Considering the Tiered Low-Carbon Optimal Dispatching of Multi-Integrated Energy Microgrid with P2G-CCS

Abstract

The paper addresses the overlooked interaction between power-to-gas (P2G) devices and carbon capture and storage (CCS) equipment, along with the stepwise carbon trading mechanism in the context of current multi-park integrated energy microgrids (IEMGs). Additionally, it covers the economic and coordinated low-carbon operation issues in multi-park IEMGs under the carbon trading system. It proposes a multi-park IEMG low-carbon operation strategy based on the synchronous Alternating Direction Method of Multipliers (ADMM) algorithm. The algorithm first enables the distribution of cost relationships among multi-park IEMGs. Then, using a method that combines a CCS device with a P2G unit in line with the tiered carbon trading scheme, it expands on the model of single IEMGs managing thermal, electrical, and refrigeration energy. Finally, the comparison of simulation cases proves that the proposed strategy significantly reduces the external energy dependence while keeping the total cost of the users unchanged, and the cost of interaction with the external grid is reduced by 56.64%, the gas cost is reduced by 27.78%, and the carbon emission cost is reduced by 29.54% by joining the stepped carbon trading mechanism.

1. Introduction

1.1. Background and Motivation

In the wake of “dual carbon” objectives, the restructuring of high carbon energy consumption becomes unavoidable [1,2,3]. As a relatively compact, integrated micro-energy interconnection system, IEMG leverages the synergistic functioning of multiple energy forms and tailors the use of renewable energy (RE) to local conditions, thereby achieving efficient and sustainable energy development. With the evolution of IEMG systems, networking micro-energy grids within a region can enhance the reliability and economy of the area’s overall energy use. The efficient collaborative operation of park IEMG systems under an energy-sharing mechanism has become a key research topic.

The resource allocation capacity of a single-park IEMG system is limited, facing challenges such as the randomness of renewable energy output, poor electrical energy quality, and low energy consumption rates [4,5]. However, through collaborative scheduling between multiple parks, energy sharing can generate synergistic effects and achieve optimal overall benefits [6]. The alliance mechanism across multiple parks enables energy sharing and interaction within the alliance, enhancing energy utilization efficiency and supply levels.

IEMGs have achieved organic coordination and optimization in power generation, transmission, conversion, consumption, and trading of various kinds of energy. However, the complexities arising from multi-energy flow coupling and multiple temporal scales make it difficult to manage. Therefore, current research primarily concentrates on optimal operation strategies for singular energy park systems, while less attention has been paid to the optimal dispatching problems of multi-park comprehensive energy systems.

1.2. Literature Review

Currently, there are mainly two approaches for the optimal dispatch of multi-energy integrated systems: centralized methods and decentralized methods [7,8]. The centralized fashion facilitates the coordinated control of the entire system, but faces challenges such as high communication requirements, heavy computational load for the central controller, information security sharing, and topology construction lacking flexibility. On the other hand, the decentralized optimization methods only require essential information from each participant agent and could solve complicated, large-scale problems via autonomous action from the agents, effectively compensating for the centralized approach’s deficits [9].

Many studies have implemented decentralized methods to tackle centralized economic dispatch issues. Among a variety of decentralized approaches, the Alternating Direction Method of Multipliers (ADMM) exhibits advantageous properties such as simplicity, superior convergence, and flexible reformulation for solving large-scale problems. It also ensures the information security of the participants. Consequently, it has been widely employed in recent years. References [10,11] utilize the ADMM algorithm to address the joint dispatch issue of microgrid clusters, mitigating communication loads and safeguarding user security simultaneously. References [12,13] leverage the ADMM algorithm to solve the carbon emission economic dispatch issue for various energy hubs. References [14,15,16] instantiate the ADMM framework, allowing upper and lower-level entities to interact via energy trading strategies, culminating in cooperative operation. Moreover, in the actual resolution of ADMM, while the iterative step sizes affect the convergence speed and not the convergence precision, a paucity of literature considers dynamically adjusting step sizes to enhance convergence speed.

In addition, as a low-carbon technology, carbon capture and storage (CCS) plays a pivotal role in transforming high-carbon emission devices for low-carbon operation, significantly contributing to the greening of energy systems. Studies [17,18] integrated power-to-gas (P2G) and CCS technologies, establishing a coupling of CO₂ capture and utilization processes. The authors of [19] created a novel approach for virtual power plant dispatch strategy by coupling CCS, P2G, and electric vehicles. Another study [20] proposed a coal-fired unit’s low-carbon and economic operation using an amalgamation of CCS and the organic Rankine cycle; and lastly, [21] demonstrated energy cascade utility through the compound power generation system, CCS, and the use of liquefied natural gas (LNG) cold energy. However, such literature related to the application of CCS technology is predominantly focused on coupling with other devices, without considering the perspective of multi-energy integrated systems.

