Multi-energy synergistic optimization in steelmaking process based on energy hub concept

1.   Introduction

The steel industry is energy-intensive and entails high emission levels [1]. Its energy cost accounts for 20% of the total operation cost [2]. The steel industry is also a major sectorof greenhouse gas emissions, accounting for approximately 7% of the total global CO₂ emissions [3]. Hence, it is crucial for steel works to use energy reasonably and effectively toreduce the operation cost and CO₂ emissions. Because of the demand for multiple energy sources (e.g., electricity and heat) and the use of multi-generation facilities (such as combined heat and power (CHP)), the energy system within steel works is essentially a multi-energy system (MES) representing a new paradigm that exploits the interaction between various energy carriers to improve the technical, economic, and environmental performance of the system [4]. Meanwhile, the metallurgical process in steel works is a comprehensive and dynamic operation [5]. Thus, there might be different combinations of energy sources used in steel works, giving rise to important issues in system optimization, specifically in determining the consumption rate of each energy and the output of each energy device to meet the loads [6]. However, owing to the complexity of MES and complex conversion relationships among various energy sources, a proper framework is required to systematically model and optimize the energy system. As an attempt to systematically model energy systems, describing energy inputs, outputs, storage, and coupling relationships in the MES [7], energy hub (EH) is widely applied to MES to improve its efficiency, flexibility, and reliability.

Several attempts have been made to optimize and model the energy system of steel works. For example, some studies [8–10] established a mixed-integer linear programming (MILP) model to optimize the byproduct gas distribution and reduce pollutant discharge. Zhang et al. [11] proposed a forecast model of the supply and demand of byproduct gas in steel works. Zhao et al. [12–13] proposed a scheduling model of a byproduct gas system under the time-of-use tariff to reduce the purchasing cost of electricity. Furthermore, the Pareto optimization between the gasholder stability and electricity cost was considered. However, only a few of the above studies [12–13] have considered the efficiency change with the operation load of energy devices, such as boilers. Most of the studies [8–11] considered a constant efficiency of such devices. Thus, the optimization results may not be quite precise to match the actual situation. Besides, the optimization problem of multi-energy coupling in steel works has beenresearched, and a mathematical programming model is widely applied to multi-period scheduling [14–17]. However, there have been few developments on the model and optimization of the energy system within steel works from the perspective of MES, making the above models not universal.

In terms of MES modeling, several researchers have studied EH from the perspectives of concepts, modeling, andoptimization. The potential of the EH concept as a comprehensive model in the future is discussed [18–19]. Moreover, the operation problem [20] and key challenges [21] of theenergy model are analyzed. The EH, as a template, is applied to design different models for MES, e.g., the selection and configuration of energy devices in the energy system [22–24]. The general and flexible modeling method is studiedto solve the problem of model coupling [25–28]. Some studiesmodeled and optimized energy systems under different scenarios based on the EH concept considering financial viability or potential reduction of greenhouse gas emissions, such as the EH network [29], distribution system [30–31], cement plant [32], and community [33].

The above literature has focused on scheduling the optimization of steel works and MES modeling. However, limited research has been conducted on the optimization of the energysystem within steel works from the perspective of MES. This paper introduces a multi-layer model based on the EH concept to systematically model and optimizes the energy system within steel works. In addition, the efficiency change with the operation load of the energy device is considered.

2.   Model

2.1   Model background

Owing to the complexity of energy production and consumption in steel works, the energy system within steel works is a typical MES that consists of different types of energy sources and energy devices. Because the steel industry is a process industry, there are many links that have characteristics existing in the EH: energy generation, transportation, storage, and consumption. For example, byproduct gases, such as blast furnace gas (BFG) and coke oven gas (COG), are relatively stable chemical energy produced by energy devices in the steelmaking process. A gasholder, which stores surplus byproduct gas, is employed to reduce gas flare. In addition, various energy sources are distributed in different places in the factory; thus, various energy pipeline networks are used to transport energy. Meanwhile, because of the demand for electricity and steam, steel works have adopted self-provided power plants that can generate steam and electricity by consuming surplus byproduct gas. To realize a normal steel production process, energy sources, such as electricity and thermal coal, should be purchased to meet the vast energy demand of the production. Therefore, the energy system in steel works is an EH with multiple energy inputs and outputs. The distribution of energy sources, such as byproduct gas and steam in steel works, is virtually a case of the energy dispatch in energy devices in the EH. Modeling and optimizing the energy system of steel works from the perspective of MES is important for energy savings and emissions reduction.

