Optimal Energy Management Strategy of Clustered Industry Factories Considering Carbon Trading and Supply Chain Coupling

Abstract

Industrial parks, characterized by the clustering of multiple factories and interconnected energy sources, require optimized operational strategies for their Integrated Energy Systems (IES). These strategies not only aim to conserve energy for industrial users but also relieve the burden on the power supply, reducing carbon emissions. In this context, this paper introduces an optimization strategy tailored to clustered factories, considering the incorporation of carbon trading and supply chain integration throughout the entire production process of each factory. First, a workshop model is established for each factory, accompanied by an energy consumption model that accounts for the strict sequencing of the production process and supply chain integration. Furthermore, energy unit models are devised for the IES and then a low-carbon and economically optimized scheduling model is outlined for the IES within the industrial park, aiming to minimize the total operational cost, including the cost of carbon trading. Finally, case studies are conducted within a paper-making industrial park located in the Zhejiang Province. Various scenarios are compared and analyzed. The numerical results underscore the model’s economic and low-carbon merits, and it offers technical support for energy conservation and emission reduction in paper-making fields.

1. Introduction

Since the Industrial Revolution, high-carbon industrial operations, characterized by their massive consumption of natural resources and vast greenhouse gas emissions, has accelerated environmental issues [1,2]. Environmental pollution and energy security have become global challenges and pose serious threats to human survival and development [3,4]. A global consensus is emerging in support of the promotion of green energy economics and the expedited transition to a low-carbon future [5,6]. The Integrated Energy System (IES) stands as a key enabler in this paradigm, seamlessly interconnecting a diverse array of energy sources, encompassing renewables, thermal energy, and natural gas [7]. These diverse sources are harmonized through various coupling mechanisms embedded within the system [8]. Meanwhile, this coupling fosters interchangeability and synergy among the manifold energy resources, thereby bolstering overall energy efficiency and facilitating the seamless integration of renewable energy sources, such as wind and solar power [9,10]. This integration, in turn, lays the foundation for the realization of a holistic spectrum of benefits, encompassing economic efficiency, energy sustainability, and environmental preservation [11].

Regarding the holistic energy optimization of industrial parks, ref. [12] focused on iron and steel enterprises and established an optimization scheduling model for the by-products of gas, steam, and electricity to effectively improve the utilization efficiency of energy. A joint scheduling model for the industrial park that combines day-ahead optimization with real-time operation was proposed in [13], but this model did not consider the constraints of production, making it difficult to apply to real industrial production. Ref. [14] proposed a two-stage optimal scheduling model for the IES of a residential area to reduce the operational cost. But this model is not suitable for a production factory with strict processes and orderliness. An optimization model for a multi-regional integrated energy system (IES) was developed in [15], taking into account carbon trading and the constraints imposed by the district heating network. However, the individual analysis of each region remains relatively simplistic in the existing research. Ref. [16] proposes an integrated demand response model that includes multiple types of flexible resources and establishes a two-layer optimal dispatch strategy to achieve the optimal operation of factories and multi-energy operators and reduce the overall peak power value of the industrial park. Although the aforementioned studies coordinate the energy systems of industrial parks with various loads, they all fail to have an in-depth understanding of the production processes of different stages and workshops of the factory and incorporate them into the energy system modeling. Especially without considering the collaborative supply chain production of multiple factories in an industrial park, optimizing the energy utilization of one factory may have an impact on the energy efficiency of the entire clustered industrial park. This requires modeling and analysis of the supply chain to understand how energy consumption is distributed across the cluster to find the overall optimal solution. As a result, the dynamic processes of intra-industrial production and the supply chain coupling characteristics between factories are ignored. Thus, this leads to suboptimal outcomes in energy management, making it difficult to apply to actual industries.

The industrial sector represents a significant source of carbon emissions and occupies a pivotal role in attaining carbon peaking and carbon neutrality objectives [17]. The integration of carbon trading mechanisms into the scheduling procedures of IES offers an effective means of reducing carbon emissions, all while ensuring the economic viability of these scheduling strategies [18,19,20]. Many studies have evaluated emission reduction strategies in industrial parks, exploring avenues such as improved industrial development and emission reduction technologies. Ref. [21] suggested a comprehensive evaluation method to assess the influence of emissions on energy consumption. Ref. [22] examined the viability and practicality of establishing an electric–thermal carbon-neutral industrial park, while conducting economic, energy, and environmental analyses under various scenarios.

In [23], a model for optimizing demand response within an electric–thermal IES was introduced, predicated on a fixed carbon price, thus enabling the realization of both economic and low-carbon operation of the IES. Ref. [24] pioneered the incorporation of a stepped carbon trading mechanism into the scheduling of a pumped storage power station equipped with battery energy storage, resulting in a notable reduction in carbon emissions. Furthermore, ref. [25] presented an optimization scheduling model tailored to an electric–gas interconnected IES, which took into account carbon trading mechanisms. This model systematically analyzed the impact of carbon trading on both economic cost and carbon emissions. Similarly, ref. [26] introduced a stepped carbon trading mechanism and devised an integrated energy system model encompassing electric, gas, and heat components, effectively curbing overall system carbon emissions. However, the existing body of academic literature primarily focuses on single factories or comprehensive energy management systems within communities. There remains a dearth of research on integrating carbon trading mechanisms into the comprehensive energy management systems of clustered industrial users. This limitation hinders the seamless coordination of production processes among various factories. In summary, the introduction of carbon trading mechanisms into the energy scheduling model of clustered industrial parks is an imperative step in propelling the industry’s transition from high-carbon emissions to a low-carbon paradigm.

Based on the aforementioned reviews, this paper puts forth an energy optimization strategy encompassing the entire production process within each factory situated in a clustered industrial park. It takes into account the stepped carbon trading mechanism and integrates supply chain coupling. The remaining sections of this paper are structured as follows: Section 2 introduces the production workshop model for every factory, delineates the diverse energy unit models within the park, and elaborates on the stepped carbon trading mechanism. In Section 3, we proceed to establish and analyze the optimized scheduling model for energy management. The efficacy of the proposed approach is scrutinized in Section 4. Section 5 encapsulates our findings with the future work being prospected.

2. Architecture of Integrated Energy System in Paper Industry Park

2.1. Production Paralell Model under Supply Chain Coupling

Production within the industry adheres to stringent sequential constraints, wherein the output materials of one production workshop serve as the input materials for the subsequent workshop. Typically, an intermediate storage warehouse stands between two workshops, functioning as a buffer for storing intermediate products awaiting entry into the following workshop. Figure 1 illustrates the operational flow of a milling production workshop featuring a storage warehouse. The presence of these intermediate storage warehouses facilitates the parallel operation of workshops that would otherwise be limited to sequential operation. This, in turn, enables optimization and scheduling in the production process. The model presented in this paper is based on the parallel operation mode.

