Patent Publication Number: US-2023151447-A1

Title: Optimal calculation method of energy operating condition in iron mill, optimal calculation device of energy operating condition in iron mill, and running method of iron mill

Description:
FIELD 
     The present invention relates to an optimal calculation method of the energy operating condition in an iron mill, an optimal calculation device of the energy operating condition in an iron mill, and a running method of an iron mill. 
     BACKGROUND 
     In general, iron mills include a large number of factories and a plurality of power generation facilities from upper processes (blast furnaces, coke ovens, steelmaking processes, etc.) to lower processes (rolling processes, surface treatment processes, etc.), and the following energy (gas, steam, and power) operation is performed. 
     That is, B gas (blast furnace gas) generated in a blast furnace, C gas (coke oven gas) generated in a coke oven, by-product gas such as LD gas (LD converter gas) generated in a converter, and M gas (mixed gas) obtained by mixing these by-product gases and adjusting a heat quantity are used in factories or power generation facilities. In a case where a gas supply amount is insufficient with respect to a factory demand (for example, a demand amount in a heating furnace of a rolling mill), it is supplemented with city gas to satisfy the factory demand. In addition, in a case where the gas supply amount to power generation facilities is insufficient with respect to a predetermined amount, it is supplemented with heavy oil. These supplemental fuels cost depending on the amount used. On the other hand, in a case where the gas supply amount is excessive with respect to the factory demand, the gas is detoxified by combustion and then released into the atmosphere, but this leads to energy loss and carbon dioxide emission and thus should be minimized. 
     In order to reduce the cost and suppress the release, it is necessary to use a gas holder that is a storage facility for by-product gases or to appropriately adjust the gas distribution amount. As an example, in a gas holder, in a situation where the supply amount of by-product gases is larger than the demand amount, the storage amount (gas holder level) of the by-product gases is increased by storing the by-product gases in the gas holder in preference to releasing, thereby suppressing the release. On the other hand, in a situation where the demand amount for by-product gases is larger than the supply amount, the stored gas is discharged from the gas holder to satisfy the demand, thereby reducing the amount of supplementary fuel used. In addition, in a case where the demand amount of by-product gases is further larger than the supply amount, the output of power generation facilities is reduced. Moreover, in a case where it is still not possible to deal with the problem, the running level of the factory may be lowered. 
     Steam is supplied by operations such as steam extraction from an exhaust heat recovery boiler from LD gas or a sintering furnace, a boiler of a coke drying quenching (CDQ) facility, and a turbine middle stage of a power generation facility (operation of obtaining steam from a turbine middle stage, the power generation amount is reduced) and is used in a factory (acid pickling tank heating in a cold rolling factory or a vacuum degassing facility). For an amount in shortage with respect to the steam demand, purchase is made from an external party. In addition, the power demand of the factory is satisfied by the amount of power generation in the CDQ, a top-pressure recovery turbine (TRT), and power generation facilities and power purchase from an electric power company. The amount of power purchased needs to be managed so as not to exceed the contract amount per hour (upper limit of the amount of power purchased). In addition, since the power purchase unit price varies depending on hours of the day, in a case where it is in hours when the unit price is high and there is an excess in the by-product gas supply amount, the operation conditions that minimize the cost varies depending on hours of the day or the supply and demand situation, such as setting the output of the power generation facilities high to reduce the power purchase amount. 
     From such a background, technology for minimizing energy operation cost in an iron mill has been proposed (see Patent Literatures 1 and 2 and Non-Patent Literature 1). 
     CITATION LIST 
     Patent Literature 
     
         
         Patent Literature 1: Japanese Patent No. 5862839 
         Patent Literature 2: JP 2004-171548 A 
       
    
     Non Patent Literature 
     
         
         Non Patent Literature 1: Yujiao Zeng, Xin Xiao, Jie Li, Li Sun, Christodoulos A. Floudas, Hechang Li, “A novel multi-period mixed-integer linear optimization model for optimal distribution of byproduct gases, steam and power in an iron and steel plant”, Energy. 2018, vol. 143, p. 881-899. 
       