In conclusion, this paper presents a tiered low-carbon optimization dispatch strategy for multi-park IEMGs incorporating P2G and CCS, grounded on the synchronized ADMM algorithm. Through the application of the revised synchronized ADMM and by taking into account the impact factors for carbon emissions, it successfully addresses the challenge of economic and low-carbon cooperative optimization. Significantly, it expedited convergence speed by dynamically adjusting iterative step sizes.

1.3. Contributions

The main contributions of this paper are as follows:

(1)

Development of a strategy founded on the synchronous ADMM algorithm: Proposing an innovative low-carbon operation approach for multi-park IEMGs, utilizing the synchronous ADMM algorithm to efficiently distribute costs amongst various IEMGs, and optimizing operations within the carbon trading framework.

(2)

Integration of CCS and P2G technologies: The research incorporates a CCS apparatus with the P2G system in a solitary electric-thermal-cooling IEMG. By exploiting the P2G protocol, it maximizes the utilization of captured CO₂ for natural gas synthesis, amplifying low-carbon operationality.

(3)

Implementation of a tiered carbon trading mechanism: Proposing the use of a tiered carbon trading mechanism to control carbon emissions, with the intent of providing economic incentives for low carbon emissions during the operation of IEMGs.

(4)

Dynamic adjustment of iterative steps within the ADMM algorithm: An innovative aspect of the research is the dynamic adjustment of iterative steps in the ADMM algorithm. The aim is to accelerate the convergence rate without compromising accuracy, which constitutes a unique methodology in the context of multiple IEMG systems.

2. Architecture of the Multi-Park IEMG System

Each IEMG mainly encompasses Combined Cooling, Heating and Power (CCHP) units, P2G units, CCS units, electric boilers, electric cooling units, energy storages, heat storages, and electric storages, controllable loads, and set loads like electricity, heating, and gas. The infrastructure of a solitary IEMG is illustrated in Figure 1 beneath. Electrical interaction can transpire among neighboring IEMGs through connecting lines, as demonstrated in Figure 2 below. A study [22] indicated high losses in heat pipes; therefore, heat sharing amidst communities is not considered.

2.1. CCHP Model

The CCHP unit can output cooling, heating, and electrical energy according to different demands, and its mathematical expression can be described by the following formula:

$$P_{\mathrm{CCHP},\mathrm{t}}=F_{\mathrm{g},\mathrm{t}}{L}_{\mathrm{H}}{\eta }_{CCHP}$$

(1)

$$H_{\mathrm{CCHP},\mathrm{t}}=P_{\mathrm{CCHP},\mathrm{t}}\frac{1-{\eta }_{\mathrm{CCHP}}-{\eta }_{\mathrm{L}}}{{\eta }_{\mathrm{CCHP}}}$$

(2)

$$H_{\mathrm{CCHP},\mathrm{H},\mathrm{t}}=H_{\mathrm{CCHP},\mathrm{t}}{\eta }_{\mathrm{He}}$$

(3)

$$C_{\mathrm{CCHP},\mathrm{t}}=H_{\mathrm{CCHP},\mathrm{t}}{\eta }_{\mathrm{HE}}CO{P}_{\mathrm{AC}}$$

(4)

wherein $P_{\mathrm{CCHP},\mathrm{t}}$ represents the output electrical power of the micro CCHP, ${\eta }_{\mathrm{CCHP}}$ represents the power generation efficiency of the micro CCHP, and $F_{\mathrm{g},\mathrm{t}}$ represents the consumed amount of natural gas; $L_{\mathrm{H}}$ represents the calorific value of natural gas; $H_{\mathrm{CCHP},\mathrm{t}}$ represents the heat output of the micro CCHP, ${\eta }_{\mathrm{L}}$ represents the heat dissipation loss rate of the micro CCHP. $H_{\mathrm{CCHP},\mathrm{H},\mathrm{t}}$ represents the amount of waste heat recovered by the waste heat recovery boiler, ${\eta }_{\mathrm{He}}$ represents the waste heat recovery efficiency of the waste heat boiler equipment. $C_{\mathrm{CCHP},\mathrm{t}}$ represents the cooling capacity of the absorption refrigerator (AC) in the CCHP unit, and $CO{P}_{\mathrm{AC}}$ represents the energy efficiency ratio of the AC in the CCHP unit.

2.2. Electric Heating Boiler Unit Model

The presence of an electric boiler (EB) ensures the heating supply for the park, and its expression is shown in the following formula:

$$H_{\mathrm{EB},t}={\eta }_{\mathrm{EB}}{f}_{\mathrm{EB},t}$$

(5)

$$P_{\min }^{\mathrm{EB}}\le P_{\mathrm{EB},t}\le P_{\max }^{\mathrm{EB}}$$

(6)

$$\Delta P_{\min }^{\mathrm{EB}}\le P_{\mathrm{EB},t}-P_{\mathrm{EB},t-1}\le \Delta P_{\max }^{\mathrm{EB}}$$

(7)

wherein ${\eta }_{\mathrm{EB}}$ represents the heat production efficiency of the EB, $f_{\mathrm{EB},t}$ represents the gas consumption required for the EB. $P_{\min }^{\mathrm{EB}}$ and $P_{\max }^{\mathrm{EB}}$ represent the upper and lower limits of the EB unit’s output, $\Delta P_{\min }^{\mathrm{EB}}$ and $\Delta P_{\max }^{\mathrm{EB}}$ represent the upper and lower limits of the ramping power of the electric boiler unit.

