A method for quantifying scheduling flexibility of short process steelmaking considering electric arc furnace thermal loss

Abstract

The application discloses a short-process steelmaking scheduling flexibility quantification method considering electric arc furnace heat loss, and belongs to the field of industrial load flexibility evaluation and steel production scheduling. The method uses furnace production decision variables to construct a variable batch resource task network model, forms a multi-stage production feasible region with device occupation, process connection, transfer time limit and product completion constraints; further establishes an energy balance between electric arc furnace input power, scrap steel heat absorption, melting temperature and heat conduction and radiation heat loss, and adopts a segmented McCormick relaxation process for continuous bilinear terms; then, the upper and lower power boundaries, the maximum duration of the boundaries and the maximum upward and downward climbing rates are solved in the unified feasible region. The application can quantify the plant-level flexibility of the short-process steel plant from three dimensions of power range, duration capability and dynamic response speed, and provide a quantitative reference for industrial load participating in power grid scheduling, demand response and auxiliary services.

Description

Technical Field

[0001] This invention relates to the field of industrial load flexibility assessment and steel production scheduling technology, and in particular to a method for quantifying the scheduling flexibility of short-process steelmaking considering heat loss from electric arc furnaces. Background Technology

[0002] The volatility and uncertainty of renewable energy output are increasing the demand for demand-side flexibility resources in the power system. Short-process steel enterprises, which primarily use electric arc furnaces, possess power regulation and production task time-shifting capabilities. They can participate in demand response, ancillary services, and power system dispatch by changing their power consumption and task start times. Accurately quantifying their adjustability is fundamental to developing executable response plans and determining the range of adjustable services available for industrial loads.

[0003] Current steel load flexibility assessments primarily target single equipment or specific processes such as electric arc furnaces, ladle furnaces, and hot rolling mills, typically expressing flexibility through adjustable power or reduced capacity over a given time period. Short-process steel production involves multiple stages, including melting, decarburization, refining, continuous casting, and rolling, with multiple constraints intertwined, such as equipment occupancy, product transfer, task priority, waiting time, and final delivery. The power range of a single piece of equipment does not equate to the actual adjustable capacity that the entire plant can deliver under multi-stage production constraints, nor does it simultaneously indicate how long that power can be maintained or how quickly it can change between adjacent scheduling periods.

[0004] Furthermore, during the melting process, the electric arc furnace converts input electrical energy into heat absorbed by the scrap steel, while simultaneously experiencing heat loss through water-cooled walls and furnace radiation. This heat loss varies with melting temperature, equipment power, melting duration, and furnace thermal parameters, thus altering the energy required to reach the final temperature and the feasible power trajectory. Existing electric arc furnace heat transfer models primarily serve thermal process analysis, while flexibility assessment models typically fail to incorporate heat loss, temperature evolution, and multi-stage production scheduling into the feasible domain, resulting in inconsistencies between the quantitative results of continuous adjustment capability and ramp-up capability and the actual melting process.

[0005] Therefore, there is an urgent need for a method to quantify the flexibility of the entire plant production process: using a variable batch resource task network model to characterize the coupling of multi-stage tasks and resources, using the energy balance and heat loss constraints of the electric arc furnace to limit the melting process, and then solving the plant-level flexibility quantification index from three dimensions: power boundary, flexibility duration, and ramp-up capability. Summary of the Invention

[0006] The purpose of this invention is to address the limitations of existing flexibility quantification methods, which are confined to single equipment or single regulation capacity and do not adequately consider multi-stage production coupling and electric arc furnace heat loss. This invention proposes a short-process steelmaking scheduling flexibility quantification method that considers electric arc furnace heat loss. This method uses both production feasibility and thermal feasibility to define the steel plant's power consumption trajectory and obtains power boundaries, sustainability duration, and maximum ramp rate within a unified feasible domain.

[0007] This invention proposes a method for quantifying the scheduling flexibility of short-process steelmaking considering heat loss from electric arc furnaces, comprising the following steps: (1) Obtain production, equipment and thermal parameters of the steel plant Acquire candidate furnace batches, processing equipment and product resources, processing and transfer tasks, equipment power and processing time range, resource generation and consumption coefficients, maximum transfer time, steel production scheduling intervals and power system reference scheduling intervals; acquire scrap steel quality, solid and liquid specific heat capacity, melting point, initial and final melting temperatures, water-cooled wall area, cooling water flow rate, inlet water temperature, ambient temperature, furnace body radiation area, emissivity, Stefan-Boltzmann constant and thermal resistance parameters.

