{{\mathrm{CO}}_2}-E_{ct}-e\right)& \hfill E_{ct}+E<E_{{\mathrm{CO}}_2}\le E_{ct}+E+e\hfill \\ P_{ct}\left(E_{{\mathrm{CO}}_2}-E_{ct}\right)+P_{ct}\alpha \left(2E_{{\mathrm{CO}}_2}-2E_{ct}-3e\right)& \hfill E_{ct}+E+e<E_{{\mathrm{CO}}_2}\le E_{ct}+E+2e\hfill \\ P_{ct}\left(E_{{\mathrm{CO}}_2}-E_{ct}\right)+P_{ct}\alpha \left(3E_{{\mathrm{CO}}_2}-3E_{ct}-6e\right)& \hfill E_{ct}+E+2e<E_{{\mathrm{CO}}_2}\le E_{ct}+E+3e\hfill \\ \dots \dots & \hfill \dots \dots \hfill \\ P_{ct}\left(E_{{\mathrm{CO}}_2}-E_{ct}\right)+P_{ct}\alpha \left(n{E}_{{\mathrm{CO}}_2}-n{E}_{ct}-\frac{n(n+1)}{2}e\right)& \hfill E_{ct}+E+ne<E_{{\mathrm{CO}}_2}+E+(n+1)e\hfill \end{array}\right.$$

(8)

where, in the carbon trading market, the Cost of System Operation ($C_{{\mathrm{CO}}_2}$) functions as a dynamic adjustment mechanism, modifying charges according to the incentive–penalty step model; this model is further defined by the baseline carbon trading price ($P_{ct}$), which anchors the market’s initial valuation of carbon credits; the actual carbon emissions of system operation ($E_{{\mathrm{CO}}_2}$), when juxtaposed with the Initial quota allocated by the government ($E_{ct}$), underscore the operational reality of emissions versus regulatory benchmarks.

The carbon price parity interval without incentives and penalties ($E$) delineates the range within which carbon prices stabilize without regulatory interference. The incentive–penalty step carbon trading model distinguishes itself through two primary intervals: the length of the step incentive interval ($e$) and the length of the step penalty interval ($e^{\prime }$), with each dictating the extent of fiscal adjustments for compliance or deviation; the degree of balance at the time of carbon allowance settlement ($n$) is assessed across multiple gradients, ensuring a nuanced evaluation of emissions management; within this framework, the carbon price penalty factor per unit of emission reduction in each class interval ($\alpha$) is activated when emissions exceed government-issued quotas, imposing financial disincentives; the carbon price incentive factor per unit of emission reduction in each class interval ($\beta$) rewards operations that maintain emissions below the stipulated benchmarks, promoting environmentally beneficial practices.

3. Optimized Operation Model of IEHS Considering Reward–Penalty Stepped Carbon Trading Mechanism with Adjustable Heat-to-Power Ratio

3.1. Objective Function Establishment

This chapter develops an operational model for HFCs and CHP based on thermoelectric ratios, employing an optimized P2G-HFC-IEHS framework. The model is engineered to ensure low-carbon, economical, and stable performance while adhering to operational constraints, leveraging a reward and punishment mechanism within carbon trading. Comprising various cost considerations—including stepped carbon trading expenses, penalties for unused renewable energy, operational costs, and energy purchase expenditures—the model is detailed through an optimally minimized objective function. Equation (9) presents the scheduling objective function.

$$C=\min \left(C_{\mathrm{WP}}+C_{\mathrm{M}}+C_{\mathrm{buy}}+C_{{\mathrm{CO}}_2}\right)$$

(9)

where $C$ represents the total operational costs, encompassing $C_{\mathrm{WP}}$, which details the fines for abandoning new energy sources. $C_{\mathrm{buy}}$ covers the expenses for energy acquisition, while $C_{\mathrm{M}}$ accounts for the costs associated with system maintenance and operations.

(1) Cost of energy purchases

$$C_{\mathrm{buy}}={\displaystyle \sum }_{t=1}^T\left({\alpha }_t{P}_{\mathrm{e},\mathrm{buy}}(t)+{\beta }_t{P}_{\mathrm{g},\mathrm{buy}}(t)\right)$$

(10)

where ${\alpha }_t$ specifies the electricity rates at a given time period t, ${\beta }_t$ denotes the gas prices at the same time interval, and $P_{\mathrm{e},\mathrm{buy}}(t)$ indicates the volume of gas procured during period t.

