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Advances in Mechanical Engineering
Volume 2013 (2013), Article ID 191963, 11 pages
Research Article

Modeling and Optimizing Energy Utilization of Steel Production Process: A Hybrid Petri Net Approach

1School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China
2Beijing Engineering Research Center of Energy Saving and Environmental Protection, Beijing 100083, China

Received 18 May 2013; Accepted 9 September 2013

Academic Editor: Gang Wang

Copyright © 2013 Peng Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The steel industry is responsible for nearly 9% of anthropogenic energy utilization in the world. It is urgent to reduce the total energy utilization of steel industry under the huge pressures on reducing energy consumption and CO2 emission. Meanwhile, the steel manufacturing is a typical continuous-discrete process with multiprocedures, multiobjects, multiconstraints, and multimachines coupled, which makes energy management rather difficult. In order to study the energy flow within the real steel production process, this paper presents a new modeling and optimization method for the process based on Hybrid Petri Nets (HPN) in consideration of the situation above. Firstly, we introduce the detailed description of HPN. Then the real steel production process from one typical integrated steel plant is transformed into Hybrid Petri Net model as a case. Furthermore, we obtain a series of constraints of our optimization model from this model. In consideration of the real process situation, we pick the steel production, energy efficiency and self-made gas surplus as the main optimized goals in this paper. Afterwards, a fuzzy linear programming method is conducted to obtain the multiobjective optimization results. Finally, some measures are suggested to improve this low efficiency and high whole cost process structure.

1. Introduction

China is the world’s largest steel producer and consumer, and the production of crude steel and apparent steel consumption are up to 683.88 and 649.85 million tons (Mt) in 2012 respectively [1]. The steel industry has been the most important end-use sector in China. Despite these achievements, its expansion are impossible to achieve without a huge increase in energy input, especially in the form of coal, which resulted in severe environmental problems in the coal mining regions and around the steel plants. The Chinese steel industry was responsible for 16.1% of primary energy consumption and 15% of associated carbon dioxide emissions in 2009. Steel production is an energy-intensive manufacturing process, so it is quite important and necessary to optimize energy system for steel production process. However, we cannot ignore economic and environmental aspects because it is essential for steel enterprises to boost productivity and reduce emissions. These key issues are the main subjects of our study.

Steel production process is extremely diverse, encompassing the extraction of natural resources, conversion into raw materials, and manufacture of finished products [2]. It covers a wide range of multiprocedures, multiobjects, multiconstraints, multimachines, and energy flow, material flow and information flow that are strongly coupled [3]. Processes may be either continuous or discrete due to machine breakdowns and some discrete procedures in the real process. Since process industry has many special features, it is quite difficult to be modeled and optimized. Meanwhile, the requirements are various for steel company when dealing with energy problem. Therefore, we should take multiobjectives optimization in this study, and fuzzy optimization method can be used to solve these difficulties conveniently, which is widely applied to engineering problems [4, 5].

Methodologies and frameworks dealing with these troubles are introduced in some researches and published literatures. Linear programming based on algorithms, such as MILP and cyclic scheduling, has been applied for planning and scheduling cases. In addition, Petri Net has an inherent attribute in representing sequent, concurrent, and conflicting logic in an intuitive and visual way.

Since the appearance of Timed Continuous Petri Net (TCPN) in 1990, some Hybrid Petri Net (HPN) models have been conducted in studying the industry systems [6, 7]. The most impressive characteristic of HPN model is that dynamic system behaviors, discrete production states, and event-driven system actions are integrated in one model structure. It naturally represents some nonlinear mechanism of the process and provides inherent restrictions of search space of optimization algorithm. Previous studies about Petri Net (PN) are certain method to show elements and their relationship abstractly, whose purpose is to seek the best decisions to achieve manufacturing system analysis, control and optimization [8]. In addition, Petri Net (PN) was widely used in iron and steel production system. Jun et al. proposed a modeling example to realize the efficient operation of the gas flow network in steel plants using Hybrid Petri Net [911]. According to the above, HPN is a feasible method to simulate and optimize the real steel production process, which is used in this study.

2. Methodology

2.1. Hybrid Petri Net

Petri Nets (PNs), firstly introduced by Petri in 1962 [12], are mathematical modelling tools used to analyze and simulate concurrent systems. Since then, Petri Nets and their concepts have been extended and applied in a variety of areas. Continuous PNs are used for modeling continuous systems. However, this model does not allow logical conditions or discrete behavior modeling (e.g., a valve may be open or closed). For permitting modeling of discrete states, Hybrid PNs were defined and presented [13, 14]. Hybrid Petri nets are made of “continuous part” (continuous places and transitions) and “discrete part” (discrete places and transitions), and included continuous and Hybrid Petri Nets, fluid stochastic petri nets, batch petri nets, hybrid flow nets, and so on [15].