[0008] (2) Construct a variable batch resource task network model for generating the plant-level feasible domain. Electric arc furnaces, argon-oxygen decarburization units, ladle refining units, continuous casting machines, rolling mills, and stage products are represented as resources, while the processing and transfer operations for each heat are represented as tasks. Heat-time production decision variables, task initiation variables, task execution status variables, and resource status variables are set. The heat-time production decision variables are used to control whether corresponding processing and transfer tasks are entered into scheduling, thus jointly determining the number of production heats and the task sequence.

[0009] The status of any resource is updated according to the following resource balance relationship: (1) in, For time period resources State value; Index for steel production scheduling periods; and These are the resource index and the task index, respectively. , and These are respectively the resource set, the task set, and the steel production scheduling time period set; This is a variable used to start the task; a value of 1 indicates the task is complete. During the period start up; n This is an index of the latency after the task starts; For the task Duration of action; For the task After starting n Resources in each time period The generation or consumption coefficient.

[0010] The production decision for each furnace and its associated tasks satisfy the following: (2) in, For the candidate furnace set; For furnace number index; For the production decision variable of each furnace, a value of 1 indicates the number of furnaces to be produced. A value of 0 indicates that no batches will be produced. ; In order to be related to the furnace Associated task index; For furnace A set of associated processing and transfer tasks.

[0011] The total transfer and waiting time between adjacent processes shall not exceed the allowable value: (3) in, This refers to the time interval for steel production scheduling. This is the product resource index corresponding to the termination location of the transfer task; For resources Transit time; For resources Maximum allowed transit and total waiting time.

[0012] The final product of the selected furnace batch is formed before the end of the scheduling cycle: (4) in, For furnace Product resource index corresponding to the final production stage; This refers to the final period of the steel production scheduling cycle.

[0013] For an electric arc furnace with power regulation capability, the power and duration for performing a melting task shall respectively satisfy: (5) in, For the task During the period The active power; This is a task execution status variable; a value of 1 indicates the task is running. During the period In the process of processing; and Tasks The lower and upper limits of power; This is the set of processing tasks corresponding to the power adjustable device.

[0014] (6) in, For processing tasks Subsequent transit task index; and Tasks The shortest and longest processing times; The steel production scheduling time period index used for summation.

[0015] Once started, the task executes continuously, and its execution state satisfies the following: (7) The cumulative energy input for the melting task meets the process requirements: (8) in, To complete the task Minimum cumulative energy required.

[0016] The aforementioned constraints, together with requirements for equipment occupancy, immediate relocation, and product delivery, constitute the multi-stage production feasible domain of the steel plant.

[0017] (3) Establish a melting process model that considers heat loss in electric arc furnace. The electrical energy input of an electric arc furnace during melting consists of two parts: heat absorbed by the scrap steel and heat loss from the electric arc furnace. (9) in, For time period Internal mission The heat absorbed by scrap steel; For time period Internal mission The resulting heat loss from the electric arc furnace.

[0018] (3-1) Calculate the heat absorbed by scrap steel and its melting state The amount of heat absorbed by scrap steel as it rises from its initial temperature to its melting point and then further to its final melting temperature is: (10) in, and These are the specific heat capacities of scrap steel in solid and liquid states, respectively. The quality of scrap steel per furnace batch; For binary melting state variables; For the task During the period The melting temperature of scrap steel.

[0019] Set a binary melting state variable to determine whether the scrap steel is in a solid or liquid state based on its temperature: (11) in, This is the melting point of scrap steel.

[0020] Utilize large M The method rewrites the above logical relationship into a linear constraint: (12) in, M It is a sufficiently large positive number.

[0021] (13) The melting temperature is within the range of initial and final temperatures: (14) in, and These are the initial melting temperature and the specified final melting temperature of scrap steel, respectively.

[0022] Temperature changes only occur during the melting process: (15) The temperature at the end of the scheduling cycle remains consistent with the temperature at the actual completion time of the melting task, and meets the specified final melting temperature: (16) (17) (3-2) Calculate heat conduction and radiation heat loss The total heat loss during the melting process consists of heat loss through water-cooled walls and heat loss through furnace radiation. (18) in, and Tasks During the period The heat loss due to heat conduction from the water-cooled wall and the heat loss due to radiation from the furnace body.

[0023] The heat loss of water-cooled walls is calculated based on the temperature rise of the cooling water: (19) in, This is the specific heat capacity of water; The density of water; For time period The volume of cooling water flowing through the water-cooled wall; and These are the cooling water outlet temperature and the inlet temperature, respectively.

[0024] Based on the Fourier thermal conductivity relation, establish the relationship between the representative temperature of scrap steel, the outlet temperature of cooling water, and the thermal resistance: (20) in, It is the equivalent thermal resistance between the furnace body and the water-cooled wall cooling system.