(2) Rewards and penalties for stepped carbon transaction costs (See (9))

(3) Penalty costs for abandoning new energy sources $C_{\mathrm{WP}}$

$$C_{\mathrm{WP}}=\left\{\begin{array}{l}{C}_{\mathrm{DG},\mathrm{cut}}={\displaystyle {\displaystyle \sum }_{t=1}^T}{\epsilon }_{\mathrm{DG}}\left(P_{\mathrm{DG},\mathrm{pre}}(t)-P_{\mathrm{DG}}(t)\right)\\ C_{\mathrm{PV},\mathrm{cut}}={\displaystyle {\displaystyle \sum }_{t=1}^T}{\epsilon }_{\mathrm{PV}}\left(P_{\mathrm{PV},\mathrm{pre}}(t)-P_{\mathrm{PV}}(t)\right)\\ 0⩽P_{\mathrm{DG}}(t)⩽P_{\mathrm{DG}}^{\max }\\ 0⩽P_{\mathrm{PV}}(t)⩽P_{\mathrm{PV}}^{\max }\end{array}\right.$$

(11)

where the costs associated with the cessation of wind operations ($C_{\mathrm{DG},\mathrm{cut}}$) are influenced by ${\epsilon }_{\mathrm{DG}}$, a coefficient that penalizes the abandonment of wind turbines; predictions of wind turbine output at a specific time, t, are denoted as $P_{\mathrm{DG},\mathrm{pre}}(t)$; the costs tied to abandoning solar energy operations are represented by $C_{\mathrm{PV},\mathrm{cut}}$, while ${\epsilon }_{\mathrm{PV}}$ indicates the penalty coefficient for photovoltaic turbine abandonment; the forecasted power output of photovoltaic units during a time period t is symbolized as $P_{\mathrm{PV},\mathrm{pre}}(t)$; $P_{\mathrm{DG}}(t)$ and $P_{\mathrm{PV}}(t)$ are the actual power outputs of wind and photovoltaic systems, respectively, at time t; the maximum outputs for wind and photovoltaic systems are indicated by $P_{\mathrm{DG}}^{\max }$ and $P_{\mathrm{PV}}^{\max }$.

(4) System operation and maintenance costs $C_{\mathrm{M}}$

$$C_{\mathrm{M}}={\displaystyle \sum }_{i=1}^N{C}_i{P}_{i,t}\mathsf{\Delta }t$$

(12)

where maintenance and operational costs for equipment $i$ within the IEHS are referred to as $C_i$; the output of a specific $i$ at time t within the IEHS is expressed as $P_{i,t}$, and $\mathsf{\Delta }t$ represents the operational duration of the device.

3.2. Constraint Establishment

3.2.1. Power Balance Constraints

(1) Electrical power constraints

In this paper, the model assumes that electricity consumption is precisely balanced by the generation, without incorporating any transactions where IIES sells electricity back to the main grid.

$$P_{\mathrm{DG}}(t)+P_{\mathrm{PV}}(t)+P_{\mathrm{CHP},\mathrm{e}}(t)+P_{\mathrm{HFC},\mathrm{e}}(t)+P_{\mathrm{e},\mathrm{buy}}(t)=P_{\mathrm{e}\_\mathrm{Load}}(t)+P_{\mathrm{e},\mathrm{EL}}(t)+P_{\mathrm{in}}^{\mathrm{e}}(t)$$

(13)

where at time t, $P_{\mathrm{e}\_\mathrm{Load}}(t)$ represents the electrical demand; $P_{\mathrm{in}}^{\mathrm{e}}(t)$ denotes the power entering the electrical storage system; $P_{\mathrm{DG}}(t)$ and $P_{\mathrm{PV}}(t)$ are the wind and light power generation at time t, respectively.