First-order hybrid Petri nets is one of Continuous and Hybrid Petri nets and defined as follows.

2.1.1. FOHPN Description

A FOHPN is a bipartite digraph described by the 7-tuples [6]:

The parameters are described below.(1) Places : is partitioned into a set of discrete places (represented by circles) and a set of continuous places (represented by double circles). The set of transitions is partitioned into a set of discrete transitions and a set of continuous transitions ( represented by double boxes). (2) Transitions : is further partitioned into a set of immediate transitions (represented as bars), a set of deterministic timed transitions (represented as black boxes), and a set of exponentially distributed timed transitions (represented as white boxes). We also denote by the set of timed transitions. Moreover, means the set of distributed timed transitions. (3) Pre- and Postincidence functions Pre and Post (represented as arcs): where all and for all (well-formed nets) are required to be satisfied the formula to ensure that the firing of continuous transitions does not change the marking of discrete places.(4) Function : specifies the timing associated with timed discrete transitions. We associate with a deterministic timed transition its (constant) firing delay and associate with an exponentially distributed timed transition its average firing rate ; that is, the average firing delay is , where is the parameter of the corresponding exponential distribution. (5) The function : specifies the firing speeds associated with continuous transitions. For any continuous transition , we let . Here represents the minimum firing speed (mfs) and represents the maximum firing speed (MFS). (6) Function RS: associates a probability value called random switch to conflicting discrete transitions.

2.1.2. Marking and Enabling

Let be an FOHPN with an initial marking , where is a function that assigns to each discrete place a nonnegative integer number of tokens, represented by black dots, and assigns to each continuous place a fluid volume.

For a discrete transition , it is enabled at if, for all , . As to continuous transition , it is enabled at if, for all , . We say that an enabled transition is strongly enabled at if, for all places , and weakly enabled at if for all places , .

2.1.3. Optimal Control Law for FOHPNs

Jinsong and Qiqiang [7] built up a linear algebraic formalism to study the problem of deriving an optimal control law for FOHPNs under the assumption of admissible instantaneous firing speed (IFS) vectors.

Let be an FOHPN with continuous transitions and incidence matrix . Let be the subset of continuous transitions enabled (not enabled) at . Let be the subset of empty continuous places.

Any admissible IFS vector at is a feasible solution of the following linear set:

The set of all feasible solutions is denoted by . And (3) is the constraint condition aiming at optimizing any given objective functions.

2.2. Iron and Steel Manufacturing Process

Currently, there are three main routes in the world for steel production, conventional integrated (pelleting, sintering, and coke plants-blast furnace-BOF route), semi-integrated (pelleting and DRI plant-EAF route), and new integrated with smelt reduction (pelleting plant-COREX-BOF/EAF route) [16]. In addition, the conventional integrated process is the most important steelmaking process (ratio of BOF steel remain about 80% [1]) in China, so we focus on this route only in this paper.

As described in Section 1, the conventional integrated process is extremely difficult to analyze. Therefore, in this paper, we set the boundaries of the iron and steel manufacturing process including pelletizing, sintering, iron making, steelmaking, steel casting, hot rolling, cold rolling, internal energy conversion system, and auxiliary production system.

2.3. Optimization Model

Based on the methodology explained in Section 2.1, the defined Hybrid Petri Net turns to be a flexible modeling process that makes sense to model steel manufacturing processes, by allowing places using actual material flow and transitions using actual manufacturing equipment. In order to reflect the actual production of steel process, one closed mass and energy balance model for each process are built to figure out the type and quantity of materials entering and leaving the process system.

In order to deal with multiobjective linear optimization problem, fuzzy linear programming method is a good way to resolve the problem [17], and this method will be adopted in this paper by software Lingo. The specific steps are as follows.

Step 1. Separate every objective function into its maximum and minimum value by solving
And and are obtained through solving the multiobjective problem as a single objective subject to the constraints equation like (3).

Step 2. Obtain the membership functions of the fuzzy objective functions for minimization goals () and maximization goals (), which are constructed as

Step 3. In order to find optimal solution () in the above fuzzy model, it is equivalent to solving the following crisp model.
Maximize : Subject to the constraints equation and ,  .

