Optimal operation of energy-intensive load considering electricity carbon market

Abstract

Energy-intensive load benefits from low electricity tariff and carbon emission, since they occupy certain amounts in the total cost of the product. This paper considers energy-intensive load participation in the electricity as well as carbon trading to reduce the cost. Firstly, an electricity-carbon model is established based on the correlation value method to calculate the carbon emissions of energy-intensive load based on their electricity consumption to realize the carbon amount. Afterwards, the baseline method is used to allocate free carbon emission quotas to energy-intensive load and a reward-penalty carbon trading price mechanism considering offset is proposed. Next, the objective function to achieve maximum benefits, and to reduce output fluctuation, and to improve new energy accommodation is proposed. The case studies show that, by comparing multi-objective function optimization, the optimization target proposed in this paper can effectively reduce wind power output fluctuations and improve wind power accommodation. Through the total participation in carbon trading and electricity market income, multi-objective optimization can increase the system income while ensuring that energy-intensive load meets production requirements under the premise of reducing carbon emissions, verifying the effectiveness of the low-carbon optimal operation model proposed in this paper.

1. Introduction

Motivated by “dual carbon” goals, the transition to low-carbon energy has been deeply promoted. At the same time, the large-scale introduction of new energy sources into the power grid realizes “clean replacement”, and the proportion of traditional thermal power units is reduced. In balancing load changes, it is necessary to balance fluctuations in the output of new energy sources; however, system regulation capacity is severely insufficient.

Energy-intensive load has become the main targets for carbon reduction due to their high energy consumption and high emission characteristics in the context of “dual carbon” goals and the construction of new power systems. Energy-intensive load has a large electricity consumption and there is a strong correlation between electricity consumption and electricity price, which has great adjustment potential [[1], [2], [3]]. From the perspective of power system stability, energy-intensive load has large individual capacities and strong controllability, with huge power regulation potential. For energy-intensive load, participating in the carbon trading market can promote the development of energy conservation and emission reduction technologies, driving industrial green transformation; economic benefits can be obtained to reduce the production costs resulting from high energy consumption.

Currently, scholars at home and abroad have conducted extensive research on energy-intensive load scheduling models. Chen et al. [4] established a load control potential assessment system based on industrial user load data, considering different time scales of load control methods. Bao et al. [5] proposed a new way to coordinate ASL with thermal power units to quickly stabilize isolated power systems with wind power fluctuations or wind curtailment. Jin et al. [6] proposed an LDG system scheduling method for steel industry based on granular causality. Dehghan-Dehnavi et al. [7] classified different industrial processes and provided effective indicators to validate the influence of different incentive programs on industrial customers. Cui et al. [8] extracted the data features of industrial parks through convolutional neural networks and adopted an improved deep learning model to decompose load data and extract potential relationships. Golmohamadi et al. [9] analyzed the load characteristics of cement enterprises and established a mathematical model to optimize the regulation of industrial sub-processes. Zhang et al. [10] analyzed the demand–response potential of electric arc furnace load in steel plants and established the corresponding optimization dispatch model to realize demand–response by regulating the power consumption of an electric arc furnace.

Currently, there is few research on the participation of energy-intensive load in electricity markets. Most studies focus on load aggregation operators participating in markets and peak shaving by load. For example, Yan [11] investigated the problem of minimizing total energy consumption in a two-machine Bernoulli line with a lower limit of machine efficiency and a lower limit of upper limit, Cai et al. [12] proposed a multi-objective coordinated dispatching method for wind power utilization considering the energy-intensive load regulation model to ensure the benefits of the power system and energy-intensive load, Zhang et al. [13] proposed a multitimescale coordinated adaptive robust operation approach where manufactory load allocation and iMEMG operation are optimally coordinated on different timescales. Han et al. [14] proposed a load participation system peak regulation control model considering spot market risks. Jing et al. [15] compared the market rules for adjustable load participating in services in China. Yang et al. [16] proposed a robust optimization strategy that considers electricity price uncertainty. Hu et al. [17] established a bidding model for load aggregation operators participating in electricity markets. Li et al. [18] proposed a complementary peak-shaving strategy for battery energy storage systems. Wang et al. [19] proposed an interruptible load peak shaving model. However, these studies ignore that load can provide multiple services. There is also few research on energy-intensive load, which mostly focuses on adjustable load or interruptible load.

For the participation of energy-intensive load in carbon trading, Wang et al. [20] proposed a two-stage scheduling model to comprehensively investigate the environmental benefits of consumers participating in both electricity and carbon emission trading markets. Yuan et al. [21] considered energy-intensive load participation in demand–response and established a “source-load” dual-side complementary coordination optimization dispatch model combining green certificate trading and carbon trading systems. Fang et al. [22] established a Stackelberg game model to identify the optimal manufacturing/remanufacturing decisions made by chain members, and compared the impacts of two different carbon allowance allocation rules on the optimal production decisions and profits, and on the environment.

Some studies have been conducted on the optimal operation of energy-intensive load by scholars both domestically and internationally. Yong et al. [23] considered demand-side load response and renewable energy uncertainty, developing a multi-objective “source-grid-load” coordinated optimization scheduling model to minimize operation cost, maximize user satisfaction and renewable energy accommodation. Conteh et al. [24] analyzed industrial load demand data to propose an interruptible demand response scheme for maximum demand index users incorporating elastic pricing concepts. It performed an economic analysis on system impacts including energy consumption, user incentives, benefits, penalties and load demand effects. The study further optimized the energy management of grid-connected battery energy storage and PV hybrid systems. Tan et al. [25] put forward a mixed integer linear programming based self-generation and load scheduling model for industrial load that took into account carbon emission permits and time-of-use electricity prices. The model incorporated electricity cost and carbon trading cost in the optimization objectives. Allman and Zhang [26] developed an optimal operation model for energy-intensive load cooperating with customers in demand response. It allowed industrial production to reduce costs by utilizing time-of-use electricity prices through providing economic incentives to customers to change their ordering schedules. Zhang et al. [27] addressed the limitation of discrete power variation industrial load providing services. It proposed methods using on-site energy storage systems to realize industrial load providing regulation or load tracking functions to overcome such discrete regulation restrictions. Zhang et al. [28] developed a multi-timescale coordinated adaptive robust operation method to mitigate the increase in operating costs and shortage of energy supply caused by renewable energy generation uncertainty. It performed industrial multi-energy microgrid operation optimization at an hourly timescale within a week, with industrial load and cogeneration units optimized at a weekly timescale in advance. Wang et al. [29] believed that it was important to study the energy quality distribution and characteristics of the system based on the characteristics of IES energy network to optimize and improve the effective energy supply capacity of the system.