(2) Thermal power balance constraints

$$\left\{\begin{array}{l}{\delta }_{1,\min }{P}_{\mathrm{hl}}(t)⩽P_{\mathrm{CHP},\mathrm{h}}(t)+P_{\mathrm{GB},\mathrm{h}}(t)+P_{\mathrm{HFC},\mathrm{h}}(t)-P_{\mathrm{h}\_\mathrm{Load}}(t)-P_{\mathrm{in}}^{\mathrm{h}}(t)⩽{\delta }_{1,\max }{P}_{\mathrm{hl}}(t)\\ P_{\mathrm{HFC},\mathrm{h}}(t)+P_{\mathrm{CHP},\mathrm{h}}(t)+P_{\mathrm{GB},\mathrm{h}}(t)=P_{\mathrm{h}\_\mathrm{Load}}(t)+P_{\mathrm{in}}^{\mathrm{h}}(t)\end{array}\right.$$

(14)

where ${\delta }_{1,\max }{P}_{\mathrm{hl}}(t)$ and ${\delta }_{1,\min }{P}_{\mathrm{hl}}(t)$ are the upper and lower limit ratios of thermal load adjustment; $P_{\mathrm{h}\_\mathrm{Load}}(t)$ is the thermal load in time period t; for the same time period t,$P_{\mathrm{in}}^{\mathrm{h}}(t)$ indicates the energy input into the thermal storage, while $P_{\mathrm{GB},\mathrm{h}}(t)$ reflects the thermal energy produced by the GB system.

(3) In the context of gas power systems

MR synthetic methane fulfills part of the gas demand, complemented by a natural gas feed. It is important to note that this analysis excludes the commercial transactions of IES gas with the superior gas network.

$$P_{\mathrm{g},\mathrm{buy}}(t)+P_{\mathrm{MR},\mathrm{g}}(t)=P_{\mathrm{g}\_\mathrm{Load}}(t)+P_{\mathrm{in}}^{\mathrm{g}}(t)+P_{\mathrm{g},\mathrm{CHP}}(t)+P_{\mathrm{g},\mathrm{GB}}(t)$$

(15)

where at any given time t, $P_{\mathrm{g}\_\mathrm{Load}}(t)$ denotes the gas demand, while $P_{\mathrm{in}}^{\mathrm{g}}(t)$ represents the energy channeled into natural gas reserves.

(4) In the context of hydrogen power systems

$$P_{\mathrm{EL},{\mathrm{H}}_2}(t)=P_{{\mathrm{H}}_2,\mathrm{MR}}(t)+P_{{\mathrm{H}}_2,\mathrm{HFC}}(t)+P_{\mathrm{in}}^{{\mathrm{H}}_2}(t)$$

(16)

where the energy directed towards hydrogen storage at time t is symbolized by $P_{\mathrm{in}}^{{\mathrm{H}}_2}(t)$.

3.2.2. Balancing Constraints across Segments

(1) For CHP, EL, MR, HFC, and wind PV operating constraints, see Equations (1)–(4) and (9)

(2) GB Operational Constraints

$$\left\{\begin{array}{l}{P}_{\mathrm{GB},\mathrm{h}}(t)={\eta }_{\mathrm{GB}}{P}_{\mathrm{g},\mathrm{GB}}(t)\\ P_{\mathrm{g},\mathrm{GB}}^{\min }⩽P_{\mathrm{g},\mathrm{GB}}(t)⩽P_{\mathrm{g},\mathrm{GB}}^{\max }\\ \mathsf{\Delta }{P}_{\mathrm{g},\mathrm{mB}}^{\min }⩽P_{\mathrm{g},\mathrm{GB}}(t+1)-P_{\mathrm{g},\mathrm{GB}}(t)⩽\mathsf{\Delta }{P}_{\mathrm{g},\mathrm{GB}}^{\max }\end{array}\right.$$

(17)

where ${\eta }_{\mathrm{GB}}$ represents the efficiency of energy transformation in the GB; at time t, $P_{\mathrm{g},\mathrm{GB}}(t)$ quantifies the energy supplied to the GB; the parameters $P_{\mathrm{g},\mathrm{GB}}^{\max }$ and $P_{\mathrm{g},\mathrm{GB}}^{\min }$ delineate the maximum and minimum permissible power inputs for the GB; $\mathsf{\Delta }{P}_{\mathrm{g},\mathrm{GB}}^{\max }$ and $\mathsf{\Delta }{P}_{\mathrm{g},\mathrm{mB}}^{\min }$ establish the maximum and minimum rates at which this power input can increase.