In industrial parks, when two factories are positioned in contiguous links or rely on each other within the supply chain, a supply chain coupling relationship becomes apparent. For example, one factory may function as the supplier of raw materials to another factory, or they may participate in the exchange of semi-finished products, as illustrated in Figure 2. This coupling relationship means that their production plans, inventory management, and various other aspects are mutually influenced. The effective management and coordination of these coupling relationships can result in improved cooperation efficiency, enhanced energy utilization efficiency, and an overall enhancement of performance across the factories.

Let $i\in \mathrm{F}=\left\{1,2,\cdot \cdot \cdot ,N\right\}$ represents the identification number of a factory in an industrial park; $n\in \mathrm{W}=\{1,2,\cdot \cdot \cdot ,N_i\}$ represents the identification number of the production workshops of factory $i$; therefore, we define ${\mathbf{\psi }}_{\mathbf{i}}$ as the model parameters of a factory $i$:

$${\psi }_i=\left\{\mathrm{W},P_{\mathrm{L}},Q_{\mathrm{L}},S_n,{\lambda }_n,R,M_n^{i\to j}\right\}$$

(1)

where $\mathrm{W}$ is the total number of workshops; $P_{\mathrm{L}}$ is the electrical load; $Q_{\mathrm{L}}$ is the thermal load; $S_n$ is the inventory level of each workshop; ${\lambda }_n$ is the operating status of each workshop; $R$ is the factory production plan; and $M_n^{i\to j}$ is the transfer volume of the semi-finished products of each workshop.

Let $t\in \{1,2,\cdot \cdot \cdot ,T\}$ represents the time interval of the dispatching time period $T$; $V_{n,t}^{i,\mathrm{out}}$ is the standard output quantity of each workshop of factory $i$ at period $t$; $V_{i,n,t}^{i,\mathrm{in}}$ is the standard input quantity of each workshop at period $t$; ${\lambda }_{i,n,t}\in \{0,1\}$ is the working state of the workshop of factory $i$ at period $t$; and ${\lambda }_{i,n,t}=1$ denotes working while the opposite means not working. Let $j\in \mathbf{F}=\left\{1,2,\cdot \cdot \cdot ,F|j\ne i\right\}$ and $M_{n,t}^{i\to j}$ represents the volume of semi-finished products exchanged from factory $i$ to factory $j$. Note that a positive number means that $i$ is transported to $j$ and a negative number means that $j$ is transported to $i$. Hence, the workshop constraints of factory $i$ under supply chain coupling between multiple factories can be obtained as follows:

$$S_{n,t}^i=\left\{\begin{array}{l}{S}_{n,0}^i+({\lambda }_{n,t}^i{V}_{n,t}^{i,\mathrm{out}}-{\lambda }_{n+1,t}^i{V}_{n+1,t}^{i,\mathrm{in}}-{\displaystyle \sum _{i=1}^F{M}_{n,t}^{i\to j}})\Delta t, t=1\\ S_{n,t-1}^i+({\lambda }_{n,t}^i{V}_{n,t}^{i,\mathrm{out}}-{\lambda }_{n+1,t}^i{V}_{n+1,t}^{i,\mathrm{in}}-{\displaystyle \sum _{i=1}^F{M}_{n,t}^{i\to j}})\Delta t, t>1\end{array}\right.$$

(2)

$$\left\{\begin{array}{l}{S}_{n,T}^i=S_{n,0}^i\\ 0\le S_{n,t}^i\le S_{n,\max }^i\end{array}\right.$$

(3)

$${\displaystyle \sum _{t=1}^T{\lambda }_{N_i,t}^i{V}_{N,t}^{i,\mathrm{out}}\ge {\mathrm{R}}^i}$$

(4)

where $S_{n,0}^i$ and $S_{n,T}^i$ are the initial and final storage quantities of the workshop’s storage warehouse $n$ of factory $i$, respectively; $S_{n,t}^i$ is the quantity of materials entering the store of the warehouse at period $t$; ${\mathrm{R}}^i$ is the quantity of production task. Note that (2) represents the dynamic relationship between the inventories of different warehouses; (3) represents the constraints in which the initial and final inventories of each warehouse are required to be equal, and the inequality in (3) represents the capacity limitations of the inventories in each time period; (4) represents the production task in the dispatching period.

The electrical and thermal energy consumed of factory $i$ can be calculated as follows:

$$P_{\mathrm{L},t}^i={\displaystyle \sum _{n=1}^{N_i}{\lambda }_{n,t}^i{P}_{n,t}^i}$$

(5)

$$Q_{\mathrm{L},t}^i={\displaystyle \sum _{n=1}^{N_j}{\lambda }_{n,t}^i{Q}_{n,t}^i}$$

(6)

where $P_{\mathrm{L},t}^i$ and $Q_{\mathrm{L},t}^i$ represent the total electrical and thermal power consumed by factory $i$ at period $t$, respectively; $P_{n,t}^i$ and $Q_{n,t}^i$ represent the electrical and thermal power consumed by workshop $n$ of factory $i$, and its value can be determined based on the typical operating conditions of the equipment in each workshop.

2.2. Energy Unit Model of Paper Industry Park

In this paper, the structure of the energy supply system of the industry park is illustrated in Figure 3, consisting of the energy production unit, the energy conversion unit, the energy storage unit, and the paper factory load unit.

The energy production unit includes the electrical energy unit, which refers to the main power grid (GRID), the wind turbines (WT), the photovoltaic panels (PV), the coal yard (COAL), and the natural gas station (GAS).

The energy conversion unit consists of gas turbines (GT), gas boilers (GB), and coal-fired units (CFU). GT are typically equipped with generators and heat recovery systems to maximize the utilization of energy generated from gas and GB only generate thermal energy. The energy conversion unit can be modeled as:

$$\left\{\begin{array}{l}{P}_{I,t}=M_{I,t}{u}_I^{\mathrm{e}}{V}_I \\ Q_{J,t}=M_{J,t}{u}_J^{\mathrm{h}}{V}_J\end{array}\right.$$

(7)

where $I\in \left\{\mathrm{GT},\mathrm{CFU}\right\}$, $J\in \left\{\mathrm{GT},\mathrm{CFU},\mathrm{GB}\right\}$, $P_{I,t}$, and $Q_{I,t}$ represent the electrical energy and thermal power produced by various energy equipment during period $t$, respectively; $M_{I,t}$ is the energy consumption of $I$ and $J$ in period $t$; $u_I^{\mathrm{e}}$ and $u_J^{\mathrm{h}}$ are the conversion efficiency of $I$ and $J$, respectively; and $V_I$, $V_J$ are the calorific value of $I$ and $J$, respectively.