    
     SUMMARY 
     Technical Problem 
     All of the technology described in Patent Literatures 1 and 2 and Non-Patent Literature 1 solve a mixed integer programming problem suitable for appropriately describing the operation condition or running rules of a plant in order to obtain the optimal energy operating condition of an iron mill or a plant. This mixed integer programming problem includes both a continuous variable and an integer variable in a decision variable vector (a variable vector obtained by searching). Here, each element of the decision variable vector is a variable indicating an energy operating condition such as gas distribution or steam distribution. As a solution to this problem, a branch and bound method, which is an explicit solution technique, is often used, but the branch and bound method is a method of efficiently searching for an optimal solution by not searching for a candidate of a solution with which the cost is unlikely to be improved even the search is performed. Then, the search is ended when a cost difference between an executable solution satisfying all the constraint conditions and a relaxed continuous solution (solution when a part of the integer variable is relaxed to a continuous variable) becomes equal to or less than a certain threshold value in the process of the search. 
     However, although the branch and bound method is basically an efficient search method, the calculation time varies depending on the structure or the scale of the problem, and a satisfactory solution may not be obtained within a set time in some cases. This is problematic particularly in an energy operation system that is required to obtain an optimal solution at constant periods. The technology described in Patent Literatures 1 and 2 and Non-Patent Literature 1 relate to a formulation method for improving the quality of a solution, and no formulation method for shortening the calculation time has been studied. In particular, there is a disadvantage that the number of decision variables increases and the calculation time increases in a case where a plurality of factories and power generation facilities are included as in an iron mill and running rules thereof are complicated. 
     The present invention has been made in view of the above disadvantages, and an object of the present invention is to provide an optimal calculation method and an optimal calculation device of the energy operating condition in an iron mill capable of shortening a time required for optimal calculation of the energy operating condition in the iron mill. Another object of the present invention is to provide a running method of an iron mill capable of running the iron mill under the optimal energy operating condition. 
     Solution to Problem 
     An optimal calculation method of an energy operating condition in an iron mill according to the present invention includes: calculating, using a total energy operation cost of the iron mill within a predetermined period of time from a current time as an evaluation function, an operation condition of an energy facility in the iron mill as a decision variable such that a value of the evaluation function decreases, at each predetermined time within the predetermined period of time, based on actual values and estimated values of a generation amount and a used amount of energy utility for each of factories comprised in the iron mill, wherein the method includes a step of calculating the decision variable by imposing an equality constraint such that the decision variable related to a power generation facility included in the energy facility is constant within a predetermined aggregation time. 
     The energy utility for each of the factories may include gas, steam, and electric power. 
     The energy facility may include a mixed gas production facility, a gas holder, a coke drying quenching facility, a top-pressure recovery turbine facility, and a power generation facility that uses by-product gas, heavy oil, or steam extraction. 
     The total energy operation cost may include a cost associated with use of heavy oil, city gas, and steam and a cost associated with purchase of electricity. 
     An optimal calculation device of an energy operating condition in an iron mill according to the present invention calculates, using a total energy operation cost of the iron mill within a predetermined period of time from a current time as an evaluation function, an operation condition of an energy facility in the iron mill as a decision variable such that a value of the evaluation function decreases, at each predetermined time within the predetermined period of time, based on actual values and estimated values of a generation amount and a used amount of energy utility for each of factories comprised in the iron mill, and includes a calculator configured to calculate the decision variable by imposing an equality constraint so that the decision variable related to a power generation facility included in the energy facility is constant within a predetermined aggregation time. 
     An operating method of an iron mill according to the present invention includes a step of operating the iron mill based on the decision variable calculated by the optimal calculation method of an energy operating condition in an iron mill according to the present invention. 
     Advantageous Effects of Invention 
     According to the optimal calculation method and the optimal calculation device of the energy operating condition in an iron mill of the present invention, a time required for the optimal calculation of the energy operating condition in the iron mill can be shortened. In addition, according to the running method of an iron mill according to the present invention, the iron mill can be run under the optimal energy operating condition. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a block diagram illustrating a configuration of an optimal calculation device of the energy operating condition in an iron mill as an embodiment of the present invention. 
         FIG.  2    is a flowchart illustrating a flow of optimal calculation processing as an embodiment of the present invention. 
         FIG.  3    is a diagram for explaining the aggregation constraint condition for decision variables. 
         FIG.  4    is a graph illustrating changes in cost in an example of the present invention and a comparative example. 
         FIG.  5    is a graph illustrating changes in electric power generation in the example of the present invention and the comparative example. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, an optimal calculation device of the energy operating condition in an iron mill as an embodiment of the present invention will be described with reference to the drawings. 
     [Configuration] 
     First, with reference to  FIG.  1   , a configuration of the optimal calculation device of the energy operating condition in an iron mill as an embodiment of the present invention will be described. 
       FIG.  1    is a block diagram illustrating the configuration of the optimal calculation device of the energy operating condition in an iron mill according to the embodiment of the present invention. As illustrated in  FIG.  1   , the optimal calculation device of the energy operating condition in an iron mill as an embodiment of the present invention includes an information processing device  1  such as a workstation. The optimal calculation device of the energy operating condition in an iron mill as an embodiment of the present invention functions as an information acquisition unit  11  and an optimal calculation unit  12  when an arithmetic processing device inside the information processing device  1  executes a computer program. The functions of these units will be described later. 
     The optimal calculation device having such a configuration shortens the time required for optimal calculation of the energy operating condition in an iron mill by executing the following optimal calculation processing. Hereinafter, the operation of the optimal calculation device when executing the optimal calculation processing will be described with reference to  FIGS.  2  and  3   . 
     [Optimal Calculation Processing] 
       FIG.  2    is a flowchart illustrating a flow of the optimal calculation processing as an embodiment of the present invention. The flowchart illustrated in  FIG.  2    starts at timing when an execution command of the optimal calculation processing is input to the information processing device  1 , and the optimal calculation processing proceeds to the processing of step S 1 . 
     In the processing of step S 1 , the information acquisition unit  11  acquires data of actual values and estimated values of the generation amount and the consumption amount of energy utility of a factory in the iron mill at the current time (t=0) as input data of the optimal calculation processing. Specifically, as illustrated in Table 1 below, the information acquisition unit  11  acquires data of actual values S B (0), S C (0), S L (0), and S St (0) and estimated values S B (k), S C (k), S L (k), and S St (k) (k=1 to N) of the generation amounts of the B gas, the C gas, the LD gas, and the steam as data of the actual values and the estimated values of the generation amount of the energy utility at the current time. In addition, as illustrated in Table 2 below, the information acquisition unit  11  acquires data of actual values D B (0), D C (0), D L (0), D M (0), D St (0), and D E (0) and estimated values D B (k), D C (k), D L (k), D M (k), D St (k), and D E (k) (k=1 to N) of consumption amounts of the B gas, the C gas, the LD gas, the M gas, the steam, and the power as the data of actual values and estimated values of consumption amounts of energy utility at the current time. Each of the estimated values is obtained by estimating the generation amount and the used amount of the energy utility of each factory on the basis of the production plan of each factory in the iron mill. The production plan includes a long-term plan of about one week in addition to a short-term plans of several hours and one to two days from the present point of time, and the accuracy becomes higher for the short-term production plans. Therefore, estimated values obtained using the production plans also have a similar tendency of accuracy. With the above, the processing of step S 1  is completed, and the optimal calculation processing proceeds to the processing of step S 2 . 
     