3.2.3. Energy Storage Operational Constraints

The study also incorporates a unified model that encapsulates electric, thermal, gas, and hydrogen energy storage systems.

$$\left\{\begin{array}{l}{S}_m(t)=(1-\epsilon )S_m(t-1)+{\eta }_{m,\mathrm{in}}{P}_{m,\mathrm{in}}(t)-\frac{P_{m,\mathrm{out}}(t)}{{\eta }_{m,\mathrm{out}}}\\ S_m(t)=S_m(t-1)+\frac{P_{out,m}(t)}{P_m^{\mathrm{cap}}}\\ S_m^{\min }⩽S_m(t)⩽S_m^{\max }\\ 0⩽P_{m,\mathrm{in}}(t)⩽B_m^{\mathrm{in}}(t)P_{m,\mathrm{in}}^{\max }\\ 0⩽P_{m,\mathrm{out}}(t)⩽B_m^{\mathrm{out}}(t)P_{m,\mathrm{out}}^{\max }\\ S_m(0)=S_m\left(T\right)\\ S_m(1)=S_m\left(T\right)\\ 0⩽B_m^{\mathrm{in}}(t)+B_m^{\mathrm{out}}(t)⩽1\end{array}\right.$$

(18)

where for the m-type energy storage device during a specific time period t, $P_{m,\mathrm{in}}(t)$ and $P_{m,\mathrm{out}}(t)$ denote the power inputs during charging and outputs during discharging, respectively. The binary variables $B_m^{\mathrm{in}}(t)$ and $B_m^{\mathrm{out}}(t)$ indicate the device’s state of operation: charging ($B_m^{\mathrm{in}}(t)$= 1, $B_m^{\mathrm{out}}(t)$ = 0) or discharging ($B_m^{\mathrm{in}}(t)$ = 0, $B_m^{\mathrm{out}}(t)$ = 1). The peak capacities for charging and discharging are captured by $P_{m,\mathrm{in}}^{\max }$ and $P_{m,\mathrm{out}}^{\max }$. The output power from the m-type device for the given period is recorded as $P_{out,m}(t)$, whereas $S_m(t)$ reflects its storage capacity. The rated maximum capacity of the device is termed $P_m^{\mathrm{cap}}$. The efficiencies with which the device charges and discharges are represented by ${\eta }_{m,\mathrm{in}}$ and ${\eta }_{m,\mathrm{out}}$, respectively. Additionally, $S_m^{\max }$ and $S_m^{\min }$ define the maximum and minimum storage capacities permissible for the device.

3.3. Model Solution

This paper develops an IEHS low-carbon economic dispatch model that incorporates a refined P2G two-stage operation with adjustable CHP and HFC thermoelectric ratios. While it operates as a single-objective optimization challenge under fully cooperative conditions, it transitions into a multi-objective optimization quandary when considering partially cooperative and non-cooperative scenarios. The model incorporates intricate constraints and employs the Bacterial Foraging Optimization Algorithm (BFOA) for resolution. This algorithm outshines traditional methods due to its bio-heuristic nature, its tendency for stochastic global searches, and its sensitivity to parameter adjustments. Traditional algorithms often struggle to maintain a balance between global and local search capabilities, which can diminish algorithmic diversity and convergence efficacy in later iterations. Therefore, BFOA is chosen for its superior performance in managing these challenges, as discussed in the literature [28]. The process of solving the model is shown in Figure 7.

4. Calculus Analysis

4.1. Algorithm Parameterization

To assess the efficacy of the proposed model, optimization of cycle operations is conducted, ensuring compliance with diverse 24-h load requirements, with operations broken down into hourly intervals. The model utilizes forecasts for wind, solar, electric, thermal, and gas demands, along with operational parameters for each segment as cited in [11]. Figure 8 displays the projected curves for these loads. A daily carbon trading volume limit is set at 4000 kg. Should this threshold be exceeded, the carbon trading price growth rate will see a 25% increment, with the baseline price of carbon trading rising by ¥0.25 per kg. Additionally, reward coefficients are set at λ = 0.2 and the carbon trading price growth rate at α = 0.25. Penalties for discarding wind-generated power are calculated at ¥0.2 per kWh; similarly, penalties for unused solar power also stand at ¥0.2 per kWh.

This study meticulously considers the impact of variable time-of-use tariffs on the system’s performance. By analyzing the fluctuations in tariffs across different periods, the model aims to minimize system costs, enhance the efficiency of load dispatch, and devise an energy storage system that mitigates discrepancies between load demands and tariff rates. Additionally, it facilitates the development of a versatile operational strategy for the system. The time-of-day tariff segments and prices are shown in

Table 1. Time-sharing tariffs and natural gas prices.