2.3. Constraints of Electrical Chillers

The cooling power of electrical chillers (EC) can be expressed by the following formula:

$$C_{\mathrm{EC},t}=CO{P}_{\mathrm{EC}}{P}_{\mathrm{EC},t}$$

(8)

wherein $P_{\mathrm{EC},t}$ represents the electrical power consumed by the EC, $CO{P}_{EC}$ represents the energy efficiency ratio of the EC, and $C_{EC,t}$ represents the electric cooling capacity of the EC.

2.4. Constraints of Electric Heating and Energy Storage

The models for electrical energy storage (EES) devices and thermal energy storage (TES) devices are as follows:

$$SO{C}_t=SO{C}_{t-1}+\left(\frac{{\eta }_{\mathrm{c}}+\frac{1}{{\eta }_{\mathrm{disc}}}}{2}{P}_{si,\mathrm{t}}+\frac{{\eta }_{\mathrm{c}}-\frac{1}{{\eta }_{\mathrm{disc}}}}{2}|P_{si,\mathrm{t}}|\right)$$

(9)

$$H_{\mathrm{t}}=\left(1-{\theta }^{\mathrm{TES}}\right)H_{\mathrm{t}-1}+\left(\frac{{\eta }_{\mathrm{h},\mathrm{c}}+\frac{1}{{\eta }_{\mathrm{h},\mathrm{disc}}}}{2}{P}_{\mathrm{TES},\mathrm{t}}+\frac{{\eta }_{\mathrm{h},\mathrm{c}}-\frac{1}{{\eta }_{\mathrm{h},\mathrm{disc}}}}{2}|P_{\mathrm{TES},\mathrm{t}}|\right)$$

(10)

$$SO{C}_{\min }\le SOC\left(t\right)\le SO{C}_{\max },H_{\min }\le H\left(t\right)\le H_{\max }$$

(11)

$$P_{si}^{\min }\le P_{si,\mathrm{t}}\le P_{si}^{\max },P_{\mathrm{TES}}^{\min }\le P_{\mathrm{TES},\mathrm{t}}\le P_{\mathrm{TES}}^{\max }$$

(12)

$$SOC(0)=SOC(24),H(0)=H(24)$$

(13)

wherein $P_{si}^{\max }$ and $P_{si}^{\min }$ represent the upper and lower limits of EES charging power, $P_{\mathrm{TES}}^{\min }$ and $P_{\mathrm{TES}}^{\max }$ represent the upper and lower limits of TES storage power, $P_{si,\mathrm{t}}$ is the charging/discharging power of EES at time $t$; ${\eta }_c$ and ${\eta }_{disc}$ are the charging/discharging efficiency of EES; ${\theta }^{\mathrm{TES}}$ denotes the thermal power loss parameter in the static state of thermal storage, ${\eta }_{\mathrm{h},\mathrm{c}}$ and ${\eta }_{\mathrm{h},\mathrm{disc}}$ are the storage efficiency of TES, $SO{C}_{\max }$ and $SO{C}_{\min }$ are the upper and lower limits of EES’s state of charge, $SOC\left(t\right)$ is the state of charge of EES at time $t$, $H_{\max }$ and $H_{\min }$ are the upper and lower limits of TES capacity, and $H_t$ is the thermal storage amount in TES at time $t$.

2.5. Model of CCS and P2G Coupling

While the micro CCHP outputs electrical power to meet the electrical load, it inevitably produces $\mathrm{C}{\mathrm{O}}_2$ to maximize carbon emission reduction and system revenue. This paper utilizes CCS to capture $\mathrm{C}{\mathrm{O}}_2$ by the micro CCHP, although it is not guaranteed that all of $\mathrm{C}{\mathrm{O}}_2$ can be absorbed, it can be maximized according to system conditions, and the captured $\mathrm{C}{\mathrm{O}}_2$ from CCHP is further supplied to the P2G unit as a raw material for synthesizing natural gas. The P2G unit generates hydrogen by electrolyzing water, which then reacts with $\mathrm{C}{\mathrm{O}}_2$ and ${\mathrm{O}}_2$ to produce CH₄; this can be supplied to the micro CCHP to continue generating electrical power, thus achieving the benefits of energy savings and emission reduction. The CCS and P2G coupling model is summarized as follows:

$$Q_{{\mathrm{CO}}_2,t}^{\mathrm{CCS}}={\eta }_{\mathrm{CCS}}{Q}_{{\mathrm{CO}}_2,t}^{\mathrm{CCHP}}$$