       
         
           
               
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
             
            
               
                   
                   
               
               
                   
                 Actual 
                   
                   
                   
                   
               
               
                   
                 Value 
               
            
           
           
               
               
               
            
               
                   
                 (Current 
                 Estimated Value 
               
            
           
           
               
               
               
               
               
               
            
               
                 Item 
                 Time) 
                 k = 1 
                 k = 2 
                 . . . 
                 k = N 
               
               
                   
               
               
                 B Gas Generation 
                 S B (0) 
                 S B (1) 
                 S B (2) 
                 . . . 
                 S B (N) 
               
               
                 Amount (Blast 
               
               
                 Furnace Total 
               
               
                 Value) 
               
               
                 C Gas Generation 
                 S C (0) 
                 S C (1) 
                 S C (2) 
                 . . . 
                 S C (N) 
               
               
                 Amount (Coke Oven 
               
               
                 Total Value) 
               
               
                 LD Gas Generation 
                 S L (0) 
                 S L (1) 
                 S L (2) 
                 . . . 
                 S L (N) 
               
               
                 Amount (Converter 
               
               
                 Total Value) 
               
               
                 Steam Generation 
                 S St (0) 
                 S St (1) 
                 S St (2) 
                 . . . 
                 S St (N) 
               
               
                 Amount (Factory 
               
               
                 Total Value) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
             
               
                   
                 TABLE 2 
               
             
            
               
                   
                   
               
               
                   
                 Actual 
                   
                   
                   
                   
               
               
                   
                 Value 
               
            
           
           
               
               
               
            
               
                   
                 (Current 
                 Estimated Value 
               
            
           
           
               
               
               
               
               
               
            
               
                 Item 
                 Time) 
                 k = 1 
                 k = 2 
                 . . . 
                 k = N 
               
               
                   
               
               
                 B Gas Consumption 
                 D B (0) 
                 D B (1) 
                 D B (2) 
                 . . . 
                 D B (N) 
               
               
                 Amount (Factory 
               
               
                 Total Value) 
               
               
                 C Gas Consumption 
                 D C (0) 
                 D C (1) 
                 D C (2) 
                 . . . 
                 D C (N) 
               
               
                 Amount (Factory 
               
               
                 Total Value) 
               
               
                 LD Gas 
                 D L (0) 
                 D L (1) 
                 D L (2) 
                 . . . 
                 D L (N) 
               
               
                 Consumption 
               
               
                 Amount (Factory 
               
               
                 Total Value) 
               
               
                 M Gas Consumption 
                 D M (0) 
                 D M (1) 
                 D M (2) 
                 . . . 
                 D M (N) 
               
               
                 Amount (Factory 
               
               
                 Total Value) 
               
               
                 Steam Consumption 
                 D St (0) 
                 D St (1) 
                 D St (2) 
                 . . . 
                 D St (N) 
               
               
                 Amount (Factory 
               
               
                 Total Value) 
               
               
                 Electric Power 
                 D E (0) 
                 D E (1) 
                 D E (2) 
                 . . . 
                 D E (N) 
               
               
                 Consumption 
               
               
                 Amount (Factory 
               
               
                 Total Value) 
               
               
                   
               
            
           
         
       
     
     In the processing of step S 2 , as illustrated in Table 3 below, the information acquisition unit  11  acquires data of actual values S StCDQ (0) and S ETRT (0) and estimated values S StCDQ (k) and S ETRT (k) (k=1 to N) of the CDQ boiler steam amount and the TRT power generation amount at the current time as input data for the optimal calculation processing. As a result, the processing of step S 2  is completed, and the optimal calculation processing proceeds to the processing of step S 3 . 
     
       
         
           
               
               
               
               
               
               
             
               
                   
                 TABLE 3 
               
             
            
               
                   
                   
               
               
                   
                 Actual 
                   
                   
                   
                   
               
               
                   
                 Value 
               
            
           
           
               
               
               
            
               
                   
                 (Current 
                 Estimated Value 
               
            
           
           
               
               
               
               
               
               
            
               
                 Item 
                 Time) 
                 k = 1 
                 k = 2 
                 . . . 
                 k = N 
               
               
                   
               
               
                 CDQ Boiler 
                 S StCDQ (0) 
                 S StCDQ (1) 
                 S StCDQ (2) 
                 . . . 
                 S StCDQ (N) 
               
               
                 Steam 
               
               
                 (All Units) 
               