Program	Timeframe	Numerical
Electricity price /[¥/(kWh)] [11]	22:00–next day 7:00	0.38
	7:00–11:00, 14:00–18:00	0.54
	11:00–14:00, 18:00–22:00	1.10
Gas price/(¥/m3)	00:00–24:00	3.50

.

In this paper, we model P2G-HFC-IEHS and optimize the operating parameters of various devices. By optimizing the device parameters, the model promotes more sustainable energy practices, supports grid stability, and facilitates the transition to a greener, more resilient energy infrastructure. Device specifications are detailed in

Table 2. Energy storage parameters.

Equipment	Capacity/kW	Capacity Upper/Lower Limit Constraints/%	Climb Constraints/%
Electricity Storage	450	90/10	20
Heat storage	500	90/10	20
Gas storage	300	90/10	20
Hydrogen storage	200	90/10	20

,

Table 3. Equipment parameters.

Equipment	Capacity/kW	Energy Conversion Efficiency [11]/%	Climb Constraints/%
CHP	800	35(Q-P)	20
		45(Q-H)	20
HFC	600	50(Q-P)	20
		42(Thermal efficiency)	20
GB	500	95	20
EL	500	87	20
MR	250	60	20

and

Table 4. Actual carbon emission model parameters.

a1	b1	c1	a2	b2	c2
36	−0.38	0.0034	3	−0.04	0.001

.

4.2. Scene Setting

To assess the effectiveness of the proposed IEHS model, six different operational models have been established for a comparative evaluation. Each model is described as follows:

Model 1: Fixed thermoelectric ratios for CHP and HFCs are utilized within the IEHS, without the capability of adjustment. This model excludes the application of both the traditional and two-stage P2G processes as well as any form of carbon trading mechanisms, including the traditional and ladder-based reward and punishment systems.

Model 2: Excluding CHP from the IEHS, this configuration allows for adjustable thermoelectric ratios in HFCs and includes the traditional P2G process but omits the two-stage P2G and the ladder-based reward and punishment carbon trading mechanisms.

Model 3: This variant excludes CHP and incorporates an adjustable heat-to-electricity ratio for HFCs, the two-stage P2G process, and the ladder-based reward and punishment carbon trading mechanism.

Model 4: Without CHP integration, this model allows for an adjustable thermoelectric ratio in HFCs and includes both the two-stage P2G process and the traditional carbon trading mechanism but does not consider the ladder-based system.

Model 5: This setup also excludes CHP and features adjustable thermoelectric ratios for HFCs, integrating the two-stage P2G process alongside the ladder-based reward and punishment carbon trading mechanism.

Model 6: Including CHP, this model in IEHS permits adjustable thermoelectric ratios for HFCs and incorporates both the two-stage P2G process and the ladder-based incentive and punishment carbon trading mechanism.

4.3. Comparative Analysis of Optimization Results of Different Models of the Proposed IEHS Model

4.3.1. Refinement of P2G Two-Phase Operational Benefit Analysis

This work advances the traditional P2G by introducing a two-stage operational approach, capitalizing on the enhanced efficiency of this method. Details regarding this operational mode have been thoroughly discussed earlier; thus, further elaboration here is unnecessary. Consequently, the analysis establishes three distinct comparison scenarios: Mode 1, Mode 2, and Mode 3. Each mode undergoes a detailed comparative analysis based on various economic and environmental metrics such as the costs associated with electricity and gas procurement, wind and solar energy curtailment, carbon emissions, carbon trading expenses, and the overall cost implications. The comparison of the three modes of operation is shown in

Table 5. Enhanced analysis contrasts the advantages derived from the initial and subsequent stages of the P2G process.

Parameter	Parameter Value [11]
	Models 1	Models 2	Models 3
Purchased power cost/¥	1963.2	1758	1056.2
Purchased gas cost/¥	12,426.7	11,862.9	12,038.6
Abandoned WI cost/¥	490.6	132.4	0
Abandoned PV cost/¥	387.3	136.2	0
Carbon emission/kg	24,712	23,835	23,298
System O&M cost/¥	2136.5	2365.6	2453.8
Total cost/¥	17,404.3	16,255.1	15,548.6

.