2.2   Energy hub

The concept of an EH was first proposed by Geidl in 2007 [7], which includes the creation of a universal framework to model the input energy, output energy, energy storage, and coupling relationships in MES. The relationship between the input and output energy is shown below.

where P_(t), L_(t), and C_(t) denote the input energy vector, output energy vector of the hub, and coupling matrix, respectively. Moreover, the coupling factor relates the n input energy to the m output energy.

An energy carrier might be converted to different forms of energy; thus, dispatch factors that represent the amount of input energy allocated to each of the hub converters must be determined. Furthermore, energy conversion efficiency must be considered in the energy conversion process. Therefore, the coupling factor depends on the dispatch factors as well as the efficiency of the energy device, causing the optimization model to be non-convex. As shown in Fig. 1, each energy flowing into the device ${{E}}^{{\rm{in}}}$ should be multiplied by the corresponding dispatch factor $\nu$, for example, the energy 2 flowing into device A is calculated by multiplying the energy 2 flowing into the EH ${{E}}_2^{{\rm{in}}}$ by its corresponding dispatch factor ${\nu _3}$, that is, ${{E}}_2^{{\rm{in}}} \cdot {\nu _3}$. An EH may have multiple inputs and outputs, and a portion of the input energy flows through several conversion devices. However, the rest may not flow through any device, which may cause mismatches in the coupling matrix.

Fig. 1.  Genetic model of the energy hub. A, B, and C represent different devices.

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Moreover, if an energy input is transformed to an energy output through more than one energy device, the coupling factor is considered for every energy conversion technology in the hub, which is a combination of many energy device efficiencies. This makes it difficult to find out the efficiency of each device. The original EH model is highly coupled, and it is complicated to update the coupling matrix if a few energy devices are replaced. Thus, the original model should be improved in the actual modeling.

2.3   Proposed model

2.3.1   Modeling method

To systematically model the energy system, a multi-layer model based on the EH concept is proposed to model an MES. As shown in Fig. 1, energy 1 flows directly out of the hub without flowing through any device. The energy flowing out of device A flows directly out of the hub because there is no subsequent device. However, energy 2 flowing through the device is completely different from energy 1, which makes it difficult to model the hub systematically.

In the proposed model (Fig. 2), virtual devices are inserted into the energy flows that flow through fewer conversion technologies, ensuring that each energy flow will flow through the same number of energy conversion technologies. In addition, when every energy flow goes through an energy conversion device, it is considered to flow through a layer of the model. Every layer can be regarded as an EH, where the input energy can be converted to output energy through one energy device. If a few of the energy devices in the system have changed, the devices in the corresponding layer are then modified. Thus, the proposed model is highly decoupled. The entire energy system is divided into multiple EHs, and the energy output of the previous EH will be used as the energy input of the next EH. Thus, the energy system is modeled by the proposed multi-layer model.

Fig. 2.  Schematic view of the multi-layer model.

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2.3.2   Variable substitution

Meanwhile, solving the coupling factor in the coupling matrix is difficult because the model is non-convex. Considering the distribution of the input energy in the EH as an example (Fig. 1), the energy input ${{{E}}^{{\rm{in}}}}$ and the dispatch factor $\nu$ are both selected as variables in the original EH model, which will cause nonlinear terms and make the model non-convex. To solve the non-convex behavior caused by the dispatch factor, this study introduces the method of variable substitution with the result shown in Fig. 2, and the energy 2 flowing into device A is directly represented by a single variable ${{E}}_{{{{\rm{A}},2}}}^{{\rm{in}}}$, thus, the impact of nonlinear terms is eliminated after the variable replacement of ${{E}}_{{{{\rm{A}},2}}}^{{\rm{in}}} = {{E}}_{\rm{2}}^{{\rm{in}}} \cdot {\nu _3}$.