               
                 TRT Power 
                 S ETRT (0) 
                 S ETRT (1) 
                 S ETRT (2) 
                 . . . 
                 S ETRT (N) 
               
               
                 Generation 
               
               
                 Amount 
               
               
                 (All Units) 
               
               
                   
               
            
           
         
       
     
     In the processing of step S 3 , the information acquisition unit  11  acquires data of actual values of the amount of fuel used in all the power generation facilities in the iron mill at the current time. Specifically, in general, the M gas obtained by mixing by-product gases and adjusting the heat quantity is used in addition to the B gas, the C gas, and the LD gas as fuel in an iron mill. In addition, when a predetermined power generation amount cannot be ensured, using heavy oil or steam extraction from a CDQ turbine may be performed. Therefore, as illustrated in Table 4 below, the information acquisition unit  11  acquires data of actual values D BxU (0), D CxU (0), D LxU (0), D MxU (0), D OxU (0), S StxU (0) (x represents the identification number of a power generation facility) of amounts of the B gas, the C gas, the LD gas, the M gas, heavy oil, and extracted steam used in all power generation facilities in the iron mill at the current time. As a result, the processing of step S 3  is completed, and the optimal calculation processing proceeds to the processing of step S 4 . 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
               
                   
                   
                   
                   
                   
                   
                 Extracted 
               
               
                 Unit 
                   
                   
                   
                   
                 Heavy 
                 Steam 
               
               
                 Number 
                 B Gas 
                 C Gas 
                 LD gas 
                 M Gas 
                 Oil 
                 Amount 
               
               
                   
               
             
            
               
                 Unit 1 
                 D B1U  (0) 
                 D C1U  (0) 
                 D L1U  (0) 
                 D M1U  (0) 
                 D O1U  (0) 
                 D St1U  (0) 
               
               
                 Unit 2 
                 D B2U  (0) 
                 D C2U  (0) 
                 D L2U  (0) 
                 D M2U  (0) 
                 D O2U  (0) 
                 D St2U  (0) 
               
               
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
               
               
                 Unit x 
                 D BxU  (0) 
                 D CxU  (0) 
                 D LxU  (0) 
                 D MxU  (0) 
                 D OxU  (0) 
                 D StxU  (0) 
               
               
                   
               
            
           
         
       
     
     In the processing of step S 4 , as illustrated in Table 5 below, the information acquisition unit  11  acquires data of actual values D BPow (0), D CPow (0), D LPow (0), and D TPow (0) of the amounts of the B gas, the C gas, the LD gas, and the city gas at the current time in a mixed gas manufacturing facility that supplies the M gas to the power generation facilities in the iron mill. In addition, as illustrated in Table 5 below, the information acquisition unit  11  acquires data of actual values D BMill (0), D CMill (0), D LMill (0), and D TMill (0) of the amounts of the B gas, the C gas, the LD gas, and the city gas at the current time in the mixed gas manufacturing facility that supplies the M gas to the factories in the iron mill. With the above, the processing of step S 4  is completed, and the optimal calculation processing proceeds to the processing of step S 5 . 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 5 
               
               
                   
               
               
                 Item 
                 B Gas 
                 C Gas 
                 LD Gas 
                 City Gas 
               
               
                   
               
             
            
               
                 M Gas for Power 
                 D BPow (0) 
                 D CPow (0) 
                 D LPow (0) 
                 D TPow (0) 
               
               
                 Generation 
               
               
                 Facilities 
               
               
                 M Gas for Factories 
                 D BMill (0) 
                 D CMill (0) 
                 D LMill (0) 
                 D TMill (0) 
               
               
                   
               
            
           
         
       
     
     In the processing of step S 5 , as illustrated in Table 6 below, the information acquisition unit  11  acquires data of gas storage amounts H BLevel (0), H CLevel (0), and H LLevel (0) and actual values H B (0), H C (0), and H L  (0) of the intake amount and discharge amount of gas holders for the B gas, the C gas, and the LD gas at the current time. With the above, the processing of step S 5  is completed, and the optimal calculation processing proceeds to the processing of step S 6 . 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 6 
               
               
                   
                   
               
               
                   
                   
                   
                 Actual Intake and 
               
               
                   
                 Item 
                 Storage Amount 
                 Discharge 
               
               
                   
                   
               
             
            
               
                   
                 B Gas Holder 
                 H BLevel (0) 
                 H B (0) 
               
               
                   
                 C Gas Holder 
                 H CLevel (0) 
                 H C (0) 
               
               
                   
                 LD Gas Holder 
                 H LLevel (0) 
                 H L (0) 
               
               
                   
                   
               
            
           
         
       
     
     In the processing of step S 6 , the information acquisition unit  11  acquires data of a unit price set value necessary for calculating the cost for energy operation of the iron mill. Specifically, as illustrated in Table 7 below, the information acquisition unit  11  acquires data of actual values C Ele  (0), C St (0), C O (0), and C T (0) and future contract values C Ele (k), C St (k), C O (k), and C T (k) (k=1 to N) of unit prices of the electric power, steam, heavy oil, and city gas at the current time. With the above, the processing of step S 6  is completed, and the optimal calculation processing proceeds to the processing of step S 7 . 
     