The energy storage unit within the park comprises both batteries (BA) and heat storage tanks (HST), both of which operate in a similar manner. Typically, they are charged during periods of low energy prices or when excess power is available, and they discharge energy and release heat during periods of peak energy consumption to alleviate peak loads. Taking the BA as an example:

$$B_{\mathrm{s},t}=\left\{\begin{array}{l}{B}_{\mathrm{s},0}\left(1-{\sigma }_{\mathrm{BA}}^{\mathrm{self}}\right)+\left(P_{\mathrm{BA},t}^{\mathrm{ch}}\cdot {\eta }_{\mathrm{BA}}^{\mathrm{ch}}-\frac{P_{\mathrm{BA},t}^{\mathrm{dis}}}{{\eta }_{\mathrm{BA}}^{\mathrm{dis}}}\right)\Delta t,t=1\\ B_{\mathrm{s},t-1}\left(1-{\sigma }_{\mathrm{BA}}^{\mathrm{self}}\right)+(P_{\mathrm{BA},t}^{\mathrm{ch}}\cdot {\eta }_{\mathrm{BA}}^{\mathrm{ch}}-\frac{P_{\mathrm{BA},t}^{\mathrm{dis}}}{{\eta }_{\mathrm{BA}}^{\mathrm{dis}}})\Delta t,t>1\end{array}\right.$$

(8)

where $B_{\mathrm{s},t}$ represents the stored electrical energy at period $i$; $B_{\mathrm{s},0}$ represents the stored electrical energy at the initial period; ${\sigma }_{\mathrm{BA}}^{\mathrm{self}}$ represents the self-discharge coefficient; and $P_{\mathrm{BA},t}^{\mathrm{ch}}$, $P_{\mathrm{BA},t}^{\mathrm{dis}}$ respectively represent the charging and discharging power during period $t$. The operating model of the HST is similar to that of the battery and will not be elaborated here.

2.3. Carbon Trading Model

The carbon trading mechanism is a market-oriented tool that encourages enterprises to reduce greenhouse gas emissions by buying and selling carbon emission quotas. It can be combined with Industrial Energy Systems (IES) to reduce carbon emissions in energy production and consumption processes and have an impact on operational decisions. In the carbon trading mechanism, enterprises are allocated a certain amount of carbon emission quota, representing their allowed greenhouse gas emissions. If the carbon dioxide emissions of an enterprise are within a given quota, the excess amount can be sold in the carbon trading market. On the contrary, if the carbon emissions exceed the given quota, the excess amount needs to be purchased from the market for carbon emission rights. Under the carbon trading mechanism, enterprises will actively adopt energy-saving and emission-reducing measures to achieve carbon emission quota savings, thereby reducing the cost of carbon emission and improving their competitiveness. At the same time, the carbon trading market can also provide enterprises with a flexible carbon reduction mechanism, enabling them to manage and plan carbon reduction strategies more effectively, thereby achieving synergy between carbon reduction and economic benefits.

The carbon trading model employed in this paper follows the carbon emission analysis method outlined in refs. [27,28], which incorporates the carbon footprint of each energy chain, extending from the production source to the load demand side, thereby enabling a more precise evaluation of the total carbon emissions within the system. As a result, this paper accounts for the carbon emissions generated by various energy sources within the paper industry park throughout the production, transportation, and utilization phases. These emissions can be calculated using the following equation:

$$E_{\mathrm{AC},t}={\displaystyle \sum _{i\in \mathsf{\Omega }}{\displaystyle \sum _{t=1}^T(k_{i,t}^{\mathrm{tran}}+k_{i,t}^{\mathrm{work}})P_{i,t}}}$$

(9)

where $E_{\mathrm{AC},t}$ is the actual carbon emissions of the industrial park during period $t$; $\mathsf{\Omega }$ is the collection of various energy storage devices and energy supply equipment in the industrial park; $k_{i,t}^{\mathrm{tran}}$ is the carbon emission coefficient of the energy associated with the $i$-th energy device during period $t$, considering the production and transportation processes; and $k_{i,t}^{\mathrm{work}}$ considers the utilization process.

The model of carbon emission quota can be expressed as:

$$E_{\mathrm{QU},t}={\displaystyle \sum _{i\in \mathsf{\Omega }}{\displaystyle \sum _{t=1}^T{k}_{i,t}{P}_{i,t}}}$$

(10)

where $E_{\mathrm{QU},t}$ is the carbon emission quota of the industrial park during the time period $t$ and $k_{i,t}$ represents the carbon emission quota coefficient of the $i$-th energy device during period $t$.

In contrast to the fixed-price carbon trading mechanism, the stepped carbon trading mechanism offers enhanced efficiency in optimizing the allocation of carbon emissions. The stepped pricing mechanism accomplishes the allocation of carbon emission rights through the division of multiple purchase intervals. The model can be expressed as follows [29]:

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

(11)

$$C_{{\mathrm{CO}}_2}=\left\{\begin{array}{l}\lambda E_{{\mathrm{CO}}_2} \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{E}_{{\mathrm{CO}}_2}\le l\\ \lambda (1+\mu )(E_{{\mathrm{CO}}_2}-l)+\lambda l \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}l\le E_{{\mathrm{CO}}_2}\le 2l \\ \lambda (1+2\mu )(E_{{\mathrm{CO}}_2}-2l)+\lambda (2+\mu )l 2l\le E_{{\mathrm{CO}}_2}\le 3l\\ \lambda (1+3\mu )(E_{{\mathrm{CO}}_2}-3l)+\lambda (3+3\mu )l 3l\le E_{{\mathrm{CO}}_2}\le 4l\\ \lambda (1+4\mu )(E_{{\mathrm{CO}}_2}-4l)+\lambda (4+6\mu )l 4l\le E_{{\mathrm{CO}}_2}\end{array}\right.$$

(12)

where $E_{{\mathrm{CO}}_2}$ represents the total amount of carbon emissions exceeding the allocated quota for the industrial park during one operational cycle; $E_{{\mathrm{CO}}_2}$ is the cost of carbon trading; $\lambda$ is the base price for carbon trading; $\mu$ is the rate of price growth; and $l$ is the length of the carbon emission.

3. Optimized Scheduling Model of Energy Management

3.1. Objective Function

To minimize the total cost of operation and carbon trading in the industry park over an optimization cycle, the objective function can be expressed as follows:

$$\min C={\displaystyle \sum _{t=1}^T[C_{\mathrm{BUY}}+C_{\mathrm{OP}}+C_{TR}]}+C_{{\mathrm{CO}}_2}$$

(13)

where $C_{\mathrm{BUY}}$ is the cost of purchasing energy; $C_{\mathrm{OP}}$ is the cost of operating and maintaining operation of the energy equipment; and $C_{TR}$ is the cost of the exchange and transfer of the semi-finished products between all industries.

1.