(14)

$$Q_{{\mathrm{CO}}_2,t}^{\mathrm{CCS}}=Q_{{\mathrm{CO}}_2,t}^{\mathrm{P}2\mathrm{G}}+Q_{{\mathrm{CO}}_2,t}^f$$

(15)

$$P_{{\mathrm{CO}}_2,t}^{\mathrm{CCS}}={\lambda }_{\mathrm{CCS}}{Q}_{{\mathrm{CO}}_2,t}^{\mathrm{CCS}}$$

(16)

$$P_{\mathrm{CCS},t}=P_{{\mathrm{CO}}_2,t}^{\mathrm{CCS}}+P_{f,t}^{\mathrm{CCS}}$$

(17)

$$F_{\mathrm{gas}}^{\mathrm{P}2\mathrm{G}}=\overline{\omega }\left(Q_{{\mathrm{CO}}_2,t}^{\mathrm{P}2\mathrm{G}}+Q_{{\mathrm{CO}}_2,t}^{\mathrm{GIRD}}\right)$$

(18)

$$P_{\mathrm{P}2\mathrm{G},t}=\beta Q_{{\mathrm{CO}}_2,t}^{\mathrm{P}2\mathrm{G}}$$

(19)

$$P_{e,\min }^{\mathrm{P}2\mathrm{G}}\le P_{\mathrm{P}2\mathrm{G},t}\le P_{e,\max }^{\mathrm{P}2\mathrm{G}}$$

(20)

$$\Delta P_{e,\min }^{\mathrm{P}2\mathrm{G}}\le P_{\mathrm{P}2\mathrm{G},t+1}-P_{\mathrm{P}2\mathrm{G},t}\le \Delta P_{e,\max }^{\mathrm{P}2\mathrm{G}}$$

(21)

wherein $Q_{{\mathrm{CO}}_2,t}^{\mathrm{CCHP}}$ represents the $\mathrm{C}{\mathrm{O}}_2$ emitted during the operation of the micro CCHP, ${\eta }_{\mathrm{CCS}}$ represents the efficiency value of CCS in capturing $\mathrm{C}{\mathrm{O}}_2$ under normal working conditions, $Q_{{\mathrm{CO}}_2,t}^{\mathrm{CCS}}$ represents the amount of $\mathrm{C}{\mathrm{O}}_2$ captured by CCS. Half of the $\mathrm{C}{\mathrm{O}}_2$ captured by CCS is stored as $Q_{{\mathrm{CO}}_2,t}^f$, $P_{f,t}^{\mathrm{CCS}}$ represents the electric power consumed for storing $Q_{{\mathrm{CO}}_2,t}^f$, and the other half is used to supply P2G for methane production $Q_{{\mathrm{CO}}_2,t}^{\mathrm{P}2\mathrm{G}}$.$P_{{\mathrm{CO}}_2,t}^{\mathrm{CCS}}$ represents the electric power consumed by the CCS device, ${\lambda }_{CCS}$ represents the capture efficiency; $\overline{\omega }$ represents the size of the balance coefficient, $\beta$ presents the efficiency of processing $\mathrm{C}{\mathrm{O}}_2$. $P_{e,\max }^{\mathrm{P}2\mathrm{G}}$ and $P_{e,\min }^{\mathrm{P}2\mathrm{G}}$ are the upper and lower limits of P2G output, $\Delta P_{e,\max }^{\mathrm{P}2\mathrm{G}}$ and $\Delta P_{e,\min }^{\mathrm{P}2\mathrm{G}}$ are the upper and lower limits of P2G ramping.

2.6. Overall Constraints

$$P_{\mathrm{gird},t}+P_{\mathrm{PV},\mathrm{cur},t}+P_{\mathrm{WT},\mathrm{cur},t}+P_{\mathrm{CCHP},t}+P_{ij,ex,t}=P_{si,t}+P_{\mathrm{load},t}+P_{\mathrm{P}2\mathrm{G},t}+P_{\mathrm{EB},t}+P_{\mathrm{CCS},t}$$

(22)

$$H_{\mathrm{GIRD},t}+H_{\mathrm{CCHP},\mathrm{H},t}+H_{\mathrm{EB},t}=H_{\mathrm{load},t}+H_t$$

(23)

$$Q_{\mathrm{GIRD},t}+F_{\mathrm{gas},t}^{\mathrm{P}2\mathrm{G}}=Q_{\mathrm{load},t}+F_{\mathrm{gas},t}$$

(24)

$$C_{\mathrm{CCHP},t}+C_{\mathrm{EC},t}=C_{\mathrm{load},t}$$

(25)

$$P_{\mathrm{GIRD}}^{\min }\le P_{\mathrm{gird},t}\le P_{\mathrm{GIRD}}^{\max }$$