       
         
           
               
               
               
               
               
               
             
               
                   
                 TABLE 7 
               
             
            
               
                   
                   
               
               
                   
                 Actual 
                   
                   
                   
                   
               
               
                   
                 Value 
               
            
           
           
               
               
               
            
               
                   
                 (Current 
                 Contract Value 
               
            
           
           
               
               
               
               
               
               
            
               
                 Item 
                 Time) 
                 k = 1 
                 k = 2 
                 . . . 
                 k = N 
               
               
                   
               
               
                 Unit Price of 
                 C Ele (0) 
                 C Ele (1) 
                 C Ele (2) 
                 . . . 
                 C Ele (N) 
               
               
                 Electric Power 
               
               
                 (Yen/kWh) 
               
               
                 Unit Price of 
                 C St (0) 
                 C St (1) 
                 C St (2) 
                 . . . 
                 C St (N) 
               
               
                 Steam (Yen/ton) 
               
               
                 Unit Price of 
                 C O (0) 
                 C O (1) 
                 C O (2) 
                 . . . 
                 C O (N) 
               
               
                 Heavy Oil 
               
               
                 (Yen/GJ) 
               
               
                 Unit Price of 
                 C T (0) 
                 C T (1) 
                 C T (2) 
                 . . . 
                 C T (N) 
               
               
                 City Gas 
               
               
                 (Yen/GJ) 
               
               
                   
               
            
           
         
       
     
     In the processing of step S 7 , the optimal calculation unit  12  uses the data acquired in the processing of steps S 1  to S 6  and executes the optimal calculation for obtaining the condition for minimizing the cost for the energy operation of the iron mill in a predetermined period (k=1 to N) from the current time. Specifically, the decision variables (variables searched in order to minimize the cost) in the optimal calculation are the amounts of the B gas, the C gas, the LD gas, the M gas, the heavy oil, and the steam extraction used in the power generation facilities illustrated in Table 8 below, the amounts of the B gas, the C gas, the LD gas, and the city gas in the mixed gas manufacturing facility D BPow (k), D CPow (k), D LPow (k), D TPow (k), D BMill (k), D CMill (k), D LMill (k), and D TMill (k) illustrated in Table 9 below, the gas storage amounts H BLevel (k), H CLevel (k), H LLevel (k) and the intake amounts and the discharge amounts H B (k), H C (k), H L (k) of the gas holders illustrated in Table 10, the amount of power purchased S EPurchase (k), the amount of steam extraction S StExtCDQ (k) from the CDQ turbine, and the amount of steam purchased S StPurchase (k) 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 8 
               
               
                   
               
               
                   
                   
                   
                   
                   
                   
                 Extracted 
               
               
                 Unit 
                   
                   
                   
                   
                 Heavy 
                 Steam 
               
               
                 Number 
                 B Gas 
                 C Gas 
                 LD Gas 
                 M Gas 
                 Oil 
                 Amount 
               
               
                   
               
             
            
               
                 Unit 1 
                 D B1U  (k) 
                 D C1U  (k) 
                 D L1U  (k) 
                 D M1U  (k) 
                 D O1U  (k) 
                 D St1U  (k) 
               
               
                 Unit 2 
                 D B2U  (k) 
                 D C2U  (k) 
                 D L2U  (k) 
                 D M2U  (k) 
                 D O2U  (k) 
                 D St2U  (k) 
               
               
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
               
               
                 Unit x 
                 D BxU  (k) 
                 D CxU  (k) 
                 D LxU  (k) 
                 D MxU  (k) 
                 D OxU  (k) 
                 D StxU  (k) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 9 
               
               
                   
               
               
                 Item 
                 B Gas 
                 C Gas 
                 LD Gas 
                 City Gas 
               
               
                   
               
             
            
               
                 M Gas for Power 
                 D BPow (k) 
                 D CPow (k) 
                 D LPow (k) 
                 D TPow (k) 
               
               
                 Generation 
               
               
                 Facilities 
               
               
                 M Gas for Factories 
                 D BMill (k) 
                 D CMill (k) 
                 D LMill (k) 
                 D TMill (k) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 10 
               
               
                   
                   
               
               
                   
                   
                   
                 Intake and 
               
               
                   
                 Item 
                 Storage Amount 
                 Discharge Amount 
               
               
                   
                   
               
             
            
               
                   
                 B Gas Holder 
                 H BLevel (k) 
                 H B (k) 
               
               
                   
                 C Gas Holder 
                 H CLevel (k) 
                 H C (k) 
               
               
                   
                 LD Gas Holder 
                 H LLevel (k) 
                 H L (k) 
               
               
                   
                   
               
            
           
         
       
     
     Meanwhile, the cost to be minimized is the sum of heavy oil as a supplemental fuel, city gas, steam, and the amount of power purchased. Each unit price is as illustrated in Table 7, and a total value f of the cost from the current time to N periods ahead is described using the unit prices as expressed in the following formula (1). In addition, the following constraint conditions (a) to (1) are set at the time of the optimal calculation. With the above, the processing of step S 7  is completed, and a series of steps of the optimal calculation processing ends. 
         f=Σ   k=1   N ( C   Ele ( k ) S   EPurchase ( k )+ C   St ( k ) S   StPurchase ( k )+ C   O ( k )Σ j=1   x   D   OjU ( k )+ C   T ( k )( D   TPow ( k )+ D   TMill ( k )))  (1)
 
     (a) B Gas Balance Constraint 
     
       
         
           
             
               
                 
                   
                     
                       S 
                       B 
                     
                     ( 
                     k 
                     ) 
                   