Cost of purchasing energy

The cost of purchasing energy refers to the expenses incurred in purchasing energy from energy suppliers to meet the internal load requirement within an industrial park. This cost encompasses the purchase of electricity $C_{\mathrm{GRID}}$, gas $C_{\mathrm{GAS}}$, and coal $C_{\mathrm{COAL}}$:

$$\left\{\begin{array}{l}{C}_{\mathrm{BUY}}=C_{\mathrm{GRID}}+C_{\mathrm{GAS}}+C_{\mathrm{COAL}}\\ C_{\mathrm{GRID}}=K_{\mathrm{GRID},t}{P}_{\mathrm{GRID},t}\\ C_{\mathrm{GAS}}=K_{\mathrm{GAS}}(\frac{Q_{\mathrm{GT},t}}{u_{\mathrm{GT}}^{\mathrm{h}}}+\frac{Q_{\mathrm{GB},t}}{u_{\mathrm{GB}}^{\mathrm{h}}})\\ C_{\mathrm{COAL}}=K_{\mathrm{COAL}}\frac{P_{\mathrm{CFU},t}}{u_{\mathrm{CFU}}^{\mathrm{e}}}\end{array}\right.$$

(14)

where $K_{\mathrm{GRID},t}$ and $P_{\mathrm{GRID},t}$ represent the time-of-use price and volume of electricity purchased from the main power grid, respectively; $K_{\mathrm{GAS}}$ represents the gas consumption coefficient, defined as the ratio of the market price of natural gas to its calorific value; and $K_{\mathrm{COAL}}$ represents the raw coal consumption coefficient, defined as the ratio of the market price of raw coal to its calorific value.

2.

Cost of operation and maintenance

Operation and maintenance cost refer to the expenses required to ensure the proper work and upkeep of equipment, systems, or facilities. It includes the cost of maintaining wind turbines $C_{\mathrm{WT}}$, photovoltaic panels $C_{\mathrm{PV}}$, batteries $C_{\mathrm{BA}}$, heat storage tanks $C_{\mathrm{HST}}$, coal-fired units $C_{\mathrm{CFU}}$, gas turbines $C_{\mathrm{GT}}$, and gas boilers $C_{\mathrm{GB}}$.

$$\left\{\begin{array}{l}{C}_{\mathrm{OP}}=C_{\mathrm{WT}}+C_{\mathrm{PV}}+C_{\mathrm{BA}}+C_{\mathrm{HST}}+C_{\mathrm{CFU}}+C_{\mathrm{GT}}+C_{\mathrm{GB}}\\ C_{\mathrm{WT}}=K_{\mathrm{WT}}{P}_{\mathrm{WT},t}\\ C_{\mathrm{PV}}=K_{\mathrm{PV}}{P}_{\mathrm{PV},t}\\ C_{\mathrm{BA}}=K_{\mathrm{BA}}(\left|P_{\mathrm{BA},t}^{\mathrm{ch}}\right|+\left|P_{\mathrm{BA},t}^{\mathrm{dis}}\right|)\\ C_{\mathrm{HST}}=K_{\mathrm{HST}}(\left|Q_{\mathrm{HST},t}^{\mathrm{ch}}\right|+\left|Q_{\mathrm{HST},t}^{\mathrm{dis}}\right|)\\ C_{\mathrm{CFU}}=K_{\mathrm{CFU}}{P}_{\mathrm{CFU},t}\\ C_{\mathrm{GT}}=K_{\mathrm{GT}}{P}_{\mathrm{GT},t}\\ C_{\mathrm{GB}}=K_{\mathrm{GB}}{P}_{\mathrm{GB},t}\end{array}\right.$$

(15)

where $K_{\mathrm{WT}}$, $K_{\mathrm{PV}}$, $K_{\mathrm{BA}}$, $K_{\mathrm{HST}}$, $K_{\mathrm{CFU}}$, $K_{\mathrm{GT}}$, and $K_{\mathrm{GB}}$ represent the cost coefficient of maintaining WT, PV, BA, HST, GT, GB, and CFU, respectively. $Q_{\mathrm{HST},t}^{\mathrm{ch}}$ and $Q_{\mathrm{HST},t}^{\mathrm{dis}}$ respectively represent the charging and discharging power of the HST during period $t$.

3.

Cost of exchange and transfer

The cost of exchange and transfer refers to the expenses incurred in the supply chain when transporting semi-finished products from one factory to another.

$$C_{\mathrm{TR}}={\displaystyle \sum _{i=1}^F{\displaystyle \sum _{n=1}^{N_i}{K}_{n,t}^{i\to j}{M}_{n,t}^{i\to j}}} (M_{n,t}^{i\to j}>0)$$

(16)

where $K_{n,t}^{i\to j}$ represents the cost coefficient of the exchange and transfer of the semi-finished products from factory $i$ to factory $j$.

4.

Cost of carbon trading

See Section 2.3 for carbon trading cost.

3.2. Operational Constraints

The energy equipment within the industrial park is interconnected with the production workshops of each factory. Moreover, each factory’s production workshop is interlinked with a supply chain coupling relationship, necessitating compliance with operational and material balance constraints across various energy equipment while adhering to their respective constraints. These constraints can be summarized as follows:

1.

Electrical/thermal power balance constraints

$$P_{\mathrm{NET},t}+P_{\mathrm{CFU},t}+P_{\mathrm{GT},t}+P_{\mathrm{WT},t}+P_{\mathrm{PV},t}-P_{\mathrm{BA},t}^{ch}+P_{\mathrm{BA},t}^{\mathrm{dis}}={\displaystyle \sum _{i=1}^F{P}_{\mathrm{L},t}^i}$$

(17)

$$Q_{\mathrm{GB},t}+Q_{\mathrm{GT},t}+Q_{\mathrm{CFU},t}-Q_{\mathrm{HST},t}^{\mathrm{ch}}+Q_{\mathrm{HST},t}^{\mathrm{dis}}={\displaystyle \sum _{i=1}^F{Q}_{\mathrm{L},t}^i}$$

(18)

2.

Constraints in workshop production

According to the constraints of supply chain coupling in Section 2.1 of the production workshop, the volumes of semi-finished products exchanged should be constrained. Hence, the upper $M_{n,\max }^{i\to j}$ and lower limits $M_{n,\min }^{i\to j}$ can be formulated as:

$$\left\{\begin{array}{l}{M}_{n,\min }^{i\to j}\le M_{n,t}^{i\to j}<M_{n,\max }^{i\to j}\\ M_{n,t}^{i\to j}=-M_{n,t}^{j\to i}\end{array}\right.$$

(19)

In the absence of temporal coupling constraints in workshop scheduling, it may result in frequent start-ups and shutdowns of workshop equipment. Hence, it becomes necessary to enforce a minimum duration of continuous operation for the workshop after scheduling.

$${\displaystyle \sum _{\delta =t}^{t+T_{n,\delta }^{i,\min }-1}{\lambda }_{n,\delta }^i}\ge T_{n,\delta }^{i,\min }({\lambda }_{n,\delta }^i-{\lambda }_{n,\delta -1}^i)$$

(20)

where $T_{n,\delta }^{i,\min }$ is the minimum duration of continuous operation for the workshop n of factory i.