(26)

$$P_{ex}^{\min }\le P_{ij,ex,t}\le P_{ex}^{\max }$$

(27)

$$P_{\mathrm{PV},e,t}+P_{\mathrm{PV},\mathrm{cur},t}=P_{\mathrm{PV},t}$$

(28)

$$P_{\mathrm{WT},e,t}+P_{\mathrm{WT},cur,t}=P_{\mathrm{WT},t}$$

(29)

$$P_{ij,ex,t}=-P_{ji,ex,t}$$

(30)

wherein $E_{gird,\mathrm{t}}$ ($E$=$P$) represents the electricity and gas exchange between the IEMG system and the main grid, $E_{load,t}$ ($E$ = $P$, $Q$, $H$, $C$) represents the electricity, carbon, heating, and cooling load of each IEMG; $P_{\mathrm{PV},\mathrm{cur},\mathrm{t}}$ and $P_{\mathrm{WT},\mathrm{cur},\mathrm{t}}$ represent the reducible output of wind and solar power; $E_{ij,ex,t}$ ($E$ = $P$) represents the electrical energy exchanged between IEMG$i$ and IEMG$j$. $P_{\mathrm{PV},e,t}$ and $P_{\mathrm{WT},e,t}$ represent the predicted output of wind and solar power; $P_{\mathrm{PV},t}$ and $P_{\mathrm{WT},t}$ represent the actual output of wind and solar power.

3. IEMG Objective Function and Solution Strategy

3.1. Optimization Objective Function for Operating Costs

$$F=f_1+f_2+f_3$$

(31)

$$f_1={\displaystyle \sum _{i=1}^N\left(\frac{C_{e,\mathrm{t}}^{buy}+C_{e,\mathrm{t}}^{sell}}{2}{E}_{e,i,\mathrm{t}}+\frac{C_{e,\mathrm{t}}^{buy}-C_{e,\mathrm{t}}^{sell}}{2}|E_{e,i,\mathrm{t}}|\right)\Delta T}$$

(32)

$$f_2={\displaystyle \sum _{i=1}^N\left({\gamma }_1{\displaystyle \sum \left|P_{ij,ex,\mathrm{t}}\right|}\right)}$$

(33)

$$f_3={\displaystyle \sum _{i=1}^N\left(C_{{\mathrm{CO}}_2}^{buy}{Q}_{\mathrm{gird},i,\mathrm{t}}^{{\mathrm{CO}}_2}\right)\Delta T}$$

(34)

wherein $N$ represents the number of IEMGs, and $F$ represents the cost objective function of the IEMG electric grid. Equation (33) refers to the cost of electricity interaction between interconnected IEMG, and Equation (34) pertains to the cost of purchasing $\mathrm{C}{\mathrm{O}}_2$. $C_{e,h,g,\mathrm{t}}^{buy}$ and $C_{e,h,g,\mathrm{t}}^{sell}$ represent the prices of buying and selling electricity, $E_{e,i,t}$ and $E_{ij,ex,t}$ ($E$ = $P$) indicate the size of the electricity interaction between an IEMG$i$ and adjacent IEMG, ${\gamma }_1$ is the unit price of electricity interaction with adjacent IEMGs, $Q_{\mathrm{gird},i,t}^{{\mathrm{CO}}_2}$ is the quantity of $\mathrm{C}{\mathrm{O}}_2$ purchasing, $C_{{\mathrm{CO}}_2}^{buy}$ is the unit price of purchases $\mathrm{C}{\mathrm{O}}_2$ from the main grid.

3.2. IEMG Optimized Chunking Solution

Considering the complexity of the equipment inside the IEMG, due to the excellent decomposition performance of the ADMM algorithm, the decomposed problem can be consistent with the original complex problem. Its model is as follows:

$$\begin{array}{l}\min {\displaystyle \sum _{i=1}^N{\displaystyle \sum _{t\in {\theta }_t}{f}_i\left(x_i\right)}}\\ s.t\left\{\begin{array}{l}{h}_i(x_i)=0\\ g_i(x_i)\ge 0\\ X_i=-X_j\\ X_i=-X_k\end{array}\right.\begin{array}{c}\hspace{0.33em}\hspace{0.33em}i\in N\end{array}\end{array}$$

(35)

wherein $f_i\left(x_i\right)$ denotes the decomposed sub-problem for solving the objective function of IEMG; $h_i(x_i)$ refers to the equality equation constraints contained in IEMG$i$, $g_i(x_i)$ represents the inequality equation constraints contained in IEMG$i$; $X_i$ indicates the interaction coupling variables between IEMG$i$ and interconnected IEMGs, $j$ and $k$ are the sets of interactive coupling variables for IEMG$i$ and its adjacent IEMGs, collectively referred to as $X_i=\left\{P_{ij},P_{ik}\right\}$, $P_{ij}$ and $P_{ik}$ represent the coupled electrical power.