As a summary, the above studies have provided crucial insights into understanding the characteristics and potential regulatory capabilities of energy-intensive load. However, the papers have primarily focused on the involvement of load in markets and peak adjustments, overlooking their potential in providing multiple ancillary services. This underscores the significance of diversified load service research and weakens the market incentives for energy-intensive load benefit promotion. While these papers reveal the potential advantages of energy-intensive load, they also emphasize the gap in research on their multifunctional applications. Therefore, it is necessary to delve deeper into exploring the diverse applications of energy-intensive load in various markets and service domains to fully tap into their potential.

To address the above deficiencies, this paper proposes an optimal low-carbon optimal operation method for energy-intensive load considering carbon trading. The main contributions are as follows:

• 1)This paper establishes an optimal operation model for energy-intensive load participation in interactive transactions, considering the internal load characteristics by proposing an electricity-carbon modeling method based on correlation values for energy-intensive load.
• 2)The low-carbon optimal operation model aims at achieving the maximum benefits from overall participation in electricity and carbon markets, minimizing new energy output fluctuations, and maximizing the new energy accommodation rate.
• 3)This paper compares the participation of energy-intensive load in carbon trading, considering reward-penalty and offset mechanisms, and alongside scenarios of non-participation. It verifies that the carbon trading mechanism used in this paper is more conducive to reducing the carbon emissions of energy-intensive load compared to traditional carbon trading mechanisms.

The rest of this paper is organized as follows. Section 2 establishes an energy-intensive load electricity-carbon model. Section 3 proposes a scheduling model for low-carbon optimized operation with energy-intensive load. Section 4 provides a comparative analysis of the seven scenarios. Section 5 discusses and analyzes this paper with previous papers. Finally, section 6 concludes the article.

2. Energy-intensive load electricity–carbon model

2.1. Energy-intensive load electricity-carbon model

Energy-intensive load refers to a load that consumes resources quickly and requires a large amount of resources compared to other load. Generally speaking, the load of enterprises with an annual energy consumption of more than 5,000 tce in iron and steel, nonferrous metals, building materials, petroleum processing and coking, chemical industry, and electricity is recognized as energy-intensive load.

When building the scheduling model, the power characteristics of the power equipment in the energy-intensive load is analyzed. The power equipment in the energy-intensive load is classified into adjustable load and non-adjustable load according to whether it can be adjusted. The adjustable load is further classified into continuously adjustable load and discretely adjustable load according to whether their power output can be continuously adjusted.

• 1)Continuously adjustable load

Continuously adjustable load refers to load that can continuously increase or decrease their active power within the adjustable range, adjust product production, and can be shut down for a limited time without damaging the equipment.

i indicates the i-th continuously adjustable load in the energy-intensive load. The scheduling model for continuously adjustable load is established as follows:

The relationship between the start–stop state variables, start variables and stop variables of the continuously adjustable load is as follows eq. (1):

$$\{\begin{array}{c}{z}_{i,t-1}^C-z_{i,t}^C+u_{i,t}^C⩾0\\ z_{i,t}^C-z_{i,t-1}^C+v_{i,t}^C⩾0\end{array}$$ (1)

The variables $z_{i,t}^C$、 $u_{i,t}^C$、 $v_{i,t}^C$ in the formulas are 0–1 integer variables, representing the start–stop state variable, start variable, and stop variable, respectively.

The minimum run time and minimum shut down time of the energy-intensive load are shown in eq. (2) and eq. (3):

$$\{\begin{array}{c}{z}_{i,t}^C-z_{i,t-1}^C\le z_{i,\tau }^C\\ \tau \in \left[t+1,\min \left(t+T_{i,\min On}^C-1,T\right)\right]\end{array}$$ (2)

$$\{\begin{array}{c}{z}_{i,t-1}^C-z_{i,t}^C\le 1-z_{i,\tau }^C\\ \tau \in \left[t+1,\min \left(t+T_{i,\min O\text{ff}}^C-1,T\right)\right]\end{array}$$ (3)

where $T_{i,\min On}^C$ is the minimum run time; T is the total time length of the optimization scheduling period; and $T_{i,\min Off}^C$ is the minimum shut down time.

Interrupting the operation can only be carried out when the load is running, as shown in eq. (4):

$$z_{i,t}^C-w_{i,t}^C⩾0$$ (4)

where $w_{i,t}^C$ is the interrupt variable.

The relationship between the longest interruption allowed to continue and the maximum number of interruptions allowed in an optimization period is shown in eq. (5):

$$\{\begin{array}{c}\sum _{\tau =k}^{k+T_{i,MaxCut}^C+1}{w}_{i,\tau }^C⩽T_{i,MaxCut}^C\\ \sum _{\tau =1}^T{w}_{i,\tau }^C⩽N_{i,MaxCut}^C\end{array}$$ (5)

where $T_{i,MaxCut}^C$ is the longest interruption allowed duration, and $N_{i,MaxCut}^C$ is the maximum number of interruptions allowed in a scheduling period.

The relationship between the load power and its participation in auxiliary services markets for peak shaving, frequency regulation and reserves is shown in eq. (6):

$$\{\begin{array}{c}{P}_{i,t}^C=p_{i,t}^C-q_{i,t}^{C,fup}-q_{i,t}^{C,pup}-q_{i,t}^{C,b}⩾z_{i,t}^C{P}_{i,\min }^C\\ P_{i,t}^C=p_{i,t}^C+q_{i,t}^{C,fdown}+q_{i,t}^{C,pdown}⩽z_{i,t}^C{P}_{i,\max }^C\end{array}$$ (6)

where $p_{i,t}^C$, $q_{i,t}^{C,fup}$, $q_{i,t}^{\mathrm{C},fdown}$, $q_{i,t}^{C,pup}$, $q_{i,t}^{C,pdown}$, $q_{i,t}^{C,b}$, respectively represent the active consumption power and peak shaving, upward and downward frequency regulation and reserve services active power provided by the continuously adjustable load at time t. and $P_{i,\min }^C$ and $P_{i,\max }^C$ are the minimum and maximum active consumption power of this load, respectively.