In the workshop, regular preventive maintenance, equipment inspections, and equipment replacements are essential to avert equipment failures that may cause unforeseen production interruptions. Consequently, it is imperative to impose a constraint on the maximum duration of continuous operation following scheduling.

$${\displaystyle \sum _{\delta =t}^{t+T_{n,\delta }^{i,\max }-1}{\lambda }_{n,\delta }^i}\le T_{n,\delta }^{i,\max }({\lambda }_{n,\delta }^i-{\lambda }_{n,\delta -1}^i)$$

(21)

where $T_{n,\delta }^{i,\max }$ is the minimum duration of continuous operation for the workshop n of factory i.

3.

Constraints of the units output upper and lower limit

The operational constraints of WT and PV can be expressed as follows:

$$\left\{\begin{array}{l}{P}_{\mathrm{WT},\min }\le P_{\mathrm{WT},t}<P_{\mathrm{WT},\max }\\ P_{\mathrm{PV},\min }\le P_{\mathrm{PV},t}<P_{\mathrm{PV},\max }\end{array}\right.$$

(22)

where $P_{\mathrm{WT},\max }$ and $P_{\mathrm{PV},\max }$ represent the maximum electrical power output of WT and PV, respectively, and $P_{\mathrm{WT},\min }$, $P_{\mathrm{PV},\min }$ represent the minimum electrical power outputs of WT and PV, respectively.

According to models of the energy conversion unit in the paper industry park, the operational constraints that need to be met are as follows:

$$\left\{\begin{array}{l}{Q}_{J,\min }\le Q_{J,t}\le Q_{J,\max }\\ \Delta Q_{J,\min }\le Q_{J,t+1}-Q_{J,t}\le \Delta Q_{J,\max }\end{array}\right.$$

(23)

where $Q_{J,\min }$ and $Q_{J,\max }$ represent the lower and upper thermal power limit of $J$, respectively, and $\Delta Q_{J,\min }$, $\Delta Q_{J,\max }$ are the lower and upper limits of climbing power of $J$, respectively.

4.

Constraints of the energy storage unit

The operation constraints of the electrical and thermal energy storage systems are the same. In this paper, the battery is taken as an example:

$$\left\{\begin{array}{l}{B}_{\mathrm{s},T}=B_{\mathrm{s},0}\\ B_{\mathrm{s},\min }\le B_{\mathrm{s},t}\le B_{\mathrm{s},\max }\\ P_{\mathrm{BA},\min }^{\mathrm{ch}}\cdot u_{\mathrm{BA},t}\le P_{\mathrm{BA},t}^{\mathrm{ch}}\le P_{\mathrm{BA},\max }^{\mathrm{ch}}\cdot u_{\mathrm{BA},t}\\ P_{\mathrm{BA},\min }^{\mathrm{dis}}\cdot v_{\mathrm{BA},t}\le P_{\mathrm{BA},t}^{\mathrm{dis}}\le P_{\mathrm{BA},\max }^{\mathrm{dis}}\cdot v_{\mathrm{BA},t}\\ 0\le u_{\mathrm{BA},t}+v_{\mathrm{BA},t}\le 1\end{array}\right.$$

(24)

where $B_{\mathrm{s},\min }$ and $B_{\mathrm{s},\max }$ are the lower and the upper limits of the state-of-charge (SOC), respectively; $B_{\mathrm{s},T}$ represents the stored electrical energy of the battery at the final period; $P_{\mathrm{BA},\max }^{\mathrm{ch}}$ and $P_{\mathrm{BA},\max }^{\mathrm{dis}}$ represent the minimum and maximum charge and discharge power of the battery, respectively; $u_{\mathrm{BA},t}, v_{\mathrm{BA},t}\in \left\{0,1\right\}$ are the charge and discharge state variables of the battery, respectively, and among them, $u_{\mathrm{BA},t}$ represents the charging state for the battery during the period $t$ and $v_{\mathrm{BA},t}$ represents the discharge state.

Moreover, during a dispatching cycle, the charging and discharging frequency of the battery will affect the operating life of the device; therefore, it is necessary to control its charging and discharging frequency:

$${\displaystyle \sum _{t=1}^T{u}_{\mathrm{BA},t}\le N_{\mathrm{ch}}}$$

(25)

$${\displaystyle \sum _{t=1}^T{v}_{\mathrm{BA},t}\le N_{\mathrm{dis}}}$$

(26)

where $N_{\mathrm{ch}}$ and $N_{\mathrm{dis}}$ represent the maximum number of times which the battery is charged and discharged within a scheduling cycle, respectively.

3.3. Solution

The standard solution model of energy utilization for the entire production process of the paper industry park can be written as:

$$\left\{\begin{array}{l}\underset{x}{\min }\hspace{0.33em}C\\ s.t.\hspace{0.33em}\left(2\right)–\left(4\right),\left(8\right),(17)–(26)\\ x=\left\{\begin{array}{l}{\lambda }_{n,t},S_{n,t},M_{n,t}^{i\to j}\\ P_{\mathrm{NET},t},P_{\mathrm{I},t},Q_{\mathrm{J},t}\\ P_{\mathrm{BA},t}^{\mathrm{ch}},P_{\mathrm{BA},t}^{\mathrm{dis}},B_{\mathrm{s},t}\\ Q_{\mathrm{HST},t}^{\mathrm{ch}},Q_{\mathrm{HST},t}^{\mathrm{dis}},H_{\mathrm{s},t}\\ P_{\mathrm{W},t},P_{\mathrm{PV},t}\end{array}\right.\end{array}\right.$$

(27)

In this context, the decision variable $x$ to be optimized encompass various factors, including the operational state of each workshop, the storage quantity within each workshop, the quantity of semi-finished products exchanged from factory $i$ to factory $j$, the electricity procured from the power grid, the energy generated by the GB, GT, and CFU, the stored electrical and thermal energy within the BA and HST, the charging and discharging power of the BA and HST, and the dispatched power of the WT and PV. The presented model is subsequently transformed into a Mixed Integer Linear Programming (MILP) problem, and the solution is achieved using MATLAB 2022b in conjunction with the CPLEX solver.

4. Experimental Verification

4.1. Case Analysis

A pulp and paper industry park located in the Zhejiang Province, China, is selected as the subject of our case study. The following provides an overview of the factory production within this industrial park. The paper production process in a factory can typically be categorized into four primary stages, each corresponding to a specific workshop, as illustrated in Figure 4 for Factory 1 and Factory 2. Furthermore, there are auxiliary factories, such as Factory 3, which supply semi-finished products for further processing. Moreover, the wastewater treatment workshop (WTW) at Factory 4 employs a combination of physical, chemical, and biological processes to eliminate or reduce pollutants present in the wastewater generated by various paper factories. This approach ensures that the wastewater adheres to the environmental regulations and discharge standards, allowing for subsequent recycling and reuse, thus safeguarding the environment and public health.

In addition to the paper production lines and associated equipment, paper factories need an Auxiliary Production System (APS) to support production and management, thereby ensuring product quality and employee safety. This system comprises an enterprise operation management system, a production guidance management system, as well as various departments and units within the factory area, including workshop facilities, water boiling stations, canteens, and more.