3.3. Synchronous ADMM Distributed Solution

Firstly, establish the optimization problem for IEMG$i$ and microgrid $j$. The Lagrangian function corresponding to its objective function is denoted by $L_i\left(x_i,X_{Ki}^t,{\lambda }_i^t\right)$ and $L_i\left(x_j,X_{Kj}^t,{\lambda }_j^t\right)$, and through appropriate transformations, introduce the dual variable $X_i$ for $X_{Ki}$, and the dual variable $X_j$ for $X_{Kj}$, then convert it to the following:

$$L_i\left(x_i,X_{Ki}^t,{\lambda }_i^t\right)=f_i\left(x_i\right)+\frac{\rho }{2}{‖X_i-X_{Ki}^t+{\lambda }_i^t‖}_2^2$$

(36)

$$L_j\left(x_j,X_{Kj}^t,{\lambda }_j^t\right)=f_j\left(x_j\right)+\frac{\rho }{2}{‖X_j-X_{Kj}^t+{\lambda }_j^t‖}_2^2$$

(37)

Let IEMG$i$ be coupled with IEMG$j$, $k$, IEMG$j$ be coupled with IEMG$i$ and $k$, $X_{Ki}^t$ and $X_{Kj}^t$ be, respectively, IEMG$i$ and the fixed reference values of the $j$ and $t+1$ iterations; then, the mean value of the mutually connected interaction coupling variables IEMG$i$, $j$ can be obtained after the $t$ iteration, as shown in the following equation:

$$X_{Ki}^t=X_{Kj}^t=\frac{\left(X_i^t+X_j^t\right)}{2}$$

(38)

Once the optimization problems for each IEMG are defined, a distributed solution is implemented. The specific steps are as follows:

(1)

In the $t+1-\mathrm{th}$ iteration, IEMG$i$ and IEMG$j$ use parallel computing methods to calculate functions $L_i\left(x_i,X_{Ki}^t,{\lambda }_i^t\right)$ and $L_i\left(x_j,X_{Kj}^t,{\lambda }_j^t\right)$, finding the minimum decision variables contained within this area. Simultaneously, they can obtain the interaction coupling variables $X_i^{t+1}$ and $X_j^{t+1}$ for each IEMG system.

$$x_i^{t+1}=\arg \min L_i\left(x_i,X_{Ki}^t,{\lambda }_i^t\right)$$

(39)

$$x_j^{t+1}=\arg \min L_j\left(x_j,X_{Kj}^t,{\lambda }_j^t\right)$$

(40)

(2)

Determined by the coupling relationship between IEMG$i$ and IEMG$j$, $X_{Ki}^t$ and $X_{Kj}^t$ are concluded and implemented as parameters in the reference values for the subsequent iteration.

(3)

Update the dual variables within the IEMG:

$${\lambda }_i^{t+1}={\lambda }_i^t+\left(X_i^{t+1}-X_{Ki}^{t+1}\right)$$

(41)

$${\lambda }_j^{t+1}={\lambda }_j^t+\left(X_j^{t+1}-X_{Kj}^{t+1}\right)$$

(42)

(4)

When the following conditions are fulfilled, the ADMM algorithm terminates the iterations, indicating its convergence. If the conditions are not met, it continues with the assessment, looping the iteration.

$${‖X_i^t+X_j^t‖}_2^2\le \delta$$

(43)

4. Tiered Carbon Emissions Trading Model

The traditional carbon trading modality has inherent flaws in its pricing mechanism, particularly due to its static pricing and lack of sufficient constraints on carbon emissions. To impose further limits on carbon emissions, this paper introduces a tiered carbon trading pricing mechanism. The mechanism segments carbon prices based on the difference between the IEMG’s actual carbon emissions and its allocated carbon emissions quota. This approach compensates for the limitations of the traditional methodology. Additionally, the multidimensional energy IEMG can obtain a certain economic reward by selling extra quotas on the carbon market. The lower the carbon emissions, the larger the carbon interval corresponding to the difference between the quota and the actual emissions—the higher the sales price for the carbon quota, and thereby the higher the revenue generated. Conversely, a higher amount of carbon emissions would result in the opposite scenario.

On this basis, by considering the actual carbon emissions from the $i-\mathrm{th}$ IEMG and the size of the carbon emissions quota allocated gratuitously, it can ascertain the actual amount of carbon emission quotas for the IEMG to trade within the carbon marketplace:

$$\left\{\begin{array}{l}{E}_{\mathrm{v}.\mathrm{buy}}={\displaystyle \sum _{t=1}^{24}{\tau }_{\mathrm{b}\mathrm{u}\mathrm{y}}{P}_{\mathrm{buy}}^t+{\tau }_g{H}_{\mathrm{buy}}^t}\\ E_{\mathrm{v}.\mathrm{g}}={\displaystyle \sum _{t=1}^{24}{\tau }_{\mathrm{v}.\mathrm{g}}\left({\eta }_{\mathrm{CCHP}}{P}_{\mathrm{CCHP},t}+H_{\mathrm{CCHP},\mathrm{H},t}\right)-Q_{{\mathrm{CO}}_2,t}^{\mathrm{CCS}}}\\ E_{P,i}=E_{\mathrm{v}.\mathrm{b}\mathrm{u}\mathrm{y}}+E_{\mathrm{v}.\mathrm{g}}\\ E_{R,i}=E_{P,i}-E_{C,i}\end{array}\right.$$