                   = 
                   
                     
                       
                         D 
                         B 
                       
                       ( 
                       k 
                       ) 
                     
                     + 
                     
                       
                         
                           
                             
                               D 
                               BPow 
                             
                             ⁢ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           + 
                           
                             
                               D 
                               BMill 
                             
                             ⁢ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         _ 
                       
                       
                         For 
                         ⁢ 
                            
                         M 
                         ⁢ 
                            
                         gas 
                       
                     
                     + 
                     
                       
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             x 
                           
                           
                             
                               D 
                               BjU 
                             
                             ( 
                             k 
                             ) 
                           
                         
                         _ 
                       
                       
                         
                           
                             
                               for 
                               ⁢ 
                                  
                               power 
                             
                           
                         
                         
                           
                             
                               generation 
                               ⁢ 
                                  
                               facility 
                             
                           
                         
                       
                     
                     + 
                     
                       
                         
                           
                             H 
                             B 
                           
                           ( 
                           k 
                           ) 
                         
                         _ 
                       
                       
                         
                           
                             
                               intake 
                               ⁢ 
                                  
                               amount 
                             
                           
                         
                         
                           
                             
                               of 
                               ⁢ 
                                  
                               gas 
                               ⁢ 
                                  
                               hold 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     (b) C Gas Balance Constraint 
     
       
         
           
             
               
                 
                   
                     
                       S 
                       C 
                     
                     ⁢ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         D 
                         C 
                       
                       ⁢ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     + 
                     
                       
                         
                           
                             
                               D 
                               CPow 
                             
                             ⁢ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           + 
                           
                             
                               D 
                               CMill 
                             
                             ⁢ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         _ 
                       
                       
                         For 
                         ⁢ 
                            
                         M 
                         ⁢ 
                            
                         gas 
                       
                     
                     + 
                     
                       
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             x 
                           
                           
                             
                               D 
                               CjU 
                             
                             ( 
                             k 
                             ) 
                           
                         
                         _ 
                       
                       
                         
                           
                             
                               for 
                               ⁢ 
                                  
                               power 
                             
                           
                         
                         
                           
                             
                               generation 
                               ⁢ 
                                  
                               facility 
                             
                           
                         
                       
                     
                     + 
                     
                       
                         
                           
                             H 
                             C 
                           
                           ( 
                           k 
                           ) 
                         
                         _ 
                       
                       
                         
                           
                             
                               intake 
                               ⁢ 
                                  
                               amount 
                             
                           
                         
                         
                           
                             
                               of 
                               ⁢ 
                                  
                               gas 
                               ⁢ 
                                  
                               holder 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     (c) LD Gas Balance Constraint 
     
       
         
           
             
               
                 
                   
                     
                       S 
                       L 
                     
                     ( 
                     k 
                     ) 
                   
                   = 
                   
                     
                       
                         D 
                         L 
                       
                       ( 
                       k 
                       ) 
                     
                     + 
                     
                       
                         
                           
                             
                               D 
                               LPow 
                             
                             ⁢ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           + 
                           
                             
                               D 
                               LMill 
                             
                             ⁢ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         _ 
                       
                       
                         For 
                         ⁢ 
                            
                         M 
                         ⁢ 
                            
                         gas 
                       
                     
                     + 
                     
                       
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             x 
                           
                           
                             
                               D 
                               LjU 
                             
                             ( 
                             k 
                             ) 
                           
                         
                         _ 
                       
                       
                         
                           
                             
                               for 
                               ⁢ 
                                  
                               power 
                             
                           
                         
                         
                           
                             
                               generation 
                               ⁢ 
                                  
                               facility 
                             
                           
                         
                       
                     
                     + 
                     
                       
                         
                           
                             H 
                             L 
                           
                           ( 
                           k 
                           ) 
                         
                         _ 
                       
                       
                         
                           
                             
                               intake 
                               ⁢ 
                                  
                               amount 
                             
                           
                         
                         
                           
                             
                               of 
                               ⁢ 
                                 
                               gas 
                               ⁢ 
                                  
                               holder 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     (d) Factory M Gas Balance Constraint 
         D   M ( k )= D   BMill ( k )+ D   CMill ( k )+ D   LMill ( k )+ D   TMill ( k )  (5)
 
     (e) Power Generation Facility M Gas Balance Constraint 
     
       
         
           
             
               
                 
                   
                     
                       ∑ 
                       
                         J 
                         = 
                         1 
                       
                       x 
                     
                     
                       
                         D 
                         MjU 
                       
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         D 
                         BPow 
                       
                       ( 
                       k 
                       ) 
                     
                     + 
                     
                       
                         D 
                         
                           C 
                           ⁢ 
                           P 
                           ⁢ 
                           o 
                           ⁢ 
                           w 
                         
                       
                       ( 
                       k 
                       ) 
                     
                     + 
                     
                       
                         D 
                         LPow 
                       
                       ( 
                       k 
                       ) 
                     
                     + 
                     
                       
                         D 
                         
                           T 
                           ⁢ 
                           P 
                           ⁢ 
                           o 
                           ⁢ 
                           w 
                         
                       
                       ( 
                       k 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     (f) Gas Holder Storage Amount 
         H   BLevel ( k )= H   BLevel ( k− 1)+ H   B ( k ) T   (7-1)
 
         H   CLevel ( k )= H   CLevel ( k− 1)+ H   C ( k ) T   (7-2)
 