(1) The pulping workshop (PUW) is a specialized industrialized facility dedicated to the production of pulp. Raw materials utilized can encompass wood, waste paper, bamboo, and various other sources. By subjecting these raw materials to a series of chemical or mechanical processes, they are disintegrated into fibers. Subsequent processes, such as cleaning, bleaching, and filtering, are employed to extract pure pulp. The workshop is equipped with key machinery including pulping machines, digesters, bleaching machines, filters, and more.

(2) The paper-making workshop (PAW) is responsible for the conversion of pulp, manufactured in the pulping workshop, into paper products. Typically, it comprises four principal processes: forming, pressing, drying, and winding, as depicted in Figure 5. The specific production process unfolds as follows: pulp is conveyed into the forming wire via the Headbox. Subsequently, a sequence of dewatering mechanisms, encompassing vacuum pressure within the forming section, mechanical pressing in the pressing section, and steam-assisted drying in the drying section, is employed to eliminate moisture and produce large, dried paper sheets. Ultimately, these paper sheets are wound onto substantial rolls by a winder for further processing. It is crucial to note that this workshop demands a substantial amount of steam for paper drying, with electricity and heat consumption accounting for 40% to 50% of the overall energy consumption in paper production. Hence, it stands as the most energy-intensive workshop within the facility.

(3) The coating and printing workshop (COW) primarily assumes responsibility for applying surface coatings and performing printing treatments on the manufactured paper to enhance its quality, visual appeal, and functionality. Key equipment within the COW comprises coating machines, printing machines, and calendars.

(4) The cutting and packaging workshop (CUW) typically encompasses equipment such as paper cutters, reel cutters, cross cutters, packaging machines, box sealers, and bundling machines. This workshop is tasked with the precise task of cutting the large paper rolls into smaller-sized sheets as per specific requirements. The cut paper sheets are subsequently sorted and packaged according to specified criteria and quality standards, facilitating their transportation and eventual sale.

4.2. Parameter Settings

The IES within the pulp and paper park includes various components such as wind turbines, photovoltaic panels, gas turbines, gas boilers, coal-fired units, heat storage tanks, and batteries. The length of dispatching time period T is 24 h with a time interval t of 1 h. The pertinent parameters of the BA and HST can be found in

Table A1. Battery parameters.

${\mathit{P}}_{\mathbf{BA},\mathbf{min}}^{\mathbf{ch}}/{\mathit{P}}_{\mathbf{BA},\mathbf{min}}^{\mathbf{dis}}$	${\mathit{P}}_{\mathbf{BA},\mathbf{max}}^{\mathbf{ch}}/{\mathit{P}}_{\mathbf{BA},\mathbf{max}}^{\mathbf{dis}}$	${\mathit{B}}_{\mathit{s},\mathbf{min}}$	${\mathit{B}}_{\mathit{s},\mathbf{max}}$	${\mathit{\sigma }}_{\mathbf{BA}}^{\mathbf{self}}$	${\mathit{B}}_{\mathit{s},0}$	${\mathit{\eta }}_{\mathbf{BA}}^{\mathbf{ch}}/{\mathit{\eta }}_{\mathbf{BA}}^{\mathbf{dis}}$	${\mathit{N}}_{\mathit{c}\mathit{h}}/{\mathit{N}}_{\mathit{d}\mathit{i}\mathit{s}}$
100 kW	500 kW	200 kW	1900 kW	0.001	800 kW	0.95	8

and

Table A2. Heat storage tank parameters.

${\mathit{Q}}_{\mathbf{HST},\mathbf{min}}^{\mathbf{ch}}/{\mathit{Q}}_{\mathbf{HST},\mathbf{min}}^{\mathbf{dis}}$	${\mathit{Q}}_{\mathbf{HST},\mathbf{max}}^{\mathbf{ch}}/{\mathit{Q}}_{\mathbf{HST},\mathbf{max}}^{\mathbf{dis}}$	${\mathit{H}}_{\mathit{s},\mathbf{min}}$	${\mathit{H}}_{\mathit{s},\mathbf{max}}$	${\mathit{\sigma }}_{\mathbf{HST}}^{\mathbf{self}}$	${\mathit{H}}_{\mathit{s},0}$	${\mathit{\eta }}_{\mathbf{HST}}^{\mathbf{ch}}/{\mathit{\eta }}_{\mathbf{HST}}^{\mathbf{dis}}$	${\mathit{N}}_{\mathit{c}\mathit{h}}/{\mathit{N}}_{\mathit{d}\mathit{i}\mathit{s}}$
100 kW	500 kW	200 kW	1900 kW	0.001	1200 kW	0.95	8

of Appendix A, respectively. Additionally, the relevant parameters for the CFU, GT, and GB are detailed in

Table A3. CFU parameters.

${\mathit{P}}_{\mathbf{CFU}\mathbf{,}\mathbf{max}}$	${\mathit{Q}}_{\mathbf{CFU},\mathbf{max}}$	${\mathit{u}}_{\mathbf{CFU}}^{\mathbf{e}}$	${\mathit{u}}_{\mathbf{CFU}}^{\mathbf{h}}$	$\mathbf{\Delta }{\mathit{Q}}_{\mathbf{CFU},\mathbf{min}}$	$\mathbf{\Delta }{\mathit{Q}}_{\mathbf{CFU},\mathbf{max}}$
1636 kW	3000 kW	0.3	0.55	−800 kW	820 kW

,

Table A4. GT parameters.

${\mathit{P}}_{\mathbf{GT}\mathbf{,}\mathbf{max}}$	${\mathit{Q}}_{\mathbf{GT},\mathbf{max}}$	${\mathit{u}}_{\mathbf{GT}}^{\mathbf{e}}$	${\mathit{u}}_{\mathbf{GT}}^{\mathbf{h}}$	$\mathbf{\Delta }{\mathit{P}}_{\mathbf{GT},\mathbf{min}}$	$\mathbf{\Delta }{\mathit{P}}_{\mathbf{GT},\mathbf{max}}$
2000 kW	2857 kW	0.35	0.50	−740 kW	760 kW

and

Table A5. GB parameters.

${\mathit{Q}}_{\mathbf{GB},\mathbf{max}}$	${\mathit{u}}_{\mathbf{GB}}^{\mathbf{h}}$	$\mathbf{\Delta }{\mathit{Q}}_{\mathbf{GB},\mathbf{min}}$	$\mathbf{\Delta }{\mathit{Q}}_{\mathbf{GB},\mathbf{max}}$
2000 kW	0.85	−740 kW	760 kW

in Appendix A. The coefficients of the carbon emission model are provided in

Table A6. Carbon emission coefficient and quota coefficient.