(44)

wherein $E_{C,i}$ presents the actual carbon emission trading amount of the $i-\mathrm{th}$ IEMG, $E_{P,i}$ is the carbon emission of IEMG, $E_{R,i}$ is the actual carbon emission, ${\tau }_{buy}$ is the parameter for calculating carbon emissions from purchased electricity, ${\tau }_g$ is the parameter for calculating carbon emissions from natural gas, ${\eta }_{CCHP}$ is the energy equivalence coefficient, and ${\tau }_{\mathrm{v}.\mathrm{g}}$ is the carbon emission quota per natural gas unit.

When $E_{R,i}<0$, it indicates that the carbon emissions of the IEMG are lower than the carbon emission quota, resulting in certain profits. The smaller the carbon emission range, the higher the corresponding carbon trading price, which is to say the following:

$$F_{CO2,i}=\left\{\begin{array}{cc}-cd-c\left(1+\alpha \right)\left(-E_{R,i}-d\right)& E_{R,i}\le -d\\ -c·\left(-E_{R,i}\right)& -d<E_{R,i}\le 0\end{array}\right.$$

(45)

wherein $F_{{\mathrm{CO}}_2,i}$ represents the stepwise carbon trading cost of the IEMG; $c$ is the benchmark price for IEMG’s carbon emission rights trading; $d$ is the carbon emission interval for the IEMG.

When $E_{R,i}>0$, it indicates that the carbon emissions of the IEMG exceed the carbon emission quota, necessitating the purchase of carbon emission allowances from the carbon trading market. The larger the carbon emission range, the higher the corresponding carbon trading price, which is to say the following:

$$F_{CO2,i}=\left\{\begin{array}{cc}c{E}_{R,i}& 0<E_{R,i}\le d\\ c\left(1+\alpha \right)\left(E_{R,i}-d\right)+cd& d<E_{R,i}\le 2d\\ c\left(1+2\alpha \right)\left(E_{R,i}-2d\right)+c\left(2+\alpha \right)d& 2d<E_{R,i}\le 3d\\ c\left(1+3\alpha \right)\left(E_{R,i}-3d\right)+c\left(3+3\alpha \right)d& 3d<E_{R,i}\le 4d\\ c\left(1+4\alpha \right)\left(E_{R,i}-4d\right)+c\left(4+6\alpha \right)d& E_{R,i}>4d\end{array}\right.$$

(46)

wherein $\alpha$ represents the growth coefficient of the carbon trading price for IEMG.

Based on the aforementioned theoretical analysis, the tiered carbon trading mechanism can be represented in Figure 3.

5. Case Simulation

Taking three industrial park IEMG systems as an example and following the distributed resolution using the ADMM, this paper integrates a P2G and CCS coupled model into a multi-park IEMG system. This is done to examine its impact on the day-ahead optimal scheduling of multiple IEMGs under two different scenarios.

Scenario 1: Basic scenario, considering the day-ahead optimal scheduling of IEMGs with traditional carbon trading of P2G and CCS.

Scenario 2: Considering the day-ahead optimal scheduling of IEMGs incorporating P2G and CCS as well as a tiered carbon trading strategy. Supplementary data related to this can be found in Appendix A.

5.1. Analysis of Results from Solving with the Synchronous ADMM Algorithm

Following the distributed optimization solution, Figure 4 illustrates the convergence of the iterative residuals and the energy interactions between neighboring IEMGs:

The above figure indicates that when the ADMM algorithm reaches the iteration limit of 21 times, the benefit functions of all IEMGs converge, thereby verifying the effectiveness of the decomposition of the original problem. The distributed algorithm allows the variables in the coupling region to approach infinitely, relieving the computing pressure of the original problem through its decomposition. Figure 5 illustrates the iteration situation of electrical interactive power. It can be observed that IEMG1 is outputting electrical power to IEMG2, IEMG2 is maintaining a power balance with IEMG3, and IEMG1 is transferring energy to IEMG3 in the early morning. In other periods when the output of wind power is low, IEMG3 submits energy to IEMG1.