2.4   Model constraints

The constraints of the model include the operating range of devices, energy distribution, energy conversion, and energy demand. To model the energy storage within the EH, all the variables are considered time-dependent and the flows through an EH at a particular time t are modeled.

2.4.1   Operating range of devices

A gasholder is a gas storage device in iron and steel works. The following constraints are imposed on the operating range of gasholders (Eq. (2)).

where $H_{g,j}^{\max }$ and $H_{g,j}^{\min }$ are the maximum and minimum levels of energy j stored in the gasholder g (g = 1, 2, 3, … G), respectively. $H_{g,j}^{{\rm{dis,}}\;\max }$ and $H_{g,j}^{{\rm{ch,}}\;\max }$ are the maximum capacities of the gasholder g of the flaring energy j and the changing level of energy j, respectively. ${H_{g,j,t}}$ and $H_{g,j,t}^{{\rm{dis}}}$ denote the level of energy j stored in the gasholder g and the energy j is flared by the gasholder g at a time period t, respectively.

Eq. (3) is the expression of the input and output capacity constraints of the energy devices, such as boilers and turbines. $E_{i,j}^{{\rm{in,}}\;\min }$, $E_{i,j}^{{\rm{in,}}\;\max }$, $E_{i,j}^{{\rm{out,}}\;\min }$, and $E_{i,j}^{{\rm{out,}}\;\max }$ denote the minimum and maximum capacity of energy j flowing into and out of device i, respectively. $E_{i,j,t}^{{\rm{in}}(n)}$ and $E_{i,j,t}^{{\rm{out}}(n)}$ are the energy j flowing into and out of device i in the layer n at time t, respectively; i = 1, 2, 3, … K; n = 1, 2, 3, …. N; t =1, 2, 3, … T.

2.4.2   Energy distribution

The energy distribution constraints of the proposed model mainly include the balance of energy flowing into the hub, the balance between adjacent layers, and the balance of energy leaving the hub. All the above balance constraints can be described by Eqs. (4)–(7).

If energy j is a byproduct gas that can be stored in the gasholder, its balance flowing into the hub can be described by Eq. (4); otherwise, Eq. (5) is the expression of the balance of energy j flowing into the hub. Eq. (6) describes the balance between adjacent layers, and Eq. (7) describes the balance of the energy out of the hub.

In the above equations, is the surplus energy j (mainly byproduct gas) produced by the main process and $\Delta t$ denotes the time interval. $E_{i,j,t}^{{\rm{in}}(n)}$ and $E_{i,j,t}^{{\rm{out}}(n)}$ denote the energy j that flows into and out of the device i in layer n at time period t, respectively. $E_{j,t}^{{\rm{hubin}}}$ and $E_{j,t}^{{\rm{hubout}}}$ represent the energy j flowing into and out of the hub at time period t, respectively.

2.4.3   Energy conversion

The energy conversion process in the EH can be described by the following constraints. The efficiency of energy might change with the change in device loads because the efficiency of energy devices cannot be constant under actual operating conditions. Therefore, this study employs the method of quadratic curve fitting to describe the relationships between the efficiency and loads of energy devices. Eq. (8) is the general expression of the quadratic curve fitting of the energy devices. Meanwhile, if a device is not a virtual device, its efficiency is related to its load (Eq. (9)); otherwise, its efficiency is equal to 1. Eq. (10) shows the energy conversion of each device.

In the equations above, ${\eta _{i,j,k}}$ is the efficiency of the device i converting energy k to energy j. ${A_0}$, ${A_1}$ and ${A_2}$ are the quadratic coefficient, the first-order coefficient, and the constant coefficient in the fitting formula, respectively.