Type of Energy	${\mathit{k}}_{\mathit{i},\mathit{t}}^{\mathbf{tran}}$ (g/kWh)	${\mathit{k}}_{\mathit{i},\mathit{t}}^{\mathbf{work}}$ (g/kWh)	Total Coefficient (g/kWh)	Carbon Quota Coefficient (g/kWh)
Coal Electricity (GRID,CFU)	1303.0	0	1303.0	798.0
Natural Gas (GB,GT)	116.4	448.3	564.7	424.0
WT	43.0	0	43	78.0
PV	54.0	0	154.5	78.0
BA/HST	91.3	0	91.3	0

of the same appendix. The base price for carbon trading $\lambda$ = $20.63 per ton; the rate of price growth $\mu$ = 0.25; and the length of the carbon emission $l$ = 13 ton. Note that both the APS and the WTW operate continuously and are not subject to optimization scheduling. In order to facilitate the analysis, this paper considers the APS as an additional workshop within Factory 1, and the WTW as an additional workshop within Factory 3. The capacity of each workshop in the paper mill of each factory is shown in

Table A7. Workshop parameters of Factory 1.

Name	${\mathit{P}}_{\mathit{n}}$ (kW)	${\mathit{Q}}_{\mathit{n}}$ (kW)	${\mathit{S}}_{\mathit{n},{\mathit{T}}_0}$	${\mathit{S}}_{\mathit{n},\mathbf{max}}$	${\mathit{M}}_{\mathit{n},\mathbf{max}}^{\mathit{i}\to \mathit{j}}$	${\mathit{M}}_{\mathit{n},\mathbf{min}}^{\mathit{i}\to \mathit{j}}$
PUW	1126	1309	4	12	2	1
PAW	1868	3227	4	12	2	1
COW	546	200	4	12	2	1
CUW	138	104	\	\	\	\
APW	316	310	\	\	\	\

,

Table A8. Workshop parameters of Factory 2.

Name	${\mathit{P}}_{\mathit{n}}$ (kW)	${\mathit{Q}}_{\mathit{n}}$ (kW)	${\mathit{S}}_{\mathit{n},{\mathit{T}}_0}$	${\mathit{S}}_{\mathit{n},\mathbf{max}}$	${\mathit{M}}_{\mathit{n},\mathbf{max}}^{\mathit{i}\to \mathit{j}}$	${\mathit{M}}_{\mathit{n},\mathbf{min}}^{\mathit{i}\to \mathit{j}}$
PUW	562.8	654.5	6	15	4	1
PAW	934	1613.5	6	15	4	1
WTW	546	200	\	\	\	\

and

Table A9. Workshop parameters of Factory 3.

Name	${\mathit{P}}_{\mathit{n}}$ (kW)	${\mathit{Q}}_{\mathit{n}}$ (kW)	${\mathit{S}}_{\mathit{n},{\mathit{T}}_0}$	${\mathit{S}}_{\mathit{n},\mathbf{max}}$	${\mathit{M}}_{\mathit{n},\mathbf{max}}^{\mathit{i}\to \mathit{j}}$	${\mathit{M}}_{\mathit{n},\mathbf{min}}^{\mathit{i}\to \mathit{j}}$
PUW	562.8	654.5	4	12	2	1
PAW	1868	3227	4	12	2	1
COW	273	100	4	12	2	1
CUW	69	52	\	\	\	\

of Appendix A. The time-of-use price for industrial and commercial users during summertime in the Zhejiang Province is adopted as the retail price. During the valley period from 1:00 to 7:00, the electricity price is $0.034 per kWh. The flat periods from 8:00 to 10:00, 16:00 to 18:00, and 22:00 to 24:00 have an electricity price of $0.073 per kWh. The electricity price during the peak period from 11:00 to 15:00 and 19:00 to 21:00 is $0.11 per kWh. The price of natural gas is fixed at $0.34 per m³, and the calorific value is set at 9.7 kWh/m³. The price of raw coal is fixed at $0.12 per kg, and the calorific value is set at 5.81 kWh/m³. Based on the LSTM prediction [30], the predicted power output for the wind turbines and photovoltaic panels is illustrated in Figure 6. Finally, the number of production tasks for finished paper for Factory 1 and Factory 2 are designated as R¹ = 15 and R² = 16, respectively.

4.3. Optimized Result

To assess the low-carbon and economic implications of the optimized scheduling model proposed in this paper, we established the following scenarios for comparative analysis:

Scenario 1: The production workshops of each factory operate as per their original plans.

Scenario 2: Optimization scheduling of the IES is conducted, accounting for supply chain coupling while excluding carbon emissions.

Scenario 3: Optimization scheduling of the IES is performed, taking carbon emissions into account while excluding supply chain coupling.

Scenario 4: The model proposed in this paper considers both supply chain coupling and carbon emissions.

Table 1. Total operating cost, carbon trading cost, and actual volume of carbon trading for each scenario.

Scenario	Volume of Carbon Trading/t	Operating Cost/$	Carbon Trading Cost/$	Total Cost/$
1	102.37	12,430	3554	15,984
2	99.798	11,107	3448	14,555
3	73.696	11,736	2370	14,106
4	73.712	11,461	2371	13,832

presents the total operational and carbon trading cost, as well as the actual carbon trading volumes for each scenario. Scenario 1 incurs high operating cost, with a total operational expense of $15,984. This outcome reflects that when the factory production workshops adhere strictly to their original plans and the IES is not involved in scheduling, it results in an impractical energy usage strategy and low energy utilization efficiency. In Scenario 2, as opposed to Scenario 1, inventory levels across various factories and storage workshops are adjusted, with most workshops scheduled to operate during off-peak hours. The IES purchases a significant amount of electricity during this period, which results in reduced operating cost. Scenario 3, introduced after implementing the carbon trading mechanism, prioritizes the dispatch of the GB and GT. However, the cost of purchasing natural gas is higher than coal, leading to an increase in operating cost. Lastly, comparing Scenario 4 with Scenario 1, which considers both supply chain coupling and carbon trading, adjusting the inventory levels in each factory workshop incurs some additional cost. This approach allows for more flexible adjustments to the energy network, resulting in a reduction of 28.658 tons in carbon emissions. Moreover, the overall cost of the industrial park are still reduced by 13.46% compared to Scenario 1, indicating the effectiveness of the scheduling model in lowering park operating expenses while curbing carbon emissions. Therefore, the model presented in this paper effectively strikes a balance between operational cost-efficiency and carbon emissions reduction.

Figure 7 illustrates the energy distribution within the entire paper-making cluster industrial park for two distinct operating scenarios: Scenario 1 and Scenario 4. In Scenario 1, each factory adheres to its original planned schedule without accounting for time-of-use electricity pricing. Consequently, numerous workshops continue to operate during peak electricity pricing periods, resulting in a substantial procurement of electricity when prices are high and the subsequent inflation of operating cost.

In contrast, Scenario 4 meticulously incorporates time-of-use electricity pricing. Due to the limitations associated with the power capacity of energy equipment and the available thermal power capacity within the industrial park, it is not feasible to schedule all loads exclusively during low-priced electricity periods. However, Scenario 4 optimizes the scheduling of controllable devices, which includes battery storage systems, thermal storage tanks, and distributed energy sources such as photovoltaic and wind power. It dynamically allocates the operating statuses of workshops across various time intervals and determines the corresponding transfer quantities for storage workshops. This strategic approach effectively shifts the overall load from high-priced electricity periods to valley and flat periods, ensuring the economic efficiency of the energy utilization strategy.