3. Case Study

3.1. Case Introduction and Data Acquisition

Chinese steel industry owns its unique characteristics, like large production capacity, ore based process, and coal dominant energy consumption structure. One typical integrated steelmaking plant with an annual ten millions tons steel production capacity, located in Yangtze River delta, is selected in our case study. Coking, sintering, pellet, iron making, steelmaking and rolling are the main processes. The auxiliary production processes are combined with heat and power, limekiln, and dynamical transition system. In order to visualize the material flow, the material flow diagram is drawn based on the real manufacturing shown in Figure 1. Main material inputs of the system are iron ore, scraps, coal, coke, flux, air/oxygen, steam and electricity. The products are mainly steel bar, steel tube, heavy plate, hot rolling steel cold rolling steel, and so on.

Figure 1: Main material flow diagram of iron and steel manufacturing process.

In this paper, we collected the data mainly from company-level questionnaire surveys and production statistics. Some data are from the plant’s technology acceptance inspection reports, which can fill the rest of the data gaps. With careful verification, we retain valid questionnaires of 2009 as the principal data source. The maximum capacity of each process is the result of all the devices under the best working condition, and the relationship between the material flow of each process is the average of the first quarter of 2009. For this steelmaking processes, 1.52 tons of sinter and 0.17 tons of pellet are required to produce 1 ton crude steel, contain pig iron and scrap, 0.99 tons pig iron is required to produce 1 ton of crude steel, and 1.02 tons of crude steel is required to make 1 ton of hot rolled steel.

3.2. FOHPN Model Building

In this section, we obtain the FOHPN model for steel production process by software named Visual Object Net. In addition, the declarations of transitions and the maximum firing speed (MFS), which is the maximum production capacity, for each continuous places, are presented in Table 1. Moreover, the declarations of places and the weights of the arcs connected these places are shown as Table 2, and the weights of the arcs are modified by the material flow of each process.

Table 1: The meaning and MFS of transition [unit: 104 t per month].
Table 2: The meaning of place and the weight of the connected arcs.

There are several statements that should be noted in our approach.(1)The elements in our model are represented as icons, shown as Figure 2.(2)We take the material inventory as a continuous place without upper limit.(3)We take the main continuous production equipment as a continuous transition, which is controlled by a discrete transition nearby. If the discrete place has a token inside, the continuous production equipment functions properly and vice versa. Obviously, the discrete place’s operational status is controlled by discrete transitions and , where . At the same time, the production capacity of the continuous production equipment means the fire speed for the corresponding continuous transition.(4)The weight of the arcs in front of the continuous transition is obtained by the related input material’s mass proportion to the transition production capacity and vice versa.

Figure 2: Icons for the elements in the FOHPN model.

The FOHPN model network is built after defining the places and transitions in steel production process shown in Figure 3. According to Section 2.1, we can obtain the constraint condition for our model as (6). Based on this constraint condition, the result is obtained from different optimization conditions like maximum mass of different products, and then analyze the material and energy flow for steel production process in any given conditions:

Figure 3: FOHPN model of the steel production process network.
3.3. The Baseline Case

In our research, we take the actual production situation as a benchmark whose data are derived from survey and statistical on the spot. Figure 4 shows the baseline case visually by e!sankey software, which is based on the average of survey and statistical data. The total of products and by-products was 85.627 × 104 tons/m, the energy consumption of the system is 22.437 GJ/t, and the self-made gas surplus amount is 1.42 × 106 m3/m.

Figure 4: The material flow analysis of steel production process in baseline case.
3.4. The Steel Production Case (Case 1)

Because many steel plants only treat the production as their main goal, we considered steel product production as the objective function in this case shown as (7), and the material flow is shown in Figure 5: where represents the total steel production of the system, including steel bar, steel tube, heavy plate, hot rolled products and cold rolled products.

Figure 5: The material flow analysis of steel production process in steel production case.
3.5. The Energy Efficiency Case (Cases 2 and 3)

As mentioned above, energy efficiency is a critical issue for steel production nowadays. Therefore, the energy efficiency case is carried out by minimizing the energy efficiency of the process system. Additionally, the self-made gas system is the important part of energy system; reducing gas losses becomes more and more important for steel plants to decrease the demand of natural resources, cut down the discharge of exhaust gas, and diminish their influence to circumstances. The objective functions and results are shown as follows.

Case  2. Minimize the energy efficiency of the process system where, , , represent the energy intensity of each procedure and represents the total energy consumption for production process, which is obtained by production data from B steel company (Figure 6).

Figure 6: The material flow analysis of steel production process in Case 2.

Case  3. Minimize self-made gas surplus amount under the steel production maximization condition where represent the surplus amount of COG (Pa1), BFG (Pc1), and LDG (Pd1) (Figure 7).