[0025] Thermal resistance is calculated from the heat transfer parameters of the water-cooled wall flow and the furnace wall: (twenty one) in, The coefficient of friction for the water-cooled wall flow; The Prandtl number of the cooling water; This refers to the wetted perimeter of the water-cooled wall. The thermal conductivity of water; The Reynolds number of the water-cooled wall; This refers to the wall thickness of the water-cooled tube. is the thermal conductivity of steel; This refers to the area of ​​the water-cooled wall; Pi is the mathematical constant of a circle.

[0026] The radiative heat loss of the furnace body is calculated based on the radiative heat transfer relationship: (twenty two) in, The emissivity of the furnace body; The outer surface radiation area of ​​the furnace body; The Stefan-Boltzmann constant; The ambient temperature.

[0027] To reduce the difficulty of solving the fourth-order temperature term, an auxiliary variable of temperature square is introduced: (twenty three) in, The square of the melting temperature is used as an auxiliary variable.

[0028] Rewrite the radiative heat loss in a continuous bilinear form: (twenty four) The product of binary and continuous variables is reconstructed using exact linearity, and the continuous bilinear terms in the radiation model are relaxed using piecewise McCormick relaxation, so that the feasible region of the steel plant with heat loss is transformed into a solvable mixed integer linear form.

[0029] (4) Map the electricity used for steel production to the reference dispatch period of the power system. Let the power system reference dispatch interval include Each steel production scheduling interval aggregates the steel electricity consumption within this reference time period into plant-level active power: (25) in, For time period The plant-level active power; To incorporate the actual power trajectory of the power-adjustable equipment, the steel mill during the time period Electricity consumption.

[0030] Therefore, a flexibility index is constructed on a time scale consistent with power grid dispatch.

[0031] (5) Quantization of power boundary The power boundary is used to describe the maximum and minimum active power that a steel plant can achieve in each reference scheduling period, under the conditions of variable batch production constraints, equipment operation constraints, and electric arc furnace heat loss constraints. The upper power boundary is obtained by solving the following optimization problem: (26) in, For power system reference dispatch period index; For reference scheduling period The plant-level active power; To and The corresponding set of steel production scheduling time period indexes; This refers to the number of steel production dispatch intervals included in a power system reference dispatch interval.

[0032] The active power at the plant level is calculated according to the following formula: (25) The lower power boundary is obtained by solving the following optimization problem: (27) The above-mentioned upper and lower power boundary optimization problems both use the multi-stage production feasible region formed in step (2) and the plant-level power consumption feasible region containing heat loss formed in step (3) as constraint sets.

[0033] (6) Quantification of flexibility duration For any reference scheduling period, the flexibility duration is represented by the number of periods during which the steel plant continuously maintains the upper or lower power boundary from that period onwards. During this maintenance, the requirements for subsequent task execution and final product completion must still be met. Taking the upper power boundary as an example, the maximum duration is obtained through the following optimization problem: (28) in, For steel mills during the period The number of time periods during which the selected power boundary is maintained; This serves as the reference scheduling period index in the duration calculation; To maintain the state variable at the boundary, a value of 1 indicates that the steel mill is in the time period. Maintain the selected power boundary; This refers to the end of the reference scheduling period; For time period The upper power boundary; For time period The plant-level active power.

[0034] Among them, the binary variable is used to identify whether the steel mill maintains the selected power boundary in the corresponding time period; the maximum duration of the lower power boundary is obtained in the same way.

[0035] (7) Quantifying climbing ability The ramp-up capability is represented by the maximum feasible rate of change of the steel plant's active power between adjacent reference scheduling periods. The maximum upward ramp-up rate is obtained through the following optimization problem: (29) in, For time period The upward slope rate; This is the reference dispatch time interval for the power system.

[0036] The maximum downhill ramp rate was obtained through the following optimization problem: (30) in, For time period The downward slope rate.

[0037] (8) Output plant-level flexibility quantification results The optimization problems corresponding to power boundary, flexibility duration, and ramping capability are solved independently, outputting the upper power boundary, lower power boundary, maximum duration of the upper boundary, maximum duration of the lower boundary, maximum upward ramping rate, and maximum downward ramping rate for each reference scheduling period, forming the steel plant-level flexibility time-series characteristics. The quantification results are used to characterize the steel plant's available adjustment range, sustainability, and dynamic response speed, providing a quantitative reference for subsequent grid dispatch analysis, demand response, and ancillary service capability assessment; the calculation process is not nested with specific power system dispatch models.

[0038] The present invention has the following beneficial effects: This invention uses a variable batch resource task network model as a plant-level feasible domain generator, which uniformly considers equipment occupancy, furnace tasks, process transfer, processing continuity and product delivery, avoiding the direct substitution of the plant's overall deliverability flexibility with the rated power of a single piece of equipment.