From the data in the table, it is evident that Mode 3 offers the lowest total operating costs, achieving reductions of ¥1855.7 and ¥706.5 compared to modes 1 and 2, respectively. Furthermore, it significantly lowers carbon emissions by 1414 kg and 537 kg compared to the aforementioned modes. In Mode 1, the non-synchronous output peaks of wind energy at night lead to considerable wind waste. Similarly, the variability in solar power generation often surpasses system regulation capabilities, resulting in excess generation being discarded. Consequently, this mode relies heavily on purchasing power and gas from higher levels, incurring the highest operational costs. Mode 2 introduces P2G technology, using electrolysis-derived hydrogen to synthesize natural gas through the MR, which is then used to meet gas demands or stored during surplus periods of wind and solar generation. This approach utilizes surplus electricity more effectively, thereby decreasing the need for higher-level gas purchases and cutting down on electricity procurement costs. Mode 3, building on the framework established by Mode 2, implements an enhanced two-stage P2G process. Although MR facilitates the conversion of hydrogen to natural gas, which initially absorbs some CO₂, the subsequent utilization of this gas in CHP and GB systems releases CO₂ again, posing challenges to achieving carbon neutrality goals. To address this, Mode 3 prioritizes the use of hydrogen in high-efficiency HFC for cogeneration, minimizing energy losses and operating without carbon emissions during peak performance. This adjustment not only contributes to carbon emission reductions but also enhances operational efficiency by storing any surplus hydrogen.

Figure 9 presents varied forecasts for wind power PV consumption across different modes. Mode 1 exhibits the highest level of wind abandonment and the least efficient wind power utilization. This inefficiency stems from the wind turbines’ high nocturnal output coupled with minimal load demand, leading to a pronounced issue of both wind and light abandonment. Conversely, Mode 2 demonstrates an enhancement in the abandonment rates of wind and light by incorporating standard P2G processes. During the dispatch cycle in this mode, the cumulative wind abandonment totals 1021.2 kW, while light abandonment reaches 151.9 kW. This reduction is attributed to P2G systems utilizing excess electricity for hydrogen production via electrolysis, subsequently used in HFCs.

4.3.2. Analysis of Carbon Trading Mechanisms for Incentives and Disincentives

This study examines the efficacy of a proposed reward–penalty carbon trading system through empirical analysis employing three distinct scenarios: Scenario 3, Scenario 4, and Scenario 5. These scenarios facilitate an examination of carbon emissions and operational costs arising from different carbon trading models. The analysis encompasses the expenses associated with sufficient electricity supply, natural gas purchases, and the costs incurred from the curtailment of wind and solar power. Additionally, the total cost of each program is compared in

Table 6. Comparison of the benefits of carbon trading mechanisms considering a ladder of rewards and penalties.

Parameter	Parameter Value [11]
	Models 3	Models 4	Models 5
Purchased power cost/¥	1056.2	837.2	535.8
Purchased gas cost/¥	12,038.6	13,963.1	14,316.6
Abandoned WI cost/¥	0	0	0
Abandoned PV cost/¥	0	0	0
Carbon emission/kg	23,298	20,786	18,983
Carbon transaction costs/¥	0	−1983.6	−2957.2
System O&M cost/¥	2453.8	2556.9	2637.2
Total cost/¥	15,548.6	15,373.3	15,917

.

Models 3, 4, and 5 were analyzed to assess their effects on carbon emissions, the costs of carbon trading, and overall expenses. Model 3, which lacks a carbon trading scheme, focuses solely on minimizing energy-related costs. Consequently, it favors cheaper natural gas despite its higher carbon footprint, leading to increased emissions. Conversely, Model 4 integrates a graduated carbon trading system, where carbon prices escalate with higher emissions. This setup encourages the optimization of unit outputs for reduced carbon emissions, and the sale of unused carbon allowances offsets the costs associated with higher carbon prices. As a result, both Models 4 and 5 exhibit significant reductions in emissions and a rise in both natural gas expenditures and overall operational costs. Specifically, Model 3’s emissions exceed those of Model 4 by 2512 kg, marking a 10.9% reduction. Model 5 introduces a reward–penalty carbon trading scheme that further lowers emissions by 1803 kg compared to Model 4, though it increases total operational costs by ¥543.7. When compared to Model 3, Model 5 reduces emissions by 4315 kg (18.5%) but raises total costs by ¥368.4. The reward–penalty system not only effectively controls emissions but also minimizes economic expenditures.