The power limits of the load are shown in eq. (7):

$$P_{i,t}^C-P_{i,t-1}^C\ge \left(P_{i,\min }^C-U_i^C\right)z_{i,t}^C-P_{i,\min }^C-M{w}_{i,t}^C$$ (7)

where $U_i^C$ is the maximum ramping capacity of the continuously adjustable load.

When the continuously adjustable load interrupts the operation, the relationship between its active consumption power, peak shaving, frequency regulation and reserve power is shown in eq. (8):

$$\{\begin{array}{c}{p}_{i,t}^C⩽\left(1-w_{i,t}^C\right)M\\ 0⩽q_{i,t}^{u,fup}⩽\left(1-w_{i,t}^C\right)M\\ 0⩽q_{i,t}^{C,fdown}⩽\left(1-w_{i,t}^C\right)M\\ 0⩽q_{i,t}^{C,pup}⩽\left(1-w_{i,t}^C\right)M\\ 0⩽q_{i,t}^{C,pdown}⩽\left(1-w_{i,t}^C\right)M\\ 0⩽q_{i,t}^{C,b}⩽\left(1-w_{i,t}^C\right)M\end{array}$$ (8)

M is a parameter introduced for linear constraint relaxation processing, which usually takes a sufficiently large number.

• 2)Discretely adjustable load

The power consumption of some load in energy-intensive load industrial enterprises cannot be adjusted, such as the case with metal smelting furnaces and monocrystalline silicon refining furnaces. Although the power consumption of individual load cannot be adjusted, the number of startup load can be increased or decreased, and the time of load startup can be changed. This paper refers to this type of load as a discretely adjustable load. This type of load cannot provide frequency regulation and reserves for the system but can provide peak shaving services for the system by changing the operating time of the load.

j represents the j-th discretely adjustable load in energy-intensive load. Based on the characteristics of discretely adjustable load, the scheduling model is established as follows:

The relationship between the start–stop state variable, start variable and stop variable of the energy-intensive load is shown in eq. (9):

$$\{\begin{array}{c}{z}_{j,t-1}^D-z_{j,t}^D+u_{j,t}^D⩾0\\ z_{j,t}^D-z_{j,t-1}^D+v_{j,t}^D⩾0\end{array}$$ (9)

In eq. (9) $z_{j,t}^D$、 $u_{j,t}^D$、 $v_{j,t}^D$ are 0–1 variables, representing the start–stop state variable, start variable and stop variable of the discretely adjustable load, respectively. When the value of these variables is 1, it represents that the discretely adjustable load is in the running state, start state and stop state at time t, respectively.

The relationship between the minimum run time and minimum shut down time of the energy-intensive load is shown in eqs. (10), (11):

$$\{\begin{array}{c}{z}_{j,t}^D-z_{j,t-1}^D\le z_{j,\tau }^D\\ \tau \in \left[t+1,\min \left(t+T_{j,\min On}^D-1,T\right)\right]\end{array}$$ (10)

$$\{\begin{array}{c}{z}_{j,t-1}^D-z_{j,t}^D\le 1-z_{j,\tau }^D\\ \tau \in \left[t+1,\min \left(t+T_{j,\min O\text{ff}}^D-1,T\right)\right]\end{array}$$ (11)

where $T_{j,\max O\text{ff}}^D$ and $T_{j,\min O\text{ff}}^D$ represent the minimum run time and minimum shut down time of each discretely adjustable load, respectively.

The startup order of each discretely adjustable load in the energy-intensive load is shown in eq. (12):

$$z_{j,t}^D⩽z_{j-1,t}^{D}j=2,3,\cdots ,J^D$$ (12)

Eq. (12) represents the number of discretely adjustable load in the energy-intensive load.

Eq. (13) constraints its participation in peak shaving as follows:

$$\{\begin{array}{c}{p}_{j,t}^D-q_{j,t}^{D,fup}⩾z_{j,t}^D{P}_{j,\min }^D\\ p_{j,t}^D+q_{j,t}^{D,fdown}⩽z_{j,t}^D{P}_{j,\max }^D\end{array}$$ (13)

where $p_{j,t}^D$, $q_{j,t}^{D,fup}$, $q_{j,t}^{D,fdown}$ represent the power consumption and peak shaving power provided to the grid by the discretely adjustable load at time t, respectively.

Since the research object of this paper is the optimized operation of energy-intensive load, non-adjustable load cannot participate in optimized operation through changing power consumption and start–stop time due to their inherent power consumption characteristics. Therefore, the optimization object of this paper does not include non-adjustable load and does not consider the scheduling model of non-adjustable load.

2.2. Energy-intensive load carbon model

In this study, we conducted an analysis of carbon emissions in energy-intensive enterprises based on carbon emission factor methods, encompassing the overall carbon emissions of the enterprises rather than solely focusing on the emissions from the electricity sector.

According to the Guidelines for Accounting and Reporting Greenhouse Gas Emissions from 24 Key Industrial Sectors issued by the National Development and Reform Commission, the sources of carbon emissions in the carbon accounting of industrial enterprises include emissions from fossil fuel combustion, process emissions from industrial production, and the implied CO₂ emissions from the purchased electricity and heat produced by the enterprise.

The calculation of total carbon emissions is shown in eq. (14):

$$E_{C{O}_2}=E_{fuel}+E_{pro}+E_{el}+E_{heat}$$ (14)

In eq. (14), $E_{C{O}_2}$ represents the total carbon emissions of the enterprise, and $E_{fuel}$ represents the carbon dioxide emissions generated from the combustion of fossil fuels, which includes: The emissions generated from the combustion of fuels such as diesel, gasoline or natural gas that are used in production processes. The emissions generated from the combustion of fuels used by auxiliary production facilities such as vehicles for internal transportation, boilers, etc. The calculation formula is shown in eq. (15):

$$E_{fuel}=\sum _{i=1}^{n}A{D}_{fuel}^i\times E{F}_{fuel}^i$$ (15)

In eq. (15), $A{D}_{fuel}^i$ represents the activity level of the i-th fossil fuel, and $E{F}_{fuel}^i$ represents the carbon dioxide emission factor of the i-th fossil fuel.