2.4.4   Energy demand

The energy out of the hub and the energy demand at period t should be exactly equal to meet the production. However, in practice, the energy supplied is greater than the energy required to improve the flexibility of the operation; thus, the constraint of energy demand is as shown in Eq. (11):

where $E_{j,t}^{\rm{dem}}$ denotes the demand of energy j at the period t.

2.5   Objective function

The two objective functions (f₁ and f₂) of the model are to minimize the economic operating cost (EOC) and the CO₂ emissions, respectively, which is expressed by Eqs. (12)–(17):

where ${C_{{\rm{EO}}}}$ and ${M_{{\rm{C}}{{\rm{O}}_{\rm{2}}}}}$ denote the economic operating cost and CO₂ emissions, respectively; ${C_{{\rm{TE}}}}$ and ${C_{{\rm{DO}}}}$ are the total energy cost (TEC) and device operating cost (DOC), respectively; ${\varphi _{{\rm{electricity}},t}}$ is the electricity price at time t; $\,{\beta _{i,j}}$ denotes the unit operating cost of device i to produce energy j; ${\alpha _j}$ and ${\gamma _j}$ are the price and carbon emission factor of energy j, respectively.

2.6   Algorithm

As mentioned above, the proposed model is a multi-objective problem. To solve this problem, a linear weighted method [34] is applied to change the multi-objective problem into a single-objective problem, which can be solved by an IPOPT solver (interior point method). Thus, the global optimal solution can be obtained. Eq. (18) shows the linear weighted method where F is the comprehensive objective function and ${\omega _i}$ is the weight of the objective function ${s_i}$.

This study calculated the optimization work in a Python environment on a personal computer (PC) with an Intel Core i5 2.40 GHz CPU and 16GB RAM. The problem is implemented in Pyomo (Python optimization modeling objects) and solved by the IPOPT solver.

3.   Case study

The optimal scheduling model of a gas–steam–powersystem of a steel enterprise is implemented to evaluate the applicability of the proposed multi-layer model. The gas–steam–power system, as part of the energy system within steel works, plays an important role in the production, as shown in Fig. 3. There are three types of byproduct gases produced in the iron- and steel-making process: BFG, COG, and Linz-Donawize gas (LDG). In addition to being burned directly to meet the heat demand of the production, the surplus byproduct gas can be used in power plants, which can generate electricity and all types of steam through generators (G), boilers, and turbines (TB) to meet the energy demand. There are three main types of steam: high-pressure (HP) steam, medium-pressure (MP) steam, and low-pressure (LP) steam. The demand for electricity is mainly met by the self-provided power plant in steel works, and the remaining part should be purchased from the grid. Furthermore, the steel work has to fully utilize the gas storage ability of gasholders to achieve peak-valley shifting of electricity generation in light of the time-of-use electricity tariff, which is significant for reducing the cost of purchasing electricity.

Fig. 3.  Schematic view of the gas–steam–electricity system in iron and steel works.

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Based on the 24-h operation data of the case enterprise, a multi-layer model is built. As shown in Fig. 4, there are three energy inputs in the studied case: byproduct gas, electricity, and coal. The optimization model is composed of four energy outputs: electricity, steam S1, steam S2, and steam S3. There is no LDG in the byproduct gas of the energy inputs because the case enterprise does not use LDG in the steam and electricity production process. Tables 1–3 list the related parameters of energy devices within the case enterprise. Moreover, Tables 4 and 5 list the heat value and carbon emission factor of fuels and the enthalpy of steam, respectively.

Table  2.  Operation parameters of boilers

Boiler	Fuel	Range of steam production / (t·h−1)	Steam type
Boiler 35 t/h #1	BFG, COG	0–35	S1
Boiler 35 t/h #2	BFG, COG	0–35	S1
Boiler 130 t/h #1	BFG, COG	90–130	S1
Boiler 130 t/h #2	BFG, COG	90–130	S1
Boiler 1025 t/h #1	BFG, COG, Coal	800–1025	S0
Boiler 1025 t/h #2	BFG, COG, Coal	800–1025	S0

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Fig. 4.  Gas–steam–electricity system construction within the case enterprise.