Figure 10 illustrates that positive carbon transaction costs are unaffected by variations in the reward coefficient; however, if these costs are negative, an increase in the reward coefficient accelerates their reduction, thereby decreasing overall system carbon emissions more rapidly. As the reward coefficient λ increases, the decline in carbon transaction costs becomes more pronounced. When these costs fall below zero, energy supply companies receive governmental incentives, enhancing the system’s profitability. A carbon trading price exceeding ¥0.4/kg makes the reward coefficient significantly influential. If the system’s carbon emissions are lower than the government’s free carbon emission quotas, an increasing λ markedly reduces carbon transaction costs, thus diminishing the system’s carbon emissions and enabling more substantial governmental subsidies.

Data from Figure 11 reveal that carbon trading prices ranging from ¥0.3 to ¥0.4/kg exert a minimal impact on gas purchase costs. Nevertheless, within the ¥0.4 to ¥0.44/kg bracket, as carbon emission restrictions intensify, the influence on gas purchase costs becomes considerable, escalating the system’s total cost. Beyond ¥0.44/kg, reaching the operational peak of the CHP unit means further increases in carbon emissions do not affect gas purchase costs. At this stage, both the system’s operating costs and carbon trading costs stabilize. Thus, considering the impact of carbon trading prices is crucial in formulating energy policies and carbon emission regulations to ensure a balance between economic efficiency and environmental sustainability.

4.3.3. CHP and HFC Adjustable Thermoelectric Ratio Operation Analysis

To assess the benefits of the proposed adjustable thermoelectric ratio in CHP and HFC systems, this study delineates two distinct operational modes, namely Mode 5 and Mode 6. Analysis of carbon emissions, along with costs associated with power and gas purchases, serves to substantiate the superiority of the adjustable ratio. The operational specifics of these modes are outlined in

Table 7. Comparison of the benefits of different heat-to-power ratios under different models.

Parameter	Parameter Value [11]
	Models 5	Models 6
Purchased power cost/¥	535.8	0
Purchased gas cost/¥	14,316.6	14,821.6
Abandoned WI cost/¥	0	0
Abandoned PV cost/¥	0	0
Carbon emission/kg	18,983	18,230
Carbon transaction costs/¥	−1572.6 2556.9	−2189.3 2396.7
System O&M cost/¥	15,917	15,029

.

Table 7 reveals that the implementation of adjustable thermoelectric ratios in CHP and HFC systems leads to significant economic and environmental benefits. Unlike Modes 6 and 5, Mode 7 eliminates the need to purchase electricity from the main grid, saving 535.8 yuan. Although gas expenses increase by ¥505, the overall energy expenditure decreases by ¥32.8. Additionally, carbon emissions dropped by 753 kg, reflecting a 3.8% reduction. The total cost also diminishes by ¥881, mirroring the same percentage decrease. This improvement stems from the adaptable thermoelectric ratios, which prevent the excess production of heat during increased electrical output, unlike in traditional fixed-ratio systems. Typically, excess heat would result in energy waste due to heat abandonment when supply surpasses demand. Furthermore, in Mode 7, when the CHP load ratio surpasses its natural level, energy costs rise minimally due to the system’s flexibility in adjusting the power-to-heat ratios, enhancing efficiency, particularly during off-peak hours from 21:00 to 8:00. This period witnesses substantial wind electricity input and a high demand for heat, allowing for optimized operation of CHP and HFC units at higher heat-to-power ratios, thus better aligning the system’s thermal and electrical outputs.

During the hours of 8:00–11:00 and 17:00–21:00, which are characterized by high electricity demand and low heat demand, heat production is mainly facilitated by GBs and a limited number of CHP units. Conversely, from 11:00 to 17:00, the demand for electricity peaks, resulting in the lowest heat-to-electricity production ratio.

Analysis of Figure 12 reveals that the minimum heat-to-electricity ratio occurs between 10:00 and 17:00. During this interval, the demand for thermal load by the Power-to-Gas Hydrogen Fuel Cell-Integrated Energy System (P2G-HFC-IES) diminishes, leading to a reduction in heat output from the HFC, GB, and CHP units. This adjustment in output is attributed to the ability of the HFC and CHP units, which operate under an adjustable heat-to-electricity ratio mode, to modulate their heat and power output in response to the system’s load requirements. Such flexibility facilitates the optimal allocation of resources across the system, thereby minimizing total operational costs.