$E_{pro}$ represents the carbon dioxide emissions generated from industrial production processes, i.e., the greenhouse gas emissions caused by physical or chemical changes in the raw materials during production processes. The sources include: the emissions generated from the use of carbonates in production processes and the CH₄ emissions generated from the anaerobic treatment of industrial wastewater, as shown in eq. (16):

$$E_{pro}=E_{cbn}+E_{wt}=\sum _{i=1}^{n}A{D}_{cbn}^i\times E{F}_{cbn}^i\times PU{R}_{cbn}^i+TOW\times E{F}_{wt}\times {10}^{-3}$$ (16)

where $E_{cbn}$ and $E_{wt}$ represent the emissions generated from the use of carbonates and CH₄ emissions produced from the anaerobic treatment of industrial wastewater in production processes, respectively. $A{D}_{cbn}^i$ represents the total consumption of carbonate i used as raw materials, desulfurizers, etc., in tons. $E{F}_{cbn}^i$ represents the carbon dioxide emission factor of carbonate i in tons: CO₂/ton of carbonate I. $PU{R}_{cbn}^i$ represents the purity of carbonate i in terms of percentage by mass. TOW represents the total amount of degradable organic matter in industrial wastewater, quantified through the application of chemical oxygen demand (COD) in kg COD. $E{F}_{wt}^i$ represents the CH₄ emission factor from the anaerobic treatment of industrial wastewater in kg: CH₄/kg COD.

The calculation formula for TOW is shown in eq. (17):

$$TOW=W\times \left(CO{D}_{in}-CO{D}_{out}\right)$$ (17)

where W represents the volume of industrial wastewater treated anaerobically in units of m³ wastewater/year. $CO{D}_{in}$ and $CO{D}_{out}$ represent the average COD concentrations of wastewater entering and leaving the anaerobic treatment system, respectively, in units of kg COD/m³ of wastewater.

The calculation methods used for the carbon emissions of E3 and E4, corresponding to the net purchased electricity and heat, respectively, are shown in eq. (18):

$$\{\begin{array}{c}{E}_{el}=A{D}_{el}\times E{F}_{el}\\ E_{heat}=A{D}_{heat}\times E{F}_{heat}\end{array}$$ (18)

where $A{D}_{el}$ and $A{D}_{heat}$ represent the net purchased electricity and heat (such as steam), respectively. $E{F}_{el}$ and $E{F}_{heat}$ represent the carbon emission factors of electricity and heat (such as steam), respectively.

2.3. Reward-penalty carbon trading price mechanism

The stepped carbon trading price mechanism sets multiple intervals for purchasing carbon emissions quotas, where the more emissions quotas purchased, the higher the corresponding purchase price. The stepped pricing structure promotes rational production and carbon emission planning among enterprises, effectively encouraging them to reduce carbon emissions. This study establishes a stepped model for carbon trading costs considering reward-penalty mechanism, dividing the carbon emission costs into two parts based on enterprise emissions:

When an enterprise's carbon emissions are less than its emission quotas, it can sell surplus quotas for profit, resulting in a negative carbon trading cost for this portion. Multiple emission intervals are set with stepped pricing, incorporating compensation coefficients for emissions below the quota. Lower emissions yield higher profits for the enterprise, incentivizing emissions reduction.

If an enterprise's carbon emissions exceed its quotas, the excess emissions incur costs within multiple intervals, implementing penalty coefficients with stepped pricing. Higher emissions lead to higher carbon trading prices.

The expression for stepped carbon trading costs is as follows eq. (19):

$$f_C=\{\begin{array}{c}-\sigma \left(2+3y\right)d+\sigma \left(1+3y\right)\left(E_L-E_{qL}+2d\right),E_L\le E_{qL}-2d\\ -\sigma \left(1+y\right)d+\sigma \left(1+2y\right)\left(E_L-E_{qL}+d\right),E_{qL}-2d\le E_L\le E_{qL}-d\\ \sigma \left(1+y\right)\left(E_L-E_{qL}\right),E_{qL}-d\le E_L\le 0\\ \sigma \left(E_L-E_{qL}\right),0\le E_L\le E_{qL}+d\\ \sigma d+\sigma \left(1+x\right)\left(E_L-E_{qL}-d\right),E_{qL}+d\le E_L\le E_{qL}+2d\\ \sigma \left(2+x\right)d+\sigma \left(1+2x\right)\left(E_L-E_{qL}-2d\right),E_{qL}+2d\le E_L\end{array}$$ (19)

where $E_L$ represents the carbon emissions of energy-intensive -consuming enterprises after offsetting, $E_{qL}$ represents the allocated carbon emission quotas for energy-intensive -consuming enterprises, $\mathit{\sigma }$ represents the base carbon trading price, x signifies the penalty factor for tiered carbon trading, set to 0.25 in this paper, $\mathit{y}$ denotes the compensation coefficient for tiered carbon trading, set to 0.2 in this paper, and $\mathit{d}$ stands for the interval length of carbon emissions, set to 200t in this paper.

3. Energy-intensive load optimization scheduling model

The main research content related to energy-intensive load low-carbon optimized operation under the conditions of carbon trading and their interrelationships are summarized in Fig. 1.

Fig. 1.

Research framework.

3.1. Objective function

In the first stage, a multi-objective optimization is performed, where the objective function is obtained by weighting and summing three single-objective optimization objectives, as shown in eq. (20):

$$\max F_1={\omega }_1{f}_1-{\omega }_2{f}_2+{\omega }_3{f}_3$$ (20)

where $f_1$, $f_2$ and $f_3$ represent the new energy accommodation rate, P ${\omega }_1$、 ${\omega }_2$ and ${\omega }_3$ are the weighting factors of the three objective functions. And the values of all three weighting factors are $\frac{1}{3}$.These values should be chosen to minimize the relative difference between ${\omega }_1{f}_1$、 ${\omega }_2{f}_2$ and ${\omega }_3{f}_3$ while maximizing and minimizing the secondary objectives of new energy accommodation rate and power fluctuations in new energy sold to the grid, respectively.