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Table  1.  Operating range of gasholders

Gasholder	Maximum capacity / km3	Minimum capacity / km3	Flare capacity / (103 m3·h−1)	Deviation capacity / (103 m3·h−1)
BFG #1	285	30	70	396
BFG #2	285	30	70	396
COG #1	140	15	30	132

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Table  3.  Operation parameters of turbines

Turbine	Steam source	Working condition	Rated power	Steam type
Turbine #1	Boiler 130 t/h #1	Back pressure	25 MW	S2
Turbine #2	Boiler 130 t/h #2	Back pressure	25 MW	S2
Turbine #3	Boiler 1025 t/h #1	Condensing	300 MW	S2, S3
Turbine #4	Boiler 1025 t/h #2	Condensing	300 MW	S2, S3

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Table  4.  Heat value, carbon emission factor [15], and market price [1] of fuels

Fuel type	Heat value	Carbon emission factor	Market price
BFG	3652 kJ/m3	0.9 t CO2/(103 m3)	50 CNY/(103 m3)
COG	17000 kJ/m3	0.81 t CO2/(103 m3)	100 CNY/(103 m3)​​​​​​​
Coal	21800 kJ/kg	2.9 t CO2/t	400 CNY/(103 m3)​​​​​​​

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Table  5.  Enthalpy of steams kJ·kg⁻¹

Steam type	Enthalpy
S0	3347.9
S1	3332.1
S2	2940.2
S3	2960.0

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To simulate the actual working conditions of the energy devices, the method of fitting the curve is adopted to describe the efficiency of boilers. Fig. 5 shows the curve fitting diagram and Table 6 summarizes the coefficients of the different types of boilers.

Fig. 5.  Quadratic fit of the efficiency of different boilers: (a) 35 t/h boiler; (b)130 t/h boiler; (c)1025 t/h boiler.

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Table  6.  Coefficients of different types of boilers

Boiler type	a	b	c
Boiler 35 t/h	−3.95802	7.96696	−3.03005
Boiler 130 t/h	−4.83891	8.95897	−3.20061
Boiler 1025 t/h	−158.71909	315.72738	−156.06833

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4.   Results and discussion

4.1   Fuel distribution

Fig. 6 shows the distribution of fuel on the different types of devices in each period. The byproduct gas consumption of the 35 t/h boiler is small but relatively stable because the 35 t/h boiler is the only energy device that can produce steam S1. The load of S1 is observed to fluctuate slightly.

The gas consumption of the 1025 t/h boiler is the largest, and its corresponding turbine has a larger load and higher power generation efficiency in generating electricity to satisfy the electricity demand. Therefore, the 1025 t/h boiler has a high priority in gas usage. In addition, the fuel of the 1025 t/h boiler includes the byproduct gas and coal, and the purchase price per calorific value of coal is the highest. Thus, reducing the energy cost will reduce coal consumption and increase the byproduct gas supply of the 1025 t/h boiler. In addition, in terms of the carbon emission factor per calorific value unit, BFG is greater than coal and COG is the lowest. Hence, it is not conducive to reduce CO₂ emissions using more BFG. In contrast, using more COG is reasonable because of its low price and carbon emission factor. However, the proportion of the byproduct gas mixed combustion is restricted by boilers in the actual production. Thus, reducing the supply of coal and increasing the amount of gas within a reasonable range will help to reduce the energy cost and CO₂ emissions. The amount of gas consumed by the 130 t/h boiler fluctuates significantly because it is the main boiler to be regulated due to its relatively low load and efficiency.

The optimization results reveal an 8.82% decrease in coal supply compared to the original results. Meanwhile, the consumption of BFG and COG increased by 3.42% and 9.79%, respectively.