Figure 7: The material flow analysis of steel production process in Case 3.

4. Results and Discussion

Production and energy utilization for each procedure of four cases are presented in Figures 8(a) and 8(b). In addition, Table 3 shows the total steel production, specific energy consumption, and self-made gas surplus amount of four different cases.

Table 3: Production and energy consumption of four different cases.
Figure 8: Production (unit: 104 t/m) and energy consumption amount (unit: GJ/m) for each procedure.

As we can see from Figure 8(a), we can find that almost every procedure’s production of Case 2 and Case 3 compared to Case 1 has been reduced by comparing the three optimized cases. In other words, to reduce energy consumption and reduce surplus production gas is bound to cause decline in steel production. Interestingly, however, the coking production in Case 1 has increased by 14.8 104 t/m compared to Case 2. It is mainly because that arcs weight of generating blast furnace gas is more than the arcs weight of generating coke oven gas, but steel production procedures consume more coke oven gas relatively. Therefore, it is a reasonable choice to minimize self-made gas surplus amount reducing the Blast furnace gas amount and increasing the amount of coke oven gas (shown in Figure 5).

By comparing the optimized cases 2 and 3, we can find that production of every procedure except cold rolling in case 2 is less than that in Case 3, and so is the total energy utilization amount, which fully demonstrates that minimizing surplus self-made gas amount could not achieve the best the overall energy saving status. In addition, the amount of gas in these three conditions is always greater than zero. This indicates that the supply of self-made gas has greatly exceeded demand for the entire steel process. Meanwhile, the steel mills also purchase a large number of external energy media; for example, the purchased natural gas reached 155 m3/m. Therefore, the process should be arranged for the consumption of gas reasonably, trying to consume self-produced gas and reduce the use of purchased natural gas, to improve this low efficiency and high whole cost situation. Figure 8(b) shows that energy utilization for every procedure from small to large ranked Cases 2, 3, 1. Where, under any circumstances, the energy consumption of the blast furnace is the largest in all procedures.

Another important thing that must be considered in our study is the production capacity of each procedure in the manufacturing process. In the first case (maximum output), sintering and pelletizing (before steelmaking procedure) work at full capacity production, which illustrate the sintering and pelletizing impose restrictions on iron-making process; coking and blast furnace are enough to spare. Therefore, in this case, a factory should add sintering and pelletizing equipment to increase their production power to raise the utilization of the facilities. BOF and refining (after steelmaking procedure) are limited by the production of BF, which cannot operate at full ability. However, on product selection, in order to achieve the maximum output, the preference is to choose iron loss smaller processes, which result in hot rolling and cold rolling equipment utilization rate dropped significantly. The cold rolling product maximized optimization has a big difference compared with the production power; therefore, in the practical production process, the raw material for cold rolling must come from stocking inventory mostly. To achieve the continuity of comprehensive process, it is necessary to design the production capacity of each process.

5. Conclusions and Suggestions

This paper provides a new method based on Hybrid Petri Nets to describe the complex behavior of the steel production process with energy utilization. Moreover, this method is conducted to model and optimize the energy utilization of one China’s typical steel plant. The main conclusions and the suggestion to improve the energy utilization and steel production are listed as follows.(1)This research describes the HPN model scientifically, including some new definitions of the method and the corresponding optimization principles, especially some analogy methods and definitions about the steel production process.(2)The Hybrid Petri Net method is a good way to simulate continuous-discrete production process in this paper, and this method provides reference for the further optimization of steel production structure. In addition, it can largely simplify the research of steel production system.(3)We perform the multiobjective optimization by fuzzy linear programming method according to some different optimization conditions and the constraints obtained by the HPN model. The optimizing results go well with the practice. At the same time, the results can give guidance for the process of, such as energy medium distribution design, and allocate some processes’ production capacity.(4)The adjustment of devices’ capacity to reduce the gas surplus can improve the energy efficiency of the completely steel production process, which can reduce the energy consumption indirectly.(5)Due to the limitation of each plants’ equipment, the steel production and specific energy consumption cannot reach the best situation contemporary. Therefore, it is essential to arrange the capacity of each plant in the integrated steel plant. The model is helpful in device configuration.(6)This model can use the computer to realize dynamic simulation and optimization on the spot, so it can guide the production process real-time. On the other hand, the modeling method of this paper can provide reference for other process industries.


This research is financially supported by the National Basic Research Program of China (973 Program) (no. 2012CB720405) and supported by the Fundamental Research Funds for the Central Universities (no. FRF-SD-12-006B). The authors also greatly thank the editors and reviewers for their comments.


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