In the first stage of day-ahead optimization, the objective function is to maximize the accommodation rate of new energy sources, as shown in eq. (21):

$$\max f_1={\eta }_W=\frac{\sum _{t=1}^T{P}_{W,G}^t\Delta t}{\sum _{t=1}^T{P}_W^t\Delta t}$$ (21)

where ${\eta }_W$ represents the accommodation rate of new energy, which is the ratio of the electricity consumed by new energy sources to their actual electricity generation at time t, $P_W^t$ is the actual power generation of new energy at time t, and $P_{W,G}^t$ is the power consumed by new energy sources at time t, which is calculated as shown in eq. (22):

$$P_{W,G}^t=P_{W,sell}^t+P_{W,ES}^t+P_{W,L}^t$$ (22)

where $P_{W,sell}^t$, $P_{W,ES}^t$ and $P_{W,L}^t$ respectively indicate the power that renewable energy is sold to the grid at time t, stored by energy storage, and supplied to high-capacity enterprises, respectively.

The objective function is the smallest fluctuation in the power sold by new energy sources to the grid, as shown in eq. (23):

$$\min f_2=\sum _{t=1}^T{\left(P_{W,sell}^t+P_{ES,W}^t-\overline{P_G}\right)}^2$$ (23)

where $P_{ES,W}^t$ represents the electricity sold to the grid together with new energy sources in terms of energy storage in order to balance fluctuations in the output of new energy sources, while $\overline{P_G}$ represents the average power sold to the grid by new energy sources and energy storage within the scheduling period, which is calculated as shown in eq. (24):

$$\overline{P_G}=\frac{1}{T}\sum _{t=1}^T{P}_{W,sell}^t+P_{ES,W}^t$$ (24)

The objective function is used to maximize the overall profit of energy-intensive load, energy storage, and new energy sources, which is composed of the revenue obtained from participating in the electricity market, the revenue obtained from participating in markets, and the anticipated carbon trading cost for the operating day, as shown in eq. (25):

$$\max f_3=C_{pv}+C_g+C_p+C_f+C_b+C_W-f_{C{O}_2}$$ (25)

where C_pv and C_g represent the revenue obtained from participating in the electricity market in terms of energy-intensive load and energy storage through price differences and absorbing new energy curtailment. C_p、C_f and C_b represent the revenue obtained from energy-intensive load and energy storage participating in markets by providing frequency regulation, peak shaving, and reserve services. C_W represents the revenue obtained from new energy power plants participating in the electricity market. $f_{C{O}_2}$ represents the carbon trading cost for energy-intensive load.

Day-ahead optimization involves obtaining the wind power generation curve, the declared output of energy-intensive load and energy storage participating in markets, as well as the next day's operation plan for energy-intensive load and energy storage.

In the second stage of intra-day optimization, the objective function is used to maximize the overall profit of energy-intensive load, energy storage, and new energy, which is composed of the revenue obtained from participating in the electricity market, deviation penalty costs, and actual carbon trading costs, as shown in eq. (26):

$$\max f_4=C_{pv}+C_g+C_W-f_C-f_{C{O}_2}$$ (26)

where C_pv and C_g represent the revenue obtained from participating in the electricity market in terms of energy-intensive load and energy storage through price differences and absorbing new energy curtailment. f_C represents the deviation penalty for the declared output, as shown in eq. (27):

$$f_c={\alpha }_W\sum _{t=1}^T\left|P_{W_1}^t-P_{W_0}^t\right|$$ (27)

where ${\alpha }_W$ is the penalty coefficient for wind power output deviation, and $P_{W_1}^t$ and $P_{W_0}^t$ represent the actual and declared wind power outputs, respectively.

3.2. Constraints

The power constraints for energy-intensive load and their participation in various electricity markets are the same as those described in Section 1.1. In addition, the production output constraints for energy-intensive load are shown in eq. (28):

$$\begin{array}{c}\{\begin{array}{c}{c}_i^{\mathrm{C}}=\sum _{t=1}^T\frac{p_{i,t}^{\mathrm{C}}}{{\eta }_i^{\mathrm{C}}}\\ c_i^D=\sum _{t=1}^T\frac{p_{i,t}^D}{{\eta }_i^D}\end{array}\\ \{\begin{array}{c}{c}_{iorder}^C\le c_i^C\le c_{i\max }^C\\ c_{iorder}^D\le c_i^D\le c_{i\max }^D\end{array}\end{array}$$ (28)

The wind power constraints are shown in eq. (29):

$$P_{W\min }\le P_{W,sell}^t+P_{ES,W}^t\le P_{W\max }$$ (29)

where $P_{W\min }$ and $P_{W\max }$ are the maximum and minimum power of wind power connected to the grid, respectively.

The energy storage constraints are shown in eq. (30):

$$-P_{ES\max }\le {P_{ES}}^t\le P_{ES\max }$$ (30)

• 1)State-of-charge constraints

The state of charge of energy storage is the ratio of the remaining energy storage capacity to the rated capacity, as shown in eq. (31):

$$SO{C}^t=\frac{E^t}{E_N}$$ (31)

where E_N is the energy storage system capacity of the new energy power station at time t, which is the total capacity of the energy storage system equipped by E_N for the new energy power plant.

In energy storage operations, in order to avoid a reduction in energy storage life caused by overcharging and discharging, the state of charge of the constrained energy storage is shown in eq. (32):

$$SO{C}_{\min }\le SO{C}^t\le SO{C}_{\max }$$ (32)

where $SO{C}_{\min }$ is the minimum state of charge of energy storage, $SO{C}_{\max }$ is the maximum state of charge of energy storage, and $SO{C}^t$ is the state of charge of energy storage at the time of t. The calculation formula is shown in eq. (33):

$$SO{C}^t=SO{C}^{t-1}+\frac{P_{ES}\Delta t}{E_N}$$ (33)

where P_ES is the period from t-1 to t, which is the charging and discharging power of the energy storage system, and P is positive for energy storage charging, and negative for vice versa. The total capacity of the energy storage system equipped by E_N for the new energy power plant is shown below.

• 2)Energy storage charge and discharge constraints

The power constraints of energy storage charging and discharging are shown in eq. (34):

$$-P_{ES\max }\le P_{ES}^t\le P_{ES\max }$$ (34)

where $P_{ES\max }$ is the maximum charging and discharging power of energy storage.