4.4. Analysis of the Overall Optimization Results of the Proposed IEHS Model

4.4.1. Analysis of Gas and Hydrogen Optimization Results

Figure 13 and Figure 14 illustrate that under the incentive-based carbon trading framework, IEHS optimizes the dual-stage operation of the P2G system. Initially, surplus electricity from wind and PV sources drives the EL process to generate hydrogen. This hydrogen is first utilized by the HFC for cogeneration. Once the HFC has reached its maximum generation capacity, any surplus hydrogen is directed towards the MR and for hydrogen storage, adhering to the energy limits set by IEHS. During the hours of 0:00–10:00 and 22:00–24:00, when wind turbines are most productive and hydrogen production exceeds demand, the system leverages the flexibility of the ML to adjust electrical output according to the high wind power output, ensuring no waste of wind energy. Prior to peak wind output, the wind-generated electricity is fully utilized to minimize waste. In the later stage, any excess hydrogen produced is channeled towards meeting gas demands after the electricity needs are met. During these times, the CHP unit operates at a lower capacity due to a smaller electricity load, resulting in minimal gas storage and promoting the efficient use of the energy gradient to enhance renewable energy consumption.

4.4.2. Analysis of Electrical and Thermal Optimization Results

Figure 15 and Figure 16 illustrate the refinement of the two-stage P2G operation within the reward and punishment carbon trading framework. This study emphasizes the interplay between energy generation systems under flexible CHP and HFC modes, which optimize equipment performance. During the early hours (0:00–10:00) and late evening (19:00–24:00), wind turbines reach their production peaks while the demand for electricity remains comparatively low. This discrepancy often results in surplus energy. To address this, surplus electricity primarily fuels the P2G system for hydrogen production via two-stage electrolysis, supporting both HFC and MR operations. Conversely, between 11:00 and 16:00, when solar energy production peaks and the system’s thermal demand is at its minimum, solar power substitutes for CHP generation. Constraints within the system ensure that HFC operates at full capacity consistently, thus minimizing energy gradient losses and significantly reducing carbon emissions. Under the demand of thermal load, due to the influence of the adjustable CHP–HFC thermoelectric ratio, the thermal energy of the fuel cell is always absorbed at full load. Coupled with the storage of excess thermal energy, the GB works for a very short period of time, which greatly improves the efficiency of energy utilization.

5. Conclusions

To expedite the achievement of the dual-carbon objective and enhance the transition towards a low-carbon framework, this study finetunes the two-phase operational mode of P2G within the IEHS framework. It incorporates a carbon trading scheme that employs incentives and penalties, examines flexible heat and power ratios in CHP and HFC systems, and establishes a minimal objective function governed by IEHS constraints to optimize economic efficiency across the entire network. Employing BFOA to solve the model, insights are derived from examining six different operational modes alongside arithmetic exemplifications.

(1) Modifying the conventional P2G process by incorporating a dual-phase HFC strategy can significantly mitigate the issue of abandoning wind and solar energies. This adaptation enhances the efficiency of harnessing wind and solar power, achieving a utilization rate exceeding 90%. Furthermore, it facilitates a 5.71% reduction in carbon emissions and minimizes losses in energy gradients, thus enhancing overall energy efficiency.

(2) Incorporating a dynamic rewards and penalties carbon trading scheme into the IEHS could potentially reduce the operating costs of this system. The BFOA was employed to address the model designed for this purpose. Comparative analysis of various carbon trading frameworks revealed that setting suitable coefficients for rewards and punishments can align the carbon prices across different systems with the cost variations observed in the economic dispatch system. Within a specified range, as the carbon price fluctuates, a decrease in the system operating costs is observed, aligning with the goals of the integrated energy system’s participation in the carbon market.

(3) In the adjustable thermoelectric ratio mode, a thermoelectric ratio below 2.1% reduces the CHP system’s contribution to energy supply, consequently diminishing carbon emissions. Conversely, maintaining a thermoelectric ratio above 0.5% and inversely tuning the thermoelectric load alongside the CHP ratio enhances unit efficiency and satisfies integrated load demands more effectively. This approach supports an increase in CHP output while minimizing energy costs. The current study does not encompass refined modeling of renewable energy tailored to fluctuating demand scenarios, nor does it address carbon management for diverse operational demands. Moreover, the implications of integrating a carbon capture system within the IEHS remain unexplored, earmarking it as a primary focus for subsequent research.