Fig. 6.  Fuel consumptions in each period: (a) BFG; (b) COG; (c) coal.

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4.2   Steam production

Fig. 7 shows the production of all types of steam. Because the demand for steam S1 and S3 are fluctuating, the boiler of 35 t/h and turbine of 1025 t/h are devices that produce these two kinds of steam have mutative steam loads. Steam S2 can be produced by the turbine with the 130 t/h and 1025 t/h boiler,although the demand for the steam is mutative. In the actual production of the enterprise, the priority of energy generated by different devices is different, and the operation cost ofdifferent energy devices to produce the same energy is unequal. The energy device with low operation cost prioritizes energy production to reduce the device operation cost. Therefore, in terms of the production of steam S2, the 130 t/h boilerhas a higher priority, and the steam production of the 1025 t/h boiler often reflects fluctuations.

Fig. 7.  Steam production in each period: (a) S1; (b) S2; (c) S3.

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4.3   Gasholder level change and electricity generation

Fig. 8 demonstrates the changes in the gasholders. The original results show that the gasholder level is in a relatively high position owing to the higher surplus gas, particularly when the electricity price is high. The level of the gasholder after optimization is lower than the original results because more surplus byproduct gas is used to generate electricity, as confirmed by the result of electricity generation. In addition, at the end of the operating period, the level of the gasholder is in a lower position owing to the massive use of byproduct gas.

Fig. 8.  Change of gasholders in the operation period: (a) BFG; (b) COG. TOU means time-of-use

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Fig. 9 presents the production of electricity, which indicates that electricity generation fluctuates with electricity price, and the maximum range of electricity production generally occurs during a high electricity price to consume the overfull surplus byproduct and reduce electricity purchase cost.

Fig. 9.  Electricity generation in each period.

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4.4   Objective function values

Table 7 summarizes the optimal results. Owing to the decrease in coal usage and electricity purchase, there is a slight drop in TEC. Moreover, power generation causes an increase in DOC. Hence, there is an opposite trend between TEC and DOC after optimization. In summary, compared with the original results, the EOC and CO₂ emissions decreased by 3.41% and 3.67%, respectively.

Table  7.  Comparison between the original and optimal results

Result	CTE / (104 CNY)	CDO / (104 CNY)	CEO / (104 CNY)	CO2 emissions / t
Optimal results	293.84	323.73	617.57	24835.78
Original results	320.53	318.86	639.39	25781.52

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5.   Conclusions

This paper proposed a multi-layer model based on the EH concept to optimize the MES in iron and steel works. Meanwhile, the method of variable substitution is adopted to eliminate the non-convex impact caused by nonlinear terms. Furthermore, the efficiency of energy devices is described by a quadratic curve fitting method close to the actual working conditions of energy devices. Finally, a case study is conducted to minimize both the EOC and CO₂ emissions of iron and steel works to evaluate the applicability of the proposed multi-layer model. This study can be summarized as follows.

(1) A multi-layer model, which is decoupled and based on the EH concept, was proposed to model and optimize the system in steel works. This model eliminates the non-convex impact caused by nonlinear terms.

(2) The proposed model was applied to a case in steel works to evaluate the applicability of the model and schedule the distribution of energy. A quadratic curve fitting method is adopted to incorporate parameters close to the actual working conditions of energy devices.

(3) The optimal results indicate that the proposed model optimizes the cost and emissions of the case enterprise. The optimal EOC decreases by 3.41% compared with the original cost in a 24-h operation, and the optimal CO₂ emissions decrease from 25781.52 to 24835.78 t, simultaneously.

(4) This model reduces TEC and CO₂ emissions by reducing the supply of coal and significantly increasing the amount of COG within a reasonable range owing to their price and attributes.

Acknowledgements

This work was financially supported by the National Key Research and Development Program of China (No. 2020YFB1711102) and the National Natural Science Foundation of China (No. 51874095). The authors gratefully acknowledge the reviewers and editors for their fruitful comments.