• 3)Energy storage purchase and sales status constraints

In order to prevent the contradiction between the purchase and sale of electricity from energy storage to the market and the charging and discharging behavior in the exchange with new energy power stations and high load power in the same time period, the purchase and selling coefficients of energy storage are constrained to avoid the occurrence of both charging and discharging energy storage in the same time period, and the constraints are shown in eq. (35) and eq. (36):

$$\{\begin{array}{c}{u}_{buy}^t=0,P_{\text{ES},\mathrm{G}}^t>0\\ u_{buy}^t=1,others\end{array}$$ (35)

$$\{\begin{array}{c}{u}_{sell}^t=0,P_{\text{ES},\mathrm{G}}^t<0\\ u_{sell}^t=1,others\end{array}$$ (36)

where $u_{buy}^t$ is the energy storage purchase coefficient, $u_{buy}^t$ is an integer variable of 0–1. $u_{buy}^t$ value of 0 means that the energy storage facility does not buy electricity at time t, and vice versa if it is 1. $u_{sell}^t$ is the energy storage selling coefficient, 0 means that the energy storage facility does not sell electricity at the t moment, and 1 is vice versa.

4. Example analysis

In the case study, let us consider a paper manufacturing company to establish a scheduling model. For this company, the paper machine and the crane are continuous adjustable loads, while the pulping machine and grinding machine are discrete adjustable load. The rated power for the electrical equipment is as follows: one paper machine with a rated power of 20 MW, one crane with a rated power of 10 MW, one pulping machine with a rated power of 5 MW, and one grinding machine with a rated power of 5 MW. The specific parameters are given below:

The maximum operating power for the paper machine is 30 MW, the minimum operating power is 15 MW, the maximum ramping rate is 10 MW/h, the minimum running time is 3 h, the minimum downtime is 3 h, the longest interruption time is 2 h, and the maximum number of interruptions is 4 times. The maximum operating power for the crane is 15 MW, the minimum operating power is 5 MW, the maximum ramping rate is 5 MW/h, the minimum running time is 3 h, the minimum downtime is 3 h, the longest interruption time is 2 h, and the maximum number of interruptions is four times. The parameters for the pulping machine and grinding machine are the same: a rated power of 5 MW, a minimum running time of 5 h, and a minimum downtime of 5 h.

In this case, based on the actual installed capacity of a paper company, the wind power capacity is 80 MW, and it is complemented by a 50 MWh battery energy storage system. The multi-objective optimization of energy-intensive load considering carbon trading in the electricity market in this study is solved using MATLAB with the CPLEX solver.

The electricity price is set as peak–flat–valley electricity price, and the price curve is shown in Fig. 2. Periods 1–7 and 24 are in the valley period, periods 8–10, 16–18, and 22–23 are in the flat period, and periods 11–15 and 19–21 are in the peak period.

Fig. 2.

Peak-to-valley tariff.

4.1. Analysis of the impact of carbon trading mechanism

Selecting the electricity consumption, production output, and carbon emissions of the company for the previous 12 months, the models for electricity-to-carbon emissions, electricity-to-production output, and production output-to-carbon emissions are established after removing anomalous data in terms of unit product energy consumption and unit product electricity consumption. These three models are then integrated to obtain the electricity-to-carbon emissions model for the company, as shown in Fig. 3.

Fig. 3.

Electricity carbon model of a paper enterprise.

The electricity-carbon model excludes a set of monthly data after data processing, and the coefficient of determination R² is 0.9622. It can be used to predict carbon emissions when optimizing the operation of energy-intensive load. The calculation of carbon emissions in this case study is obtained by using this electricity–carbon model.

To verify the rationality and effectiveness of the carbon pricing mechanism considering the reward–penalty and offset mechanisms proposed in this chapter, four scenarios are designed to compare the commonly used stepped carbon pricing mechanism and the traditional carbon pricing mechanism. In the calculation of carbon emission costs, the carbon emissions are calculated based on the electricity consumption input into the electricity–carbon model as mentioned above. The four scenarios are defined as follows:

Scenario 1: Energy-intensive load participating in carbon trading with reward–penalty and offset mechanisms.

Scenario 2: Energy-intensive load participating in carbon trading with a stepped pricing mechanism.

Scenario 3: Energy-intensive load participating in carbon trading with a fixed pricing mechanism.

Scenario 4: Energy-intensive load not participating in carbon trading.

Firstly, the model is solved for Scenario 1 to obtain the optimization results for the ahead and intraday horizons.

Fig. 4(a) and (b) represent the optimization results for the papermaking enterprise and energy storage ahead horizon under Scenario one. From Fig. 4(a), it can be observed that the papermaking enterprise primarily utilizes electricity during off-peak hours and periods of surplus wind power. It tends to absorb wind power curtailment during periods of surplus wind power and predominantly relies on wind power within normal operating ranges. This is because, under a carbon trading mechanism, higher proportions of renewable energy in the electricity source for energy-intensive load lead to lower carbon emissions after offsetting mechanisms, thus reducing carbon trading costs. The papermaking enterprise mainly provides load-shedding services in the market, which helps reduce electricity costs while benefiting from services like peak shaving and frequency regulation. Fig. 4(b) shows that, during the 20–23 timeframe, as energy-intensive load utilize wind power, there is significant fluctuation in grid-connected wind power. Energy storage provides grid-connected electricity for wind power during the 21–23 timeframe, thus balancing wind power fluctuations. In the 0–15 timeframe, energy storage primarily supplies energy-intensive load operations, reducing their electricity costs or benefiting from the market. Energy storage engages less in power purchasing or selling activities, focusing instead on energy consumption and providing benefits. It supplies electricity to energy-intensive load to reduce their electricity purchasing costs during their operations.

Fig. 4.

Optimization results in Scenario 1.

Fig. 4(c) and (d) show the intraday optimization results for the papermaking enterprise and energy storage under Scenario one. Compared to the ahead horizon optimization results, the papermaking enterprise adjusts the operating time and power of certain electrical devices to minimize electricity costs while ensuring the provision of contracted production output. The papermaking enterprise's integration of wind power may have slight differences compared to the ahead horizon optimization results due to discrepancies between actual wind power generation and forecasted values. When the actual wind power output exceeds the previously declared value, such as in the 17–27 and 59–68 timeframes, energy storage absorbs surplus renewable energy and discharges during periods of high electricity prices or energy-intensive load operations, thereby benefiting from energy transfers. During the 81–85 and 90–92 timeframes, when wind power curtailment is relatively low and electricity prices are higher due to peak hours, energy storage provides a portion of the electricity demand for energy-intensive load, reducing their electricity costs. In the 88–92 timeframe, it can be observed that due to wind power output forecasting errors, the actual wind power generation is lower than the previously declared value. Energy storage discharges electricity to increase the grid-connected wind power output and mitigate the penalty for wind power output deviation.