5.2. Analysis of IEMG Energy Supply Operations

Using IEMG1 in Scenario 2 as an example, see Appendix A for IEMG2 and IEMG3. The optimal power operation strategy results can be seen in Figure 6, showing that power interaction always exists between IEMG1 and the other IEMGs, mainly as interactive power. From Figure 6, it is observed that from 0:00 to 24:00, its operating output always remains at the utmost, indicating that IEMG’s own electrical power can meet its electrical load demand. Also, it signifies the frequent power trade among IEMGs, highlighting the clear cooperation advantage among IEMGs. With the combination of IEMG’s benefits, it can be noticed that all three IEMGs have shifted their costs to negative values after cooperation, signifying that IEMG has made profits. In the figure, it can also be seen that renewable energy output within IEMG plays a significant role, stating that the absorption rate of renewable energy within the grid system is quite high at this time. With the support of CCHP and GB’s output and considering energy storage, their charge–discharge coordination also helps to flatten the electric load demand of the IEMG system. Because the IEMG system has cooling and heating load demands, when CCHP has a larger cooling and heating load demand, its output is quite visible. From the figure, it can be seen that from 10:00 to 11:00, when the electric load is at peak and the cooling and heating load demand is also large, CCHP maintains a high output level. From 11:00 to 12:00, even though the electric load demand decreases, the cooling and heating load demand is still large, so CCHP still provides the electric load output. At 14:00, 16:00, 19:00, and 21:00, CCHP showcases a higher electric power output level, and under the alternation of EC and GB, it achieves the most optimal and reasonable operation of each facility. When CCHP’s output is insufficient, IEMG will purchase electricity from the external grid to fulfill IEMG’s internal electric load demand. When IEMG’s internal electric load demand is low, IEMG will actively sell electricity to the external grid, thereby making certain profits.

In terms of the optimal thermal power operation strategy results, it can be seen from Figure 7 that the thermal load curve is relatively smooth. From 8:00 a.m. to 10:00 p.m., the entire thermal load demand is at its peak stage. This time period is also the most concentrated stage of CCHP unit output, demonstrating that CCHP plays a significant role in compensating for the GB’s output limitations. Meanwhile, thermal storage is also working during the peak period. However, when the thermal load demand is at a moderate stage, between 0:00 and 6:00, thermal storage primarily acts as heat storage. When the heat storage is almost full, to ensure storage capacity, it has to discharge heat. Thus, at 2:00 and 5:00, to coordinate with the output of the GB unit, the system opts for thermal storage to discharge heat to prevent excessive heat retention, which could affect the lifespan of the storage. From 23:00 to 24:00, when the system load is at its lowest, GB maintains its output, and the remaining thermal storage dissipates heat to maintain the system’s thermal load balance.

Regarding the results of the optimal cold power operation strategy, as can be seen in Figure 8, the cold load curve also exhibits a flatter. From 0:00 to 8:00 in the morning, the whole cold load demand is in a flat phase. During this time, the EC unit’s output is the most concentrated, revealing that the EC plays a valuable role in compensating for CCHP’s output constraints. When the cold load demand is in the peak phase, from 9:00 to 20:00, the EC unit’s output is in combination with CCHP’s output of cold energy. From 21:00 to 24:00, at this time when the system load is at a low stage, the EC, alternating with the output of CCHP, achieves the balance of the cold load.

5.3. IEMG Benefit Analysis

From the benefit analysis of IEMG1 in

Table 1. Cost of IEMG1 in traditional carbon trading and tiered carbon trading.

IEMG1	Traditional Carbon Trading Cost/RMB	Tiered Carbon Trading/RMB
Interaction cost	17,782,129	7,709,822
Gas cost	57,276,394	41,368,711
Carbon emission cost	5,093,506	35,881,761
Energy supply revenue	414,171,202	395,795,342
Microgrid income	466,210,842	310,835,047
Total cost of user	4,534,891	4,534,891

, it significantly reduced external energy dependence while keeping the total cost to the user unchanged; by joining the ladder carbon trading mechanism, the cost of interaction with the external grid has been reduced by 56.64%, the cost of gas has been reduced by 27.78%, and the cost of carbon emissions has been reduced by 29.54%. At the same time, multi-park IEMG systems are more inclined to choose tiered carbon trading. Under the premise of the same energy sales to users by IEMG, the cost of tiered carbon trading and energy purchases is lower than that of traditional carbon trading methods. The details for IEMG2 and IEMG3 can be found in Appendix A.

6. Conclusions

This paper takes microgrid as the principal entity of the IEMG system to solve and analyze the issue of day-ahead optimal operation scheduling in the IEMG system. The conclusions of this paper are as follows:

(1)

Based on the synchronous ADMM algorithm, a distributed solution has been implemented, ensuring the information security of each region.

(2)

Through the solution and analysis of multiple instances of IEMG groups for energy optimization of the IEMG system, it validates the effectiveness and quickness of the proposed method in addressing the complex interactions of multiple IEMGs.

(3)

In this paper, without taking into account the flow of the energy network within the system, it validates the positive impact of introducing tiered carbon trading on both the system’s carbon emissions and its economic efficiency. Significantly reduced external energy dependence while keeping the total cost to the user unchanged; by joining the ladder carbon trading mechanism, the cost of interaction with the external grid has been reduced by 56.64%, the cost of gas has been reduced by 27.78%, and the cost of carbon emissions has been reduced by 29.54%.

In subsequent work, it should consider the tide problems existing in different energy transmissions and propose a more comprehensive model construction.