         H   LLevel ( k )= H   LLevel ( k− 1)+ H   L ( k ) T   (7-3)
 
     Where T represents a fixed time interval. 
     (g) Power Generation Facility Model 
     
       
         
           
             
               
                 
                   
                     
                       S 
                       
                         E 
                         ⁢ 
                         1 
                         ⁢ 
                         U 
                       
                     
                     ( 
                     k 
                     ) 
                   
                   = 
                   
                     
                       f 
                       1 
                     
                     ( 
                     
                       
                         
                           
                             D 
                             
                               B 
                               ⁢ 
                               1 
                               ⁢ 
                               U 
                             
                           
                           ( 
                           k 
                           ) 
                         
                         + 
                         
                           
                             D 
                             
                               C 
                               ⁢ 
                               1 
                               ⁢ 
                               U 
                             
                           
                           ( 
                           k 
                           ) 
                         
                         + 
                         
                           
                             D 
                             
                               L 
                               ⁢ 
                               1 
                               ⁢ 
                               U 
                             
                           
                           ( 
                           k 
                           ) 
                         
                         + 
                         
                           
                             D 
                             
                               M 
                               ⁢ 
                               1 
                               ⁢ 
                               U 
                             
                           
                           ( 
                           k 
                           ) 
                         
                         + 
                         
                           
                             D 
                             
                               O 
                               ⁢ 
                               1 
                               ⁢ 
                               U 
                             
                           
                           ( 
                           k 
                           ) 
                         
                       
                       , 
                       
 
                       
                         
                           S 
                           
                             St 
                             ⁢ 
                             1 
                             ⁢ 
                             U 
                           
                         
                         ( 
                         k 
                         ) 
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   
                     8 
                     - 
                     1 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     
                       S 
                       
                         E 
                         ⁢ 
                         2 
                         ⁢ 
                         U 
                       
                     
                     ( 
                     k 
                     ) 
                   
                   = 
                   
                     
                       f 
                       2 
                     
                     ( 
                     
                       
                         
                           
                             D 
                             
                               B 
                               ⁢ 
                               2 
                               ⁢ 
                               U 
                             
                           
                           ( 
                           k 
                           ) 
                         
                         + 
                         
                           
                             D 
                             
                               C 
                               ⁢ 
                               2 
                               ⁢ 
                               U 
                             
                           
                           ( 
                           k 
                           ) 
                         
                         + 
                         
                           
                             D 
                             
                               L 
                               ⁢ 
                               2 
                               ⁢ 
                               U 
                             
                           
                           ( 
                           k 
                           ) 
                         
                         + 
                         
                           
                             D 
                             
                               M 
                               ⁢ 
                               2 
                               ⁢ 
                               U 
                             
                           
                           ( 
                           k 
                           ) 
                         
                         + 
                         
                           
                             D 
                             
                               O 
                               ⁢ 
                               2 
                               ⁢ 
                               U 
                             
                           
                           ( 
                           k 
                           ) 
                         
                       
                       , 
                       
 
                       
                         
                           S 
                           
                             St 
                             ⁢ 
                             2 
                             ⁢ 
                             U 
                           
                         
                         ( 
                         k 
                         ) 
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   
                     8 
                     - 
                     2 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             	 
             ⋮ 
           
         
       
       
         
           
             
               
                 
                   
                     
                       S 
                       ExU 
                     
                     ( 
                     k 
                     ) 
                   
                   = 
                   
                     
                       f 
                       x 
                     
                     ( 
                     
                       
                         
                           
                             D 
                             
                               B 
                               ⁢ 
                               x 
                               ⁢ 
                               U 
                             
                           
                           ( 
                           k 
                           ) 
                         
                         + 
                         
                           
                             D 
                             
                               C 
                               ⁢ 
                               x 
                               ⁢ 
                               U 
                             
                           
                           ( 
                           k 
                           ) 
                         
                         + 
                         
                           
                             D 
                             
                               L 
                               ⁢ 
                               x 
                               ⁢ 
                               U 
                             
                           
                           ( 
                           k 
                           ) 
                         
                         + 
                         
                           
                             D 
                             MxU 
                           
                           ( 
                           k 
                           ) 
                         
                         + 
                         
                           
                             D 
                             OxU 
                           
                           ( 
                           k 
                           ) 
                         
                       
                       , 
                       
 
                       
                         
                           S 
                           StxU 
                         
                         ( 
                         k 
                         ) 
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   
                     8 
                     - 
                     x 
                   
                   ) 
                 
               
             
           
         
       
     
     Where f n  (n=1, 2, . . . , x) represents a power generation model having an input heat amount and a steam extraction amount of a power generation facility as arguments. 
         S   ECDQ ( k )= f   CDQ ( S   StCDQ ( k ), S   StExtCDQ ( k ))  (9)
 
     Here, f CDQ  represents a power generation model having a boiler steam amount and a steam extraction amount of the CDQ as arguments. 
     (h) Power Balance Constraint 
         D   E ( k )= S   ETRT ( k )+ S   ECDQ ( k )+Σ j=1   x   S   EjU ( k )+ S   EPurchase ( k )  (10)
 
     (i) Steam Balance Constraint The steam generation amount and the steam consumption amount at time k (=1 to N) are equal. 
     