For scenarios two and three, the optimization results produced when participating in the day-ahead electricity market, and carbon trading, as well as participating in the intraday electricity market and carbon trading, are shown in Fig. 5, Fig. 6, Fig. 7, respectively. Fig. 5, Fig. 6, Fig. 7 represent the day-ahead optimization results for a papermaking company under Scenario two, Scenario three, and Scenario four, respectively. Through a comparison with Fig. 3(a), it can be seen that the operating time of the papermaking company is basically the same under the four carbon trading price mechanisms. This is due to the guidance provided by electricity market prices. Fig. 5, Fig. 6, Fig. 7 represent the intraday optimization results for the papermaking company under Scenario two, Scenario three, and Scenario four, respectively. The start–stop time of each piece of equipment is basically the same as the day-ahead results, achieving optimal operation through adjustments in the intraday electricity market. Under the fixed carbon price mechanism, the papermaking company has the highest total electricity consumption, followed by the reward–penalty and offset mechanism, and the least electricity consumption is achieved under the stepped carbon price mechanism. The fixed carbon price mechanism lacks sufficient constraints in terms of carbon emissions, resulting in higher electricity consumption for the company. The stepped carbon price mechanism has stronger constraints in terms of carbon emissions; therefore, the company reduces production to achieve lower carbon emission costs. The introduction of offset mechanisms allows the company to increase electricity consumption while controlling carbon emissions by consuming excess electricity from new energy sources, thus achieving economical low-carbon operation for the company.

Fig. 5.

Optimization results of papermaking enterprises in Scenario 3.

Fig. 6.

Optimization results of papermaking enterprises in Scenario 3.

Fig. 7.

Optimization results of papermaking enterprises in scenario 4.

Table 1 compares the carbon trading costs, carbon emissions, profit, and proportion of new energy electricity consumption for energy-intensive load under three different carbon trading price mechanisms. Comparing scenarios one, two, and three, it can be seen that Scenario three, with a fixed price carbon trading mechanism, has the highest total carbon emissions and carbon emissions from participating in carbon trading. Scenario one, which considers a reward–penalty carbon trading price mechanism considering offset mechanisms, has the lowest carbon emissions from participating in carbon trading, the lowest carbon trading costs, and the highest overall profit. Scenario two, with a stepped carbon trading price mechanism, has the lowest total carbon emissions. By comparing the proportion of new energy electricity consumption to total electricity consumption for energy-intensive load, it can be seen that Scenario one has the highest proportion of new energy electricity consumption. This indicates that considering a reward–penalty carbon trading mechanism and offset mechanisms can better guide companies to reduce carbon emissions and trading costs by using more renewable energy electricity, thereby increasing profits. Compared with Scenario four, which does not participate in carbon trading, it has the highest carbon emissions and the lowest proportion of new energy electricity consumption. Although Scenario four has the highest total profit, it cannot be compared with other scenarios in terms of total profit as it does not have carbon trading costs.

Table 1.

Comparison of different carbon trading mechanisms.

Scenario	Carbon Trading Cost (CNY)	Total Carbon Emissions (tCO2）	Carbon Emissions from Participating in Carbon Trading (tCO2)	Overall Profit (CNY)	Proportion of New Energy Electricity Consumption (%)
1	1018.8	1218.1	203.5	1091.2	29.2
2	1097.8	1205.5	215.6	1058.4	18.3
3	1088.4	1222.6	217.6	1078.1	16.7
4	0	1501.9	225.8	2165.1	15.9

Comparisons of second-stage objective functions in four scenarios are shown in Table 2. Table 2 indicates that Scenario 1 has a higher wind power accommodation rate compared to the other scenarios because it considers offset mechanisms. Energy-intensive load can offset a portion of carbon emissions by using electricity from new energy power plants, thereby reducing carbon trading costs while ensuring maximum wind power accommodation. The overall profit from intraday trading is higher than that from day-ahead trading in all four scenarios, which further confirms that participating in the intraday electricity market can adjust operational plans to achieve maximum profit. Except for Scenario 4, which does not engage in carbon trading, Scenario 1 achieves the highest overall profit. Additionally, according to Table 1, Scenario 1 has the smallest carbon emissions from participating in carbon trading, which demonstrates that the proposed carbon trading mechanism considering reward–penalty and offset mechanisms can reduce carbon emissions while achieving economic goals.

Table 2.

Comparison of objective function.

Scenario	f1 wind power accommodation rate (%)	f2 wind power output fluctuation (MW)	f3 overall profit from day-ahead (CNY)	f4 overall profit from intraday (CNY)
1	91.93	412.75	1023.9	1091.2
2	88.50	470.32	988.2	1058.4
3	89.11	468.03	1012.9	1078.1
4	89.45	435.97	2100.1	2165.1

4.2. Impact analysis of objective functions

In addition to introducing carbon emission trading, two objective functions related to new energy output, namely Equation (20) and Equation (22), are included. These objective functions optimize the output fluctuations and accommodation rate of new energy.

Scenario 5: Objective functions prioritize maximum overall profit and minimum new energy output fluctuations. Scenario 6: Objective functions prioritize maximum overall profit and maximum new energy accommodation rate. Scenario 7: Objective function prioritizes maximum overall profit.

Fig. 8 compares the wind power outputs of Scenario 1, Scenario 5, Scenario 6, and Scenario 7 is the case where the objective functions are the maximum overall profit combined with either minimum new energy output fluctuations or maximum new energy accommodation rate. From the figure, it can be observed that Scenario 1 achieves a balance between low output fluctuations and high accommodation rates. Scenario 5 minimizes output fluctuations but sacrifices a portion of new energy generation. Scenario 6 has higher output fluctuations but achieves a high accommodation rate of new energy. Scenario 7 has the highest output fluctuations with an intermediate accommodation rate.

Fig. 8.

Wind power output comparison of scenario 1, 5, 6, 7.

Comparisons of wind power optimization results in the four scenarios become clearer when considering the accommodation rate and output fluctuations. Table 3 presents the impacts of different optimization objectives on wind power.

Table 3.

Effect of objective function on wind power output.