As demonstrated in Figure 8, after participating in the optimization scheduling of the IES, the various workshops within each factory achieve different degrees of load shifting, resulting in the redistribution of electrical energy from high-priced and high-load periods to low-priced and low-load periods, while adhering to the constraints of the production sequence. Moreover, the energy consumption types vary among different workshops within each factory, and a certain coupling relationship exists between electrical and thermal energy. As seen in Figure 7b, if the electrical load is shifted, the corresponding thermal energy is also adjusted accordingly.

This observation underscores the interconnected nature of energy consumption within the industrial park. The optimization scheduling process not only accounts for electricity load but also considers the associated thermal energy requirements. By strategically shifting the load, a more balanced and efficient overall energy utilization within the system is achieved.

4.4. Analysis of IES Scheduling

The distribution of electrical and thermal energy within the IES in the paper-making industry park is depicted in Figure 9 and Figure 10 for Scenario 1 and Scenario 4, respectively. From Figure 9, the following related issues can be identified. Firstly, the energy distribution in the park is fixed, and the operational status of the workshops has not been adjusted accordingly based on external factors such as fluctuations in energy prices. This may result in the park being unable to flexibly respond to price changes when purchasing energy, thus failing to minimize energy procurement cost to the greatest extent possible. Secondly, distributed energy has not been fully utilized in the park. Distributed energy refers to the energy generated within the park, such as solar energy, wind energy, etc., which is beneficial for reducing external energy purchases and carbon emissions. The above indicates that the park has potential efficiency losses in energy consumption.

On the contrary, the model proposed in this paper addresses these issues. As shown in Figure 10, the WT dispatch their electrical power during the valley period. This decision is driven by the fact that the amount of carbon emissions exceeding the allocated quota of the WT is negative, implying that it can offset the surplus carbon emissions. Although the operational cost of the WT is higher than purchasing electricity from the grid during the valley period, factoring in the cost of carbon trading ultimately results in superior economic benefits. Furthermore, the maintenance cost of the WT is lower than procuring electricity from the main power grid during peak and flat periods. Consequently, the IES prioritizes the dispatch of the WT to provide energy. In summary, the WT operate at full load throughout all periods.

The BA significantly contribute to “peak shaving and valley filling” throughout the entire scheduling cycle. They charge during the valley period from 5:00 to 7:00 and discharge during peak periods, capitalizing on the price differential between peak and valley electricity rates to curtail system operating cost. The HST play a pivotal role in “peak load compensation” across the scheduling cycle. The workshops are efficiently dispatched to the valley period, and their operation, which operates at or near the rated power of the GT, GB and CFU, may not fully meet the system’s heat energy demand. In this scenario, the HST operate in a discharging state to fulfill the additional heat energy demand.

In the flat periods from 8:00 to 10:00 and 16:00 to 18:00, the electricity supply is primarily sourced from the GT, WT, and PV. During this timeframe, the GT, GB and CFU provide thermal energy. Conversely, during the peak periods from 11:00 to 15:00 and 19:00 to 20:00, the cost of electricity generation from distributed energy sources, such as the PV and WT, is lower than that from the main power grid. As a result, the scheduling strategy obtained maximizes the utilization of these distributed energy sources, thereby reducing the electricity demand from the main power grid.

4.5. Inventory Analysis

Figure 11 illustrates the changes in intermediate product inventory for each hour after the scheduling of the three factories. During the valley periods from 1:00 to 2:00, the inventory levels of the storage warehouse of the PAW in Factory 11 significantly decreased. This is because, during these periods, Factory 2 transfers a portion of semi-finished products to other factories to alleviate inventory constraints between production workshops in other factories. This is beneficial for scheduling more workshops to operate during the valley periods, further reducing the energy cost of the system. This approach ensures that the factories can meet their daily production targets while effectively responding to the comprehensive energy demand.

4.6. Analysis of Carbon Emissions in Paper Production

After taking into account the carbon trading mechanism, the IES considers two factors. Firstly, for natural gas, the carbon emissions exceeding the allocated quota are relatively small. In this case, the IES will operate two types of energy equipment, namely GB and GT. Secondly, the carbon emissions exceeding the allocated quota for PV and WT are smaller than others, even with negative values for the WT. These can absorb the overall carbon emissions of the industrial park. As a result, the IES prioritizes scheduling the output of these distributed energy sources, leading to a significant reduction in carbon emissions within the industrial park.

Figure 12 provides an overview of the carbon trading volume for Scenarios 1 and 4 across different time periods. As depicted in the figure, it exhibits higher carbon emissions during the price valley period in Scenario 4. This can be attributed to the majority of the paper mill’s operations being scheduled during this period, resulting in significant energy consumption and carbon emissions. Conversely, during the price peak period, carbon emissions decrease significantly for two main reasons. Firstly, the contribution of PV and WT helps reduce carbon emissions in Scenario 4. Secondly, during this period, the operating workshops in every factory have a lower load, resulting in lower carbon emissions. For example, in Scenario 1, the factories in the park adhere to their original plans, and the differences in carbon emissions in these scenarios are primarily due to the workshop operations, which obviously bring high carbon emissions.

Figure 13 illustrates the relationship between the volume of carbon trading and the carbon trading price in the industrial park. The graph reveals that as carbon emissions increase, the cost of carbon trading exhibits an upward trend. Towards the end of the graph, a steep rise in carbon trading cost is evident due to the combination of the highest baseline carbon trading price and a significant volume of carbon emissions. By imposing incrementally higher carbon trading cost, businesses face economic incentives to reduce carbon emissions and explore cleaner, lower-carbon production methods. This mechanism serves as a driver for carbon reduction and contributes to the realization of sustainable development goals.

5. Conclusions

In this paper, through an analysis of the paper production process and the parallel production constraints within supply chain coupling, an economic scheduling model based on stepped carbon trading is established to optimize the operation of the IES within a paper-making park. To demonstrate the effectiveness of this model, we selected a paper cluster industrial park as an example simulation, which resulted in the reduction of overall cost by 13.46% and overall carbon emissions by 28.658 tons. With the consideration of supply chain coupling, factories can flexibly adjust workshop operations and maximize energy utilization. The introduction of a stepped carbon trading mechanism results in reduced carbon emissions and an overall decrease in operating cost within the paper industry park. This strategy effectively enhances both the economic and low-carbon dimensions of energy utilization within the pulp and paper industry and promotes the development of the industry in a more environmentally friendly and sustainable direction.

Since various industrial production links are different, the supply chain is complex, and the load characteristics vary greatly, this paper only studies the paper-making industry. Future research endeavors may include applying the model to other types of industries, and further refining the model and operational constraints of the IES to ensure its practicality in real-world applications.