       
         
           
             
               
                 
                   
                     
                       S 
                       St 
                     
                     ( 
                     k 
                     ) 
                   
                   = 
                   
                     
                       
                         
                           D 
                           St 
                         
                         ( 
                         k 
                         ) 
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             1 
                           
                           x 
                         
                         
                           
                             S 
                             StjU 
                           
                           ( 
                           k 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         S 
                         StExtCDQ 
                       
                       ( 
                       k 
                       ) 
                     
                     + 
                     
                       
                         S 
                         StPurchase 
                       
                       ( 
                       k 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     (j) Upper and Lower Limits Constraint 
     An inequality constraining the upper and lower limits of a decision variable is set. For example, let a decision variable be V, an upper limit value thereof be U x , and a lower limit value thereof be L x , an inequality constraint expressed in the following formula (12) is obtained. 
         L   x   ≤V ( k )≤ U   x   (12)
 
     (k) Aggregation Constraint Condition for Decision Variables for Calculation Time Reduction 
     A constraint is provided to shorten the calculation (search) time by aggregating decision variables after a specified time and searching with the same value. For example, in a case where the terminal time is T×24 periods ahead of the current time as illustrated in  FIG.  3 ( a ) , a constraint is provided in which the specified time is aggregated in units of 3×T periods halfway after T×13 periods and search is performed with the same value during these periods as illustrated in  FIG.  3 ( b ) . Specifically, in the process of creating the constraint condition corresponding to N periods from the current time, the following aggregation constraint is imposed when the following condition 1 and condition 2 are simultaneously satisfied with the specified time as being J and the aggregation number as being n (natural number). Note that, in the present embodiment, the aggregation constraint condition is imposed on decision variables related to the power generation facilities. This is because it is difficult to make changes for a supply and demand facility of a factory since the supply and demand plan is set, whereas it is easy to change the operation condition of a power generation facility. In addition, it is preferable to set the designated time at a time after a time at which the accuracy of a production plan that an operator wants to know as reference information becomes relatively low. 
     (Condition 1) After the designated time J, equal to or less than the final time N. That is, J+1≤t≤N holds. 
     (Condition 2) Remainder determination (t−J) mod n=1 holds. This is a condition that the remainder obtained when (t−J) is divided by n is 1. 
     (Aggregation Constraint) An equality constraint V(t)=V(l) is set for l=t+1, . . . , min(t+n−1, N). 
     (1) Change Rate Constraint 
     In the case of defining the change rate, if the upper limit value is denoted by U v  and the lower limit value is denoted by L v , inequality constraints expressed in the following formulas (13) and (13)′ are obtained. 
         k= 1,2, . . . , J  where,  L   v ≤( V ( k )− V ( k− 1))/ T≤U   v   (13)
 
         k=J+ 1, . . . , N  where,  n L   v ≤( V ( k )− V ( k− 1))/ T≤nU   v   (13)′
 
     Here, formula (13)′ is necessary for increasing the change rate depending on the aggregation number n of the decision variable and thereby providing a change rate equivalent to that at a time at which the aggregation is not performed. 
     EXAMPLES 
     In an example of the invention, the terminal time is twelve periods ahead (one period lasts five minutes), and the optimal calculation was performed by setting the aggregation number to 6 after 7 periods for a plurality of decision variables representing the amount of fuel used at a plurality of power generation facilities, whereas in a conventional example, although the terminal time is twelve periods ahead, the optimal calculation was performed without performing aggregation, and the both results were compared. Note that calculation conditions for the both are the same except for whether or not decision variables are aggregated (cost unit price, supply and demand measurement values, etc. Processing of steps S 1  to S 6  illustrated in  FIG.  2   ), and the same computer was used for both calculations. As a result, the ratio of the calculation times between the conventional example and the example of the invention (=present example/conventional example) was about 0.90, and a 10% reduction in calculation time was achieved. This can be said to be an effect of the constraint condition in which the decision variables are aggregated in the present example. At this point, as illustrated in  FIG.  4   , the cost was almost equivalent to that of the conventional example up to the sixth period, and the cost of the present example became higher than that of the conventional example at and after the seventh period for which the aggregation was performed. This is because the search range is constrained by the aggregation of decision variables so that the power generation amount at and after the seventh period becomes a constant value as illustrated in  FIG.  5   , for example. Meanwhile, a utilization method is presumed in which the optimal calculation is executed at constant periods and the operator follows the calculation result of the time before the aggregation is performed and refers as reference values to the time after the aggregation is performed, and thus the influence on the cost is minor. 
     Although the embodiments to which the invention made by the present inventors is applied have been described above, the present invention is not limited by the description and the drawings included as a part of the disclosure of the present invention according to the present embodiments. That is, other embodiments, examples, operation techniques, and the like made by those skilled in the art on the basis of the present embodiment are all included in the scope of the present invention. 
     INDUSTRIAL APPLICABILITY 
     According to the present invention, it is possible to provide an optimal calculation method and an optimal calculation device of the energy operating condition in an iron mill capable of shortening a time required for optimal calculation of the energy operating condition in the iron mill. In addition, according to the present invention, it is possible to provide a running method of an iron mill capable of operating the iron mill under the optimal energy operating condition. 
     REFERENCE SIGNS LIST 
     
         
         
           
               1  INFORMATION PROCESSING DEVICE 
               11  INFORMATION ACQUISITION UNIT 
               12  OPTIMAL CALCULATION UNIT