Scenario	Wind power accommodation rate (%)	Wind power output fluctuations (MW)
1	91.93	412.75
5	85.17	396.92
6	92.56	616.56
7	89.77	716.64

From the table, it can be concluded that Scenario 5 has the lowest output fluctuations but the lowest accommodation rate. Scenario 6 achieves the highest accommodation rate but has higher output fluctuations. Scenario 7 has a higher accommodation rate but the highest output fluctuations. Scenario 1 strikes a balance between wind power accommodation rate and output fluctuations.

In Fig. 9, the results of energy storage and paper mill optimization are combined and presented for Scenario 1, Scenario 5, Scenario 6, and Scenario 7.

Fig. 9.

Optimization results of papermaking enterprises and energy storage in various scenarios.

Through the analysis in Fig. 9, the optimization results of paper-making enterprises and energy storage in different scenarios can be compared. Comparing scenarios 1, 5, 6, and 7, it can be observed that the operation of energy-intensive load and energy storage is generally the same, with slight differences in some time periods. For example, by comparing the time periods 15 in Fig. 9 (a) and 9 (b), 9 (c), and 9 (d), it can be seen that the energy storage device provides electricity to energy intensive loads in scenarios 1 and 5, while absorbing wind in scenarios 6 and 7. This is because scenarios 1 and 5 have the objective function of balancing the fluctuations in new energy output, which leads to a decrease in wind power output fluctuations in this time period. In scenarios 6 and 7, wind power supplies electricity to energy-intensive load, reducing the power purchasing cost for energy-intensive load and lowering their carbon trading cost through offset mechanisms, thereby maximizing economic objectives. In time period 18, scenarios 1, 5, and 7 choose energy storage for selling electricity and providing capacity backup, while scenario 6 chooses energy storage to absorb wind power. This is because scenario 6 aims to maximize the accommodation of new energy, so it chooses to store wind power through energy storage, which not only increases wind power accommodation but also increases overall revenue by taking advantage of price differentials.

Comparisons of profits among scenarios 1, 5, 6, and 7 in each transaction are shown in Table 4.

Table 4.

Effect of objective function on trading returns.

Scenario	Day-ahead electricity revenue (CNY)	Revenue from the load (CNY)	Intraday electricity revenue (CNY)	Carbon trading cost (CNY)	Total revenue (CNY)
1	−42.93	1801.5	308.48	1018.8	1091.2
5	−52.72	1804.5	269.47	1097.8	976.2
6	−43.90	1806.0	298.99	1027.5	1077.5
7	−42.57	1809.0	294.49	1027.5	1075.9

Table 4 provides a comparison of scenarios 1, 5, 6, and 7 in terms of their participation in the day-ahead electricity market, revenue from the load, intraday electricity market, carbon trading, and total revenue. Through the comparison, it can be concluded that scenario 1, which considers total revenue, wind power output fluctuations, and accommodation, achieves the highest revenue in all markets except for lower market revenue and slightly lower day-ahead electricity market revenue compared to scenario 7.

5. Discussion

The optimization and scheduling of energy-intensive load under the source–load interaction peak shaving mode [30], which involves load aggregation entities participating in the market, have a relatively simple modeling approach. Only the cement industry is chosen as a representative for modeling energy-intensive load, focusing on modeling adjustable load. In scenario 2, the wind power accommodation rate is 72.37 %. However, when energy-intensive load is considered market participants in the electricity market, the load devices of energy-intensive load are categorized, and the ability of load to provide multiple services is emphasized. In scenario 1 of this study, the wind power accommodation rate is 91.93 %. Research on energy-intensive load only considers their integration of new energy consumption [31] or their collaboration with energy storage, without considering energy-intensive load as market participants in trading. Additionally, optimizations for energy-intensive load involve power system optimization and scheduling, park optimization and scheduling, or participation in day-ahead market transactions. Incorporating energy-intensive load as market participants in the optimization and operation of the market can fully utilize their adjustable characteristics.

Under the low-carbon economic operation approach considering flexible load [32], the integration capacity of wind power is improved after the participation of flexible load in scheduling. This approach incorporates the optimization objective of minimizing carbon emissions in economic dispatch. However, it does not consider using energy-intensive load to offset carbon emissions from new energy generation through scheduling. Therefore, the new energy integration capacity achieved through the method of energy-intensive load participation in carbon trading exceeds that of the low-carbon economic operation approach considering flexible load.

6. Conclusion

This study focuses on energy-intensive load and develops a low-carbon optimization strategy for their participation in electricity markets and carbon trading, considering the integration of energy storage and new energy power plants. The objective is to reduce carbon emissions while ensuring product output and benefiting from participating in electricity markets. The main research achievements of this study are as follows:

One achievement is analyzing the electricity consumption characteristics of energy-intensive load and establishing an optimization scheduling model for their participation. This model prompts an electricity-carbon modeling method tailored for energy-intensive load. An in-depth investigation into low-carbon optimization operations involving carbon trading is conducted. A carbon pricing mechanism, inclusive of reward-penalty and offset systems, is designed, and carbon emission quotas based on the product output of energy-intensive load are allocated using a baseline method.

Simultaneously, a low-carbon optimization operational model is developed to maximize total revenue from electricity and carbon emission markets, minimizing fluctuations in new energy output, and enhancing the integration of new energy sources. This model is solved using MATLAB with the CPLEX solver. Case study analyses demonstrate that the proposed carbon trading mechanism outperforms traditional approaches, significantly reducing the carbon emissions of energy-intensive loads. Moreover, comparisons among diverse optimization objectives indicate that optimizing new energy output effectively diminishes wind power fluctuations, and bolsters wind power integration, and concurrently enhances system revenue while reducing carbon emissions. This underscores the practical effectiveness of a multi-objective, interactive-trading-based low-carbon optimization operational model.

Data availability statement

Data included in article/referenced in article.

CRediT authorship contribution statement

Bowen Zhou: Writing – review & editing, Writing – original draft, Supervision, Methodology, Formal analysis, Data curation, Conceptualization. Jianing Li: Writing – original draft, Software, Methodology, Conceptualization. Qihuitianbo Liu: Writing – review & editing, Validation, Software, Data curation. Guangdi Li: Supervision, Formal analysis. Peng Gu: Supervision, Formal analysis. Liaoyi Ning: Writing – review & editing, Visualization. Zhenyu Wang: Validation.

Declaration of competing interest

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work. There is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled “Optimal operation of energy-intensive load considering electricity carbon market”.