[0039] This invention incorporates the input electrical energy of the electric arc furnace, the heat absorption of scrap steel, temperature evolution, and heat loss through conduction and radiation into the scheduling constraints, so that the power trajectory used for flexibility quantification simultaneously meets the melting final temperature and energy conversion requirements, thereby more accurately revealing the impact of thermal inertia on continuous regulation capability and ramp-up capability.

[0040] This invention describes the flexibility of steel plants from three complementary dimensions: power boundary, flexibility duration, and ramp-up capability. It not only provides the adjustable power range, but also the duration that the range can be maintained and the maximum power change rate that can be achieved in adjacent time periods, forming a quantitative result of plant-level flexibility for grid operation. Detailed Implementation

[0041] The invention will be further illustrated below using a short-process steel plant comprising an electric arc furnace, an argon-oxygen decarburization unit, a ladle refining unit, a continuous casting machine, and a rolling mill as an example. The steel production scheduling interval is 5 minutes, the power grid reference scheduling interval is 15 minutes, and the scheduling cycle is from 00:00 to 06:00.

[0042] (1) Constructing a multi-stage production feasible domain The candidate furnace set contains 8 furnaces. Production decision variables are set for each furnace, and its associated processing and transfer tasks are controlled according to equation (2).

[0043] The resource status is updated as the task starts according to formula (1).

[0044] The production feasible domain is also subject to maximum transfer time constraints and final product completion constraints according to Equations (3) and (4), respectively.

[0045] The adjustable power, variable duration and minimum cumulative energy of the electric arc furnace melting task are constrained by Equations (5), (6) and (8), respectively.

[0046] The solution selected six heats for production, with each heat processed in the following order: electric arc furnace, argon-oxygen decarburization, ladle refining, continuous casting, and rolling. The resulting plant-level power feasible region preserves the coupling relationship between heat selection and multi-stage tasks.

[0047] (2) Calculate the energy distribution during the electric arc furnace melting process. The input electrical energy for each period of the melting task is allocated to the heat absorption of scrap steel and the heat loss of the electric arc furnace according to formula (9).

[0048] The heat absorbed by scrap steel is calculated according to formula (10) from two parts: solid-state heating and liquid-state heating.

[0049] The melting state variables shown in equations (11) to (13) and the large M constraint are used to distinguish between two states where the temperature is below or not below the melting point.

[0050] At the same time, apply temperature boundaries, temperature-task execution relationship and endpoint temperature maintenance relationship according to equations (14) to (17) to ensure that the specified temperature is reached when the melting task is completed.

[0051] (3) Calculate the heat loss of the electric arc furnace In the embodiment, the electric arc furnace is equipped with a water-cooled wall. During the melting stage, the scrap steel surrounds the high-temperature heat source in a solid-liquid coexistence state, so heat conduction and radiation are the main heat loss channels. The total heat loss, heat conduction heat loss and radiation heat loss are calculated according to Equations (18), (19) and (22), respectively.

[0052] The cooling water outlet temperature and thermal resistance are calculated according to equations (20) and (21), respectively.

[0053] The temperature square auxiliary variable is defined by equation (23), and the fourth-order temperature term in the radiative heat loss is rewritten as a continuous bilinear term according to equation (24).

[0054] Piecewise McCormick relaxation was applied to the continuous bilinear terms. In tests with 4, 8, 16, and 32 segments respectively, increasing the number of segments continuously reduced the approximation error of heat loss; with 16 segments, the maximum errors of the thermal conductivity and radiation correlation quantities were 0.1979% and 0.2452% respectively, achieving a balance between approximation accuracy and computational scale. In the example, the melting heat loss of the six selected furnace cycles was 5.63 × 10⁻⁶. 4 MJ indicates that including heat loss in the feasible region can explicitly reflect the additional input energy required to meet the endpoint temperature.

[0055] (4) Calculate the plant-level power boundary For each 15-minute reference scheduling period, the upper power boundary and lower power boundary are solved according to equations (26) and (27), respectively.

[0056] Both optimization problems mentioned above use the aforementioned multi-stage production feasible region and the plant-level power consumption feasible region containing heat loss as constraint sets.

[0057] The lower power boundary of the embodiment is zero for some periods, indicating that the load during those periods can be reduced by moving the processing tasks that have not yet started. The upper power boundary during the melting stage is close to 150 MW, and subsequent processes form a lower boundary due to the smaller equipment power. The power boundary is generally similar whether heat loss is considered or not, because the boundary is mainly constrained by the rated power range of the equipment and rigid operating conditions.

[0058] (5) Calculate the boundary duration Taking the power boundary above as an example, its maximum duration is solved according to equation (28).

[0059] The maximum duration of the lower power boundary was calculated in the same manner. The results show that the maximum duration is simultaneously limited by the current time period, the latest task start time, and the remaining process completion time. The melting thermal inertia introduced by the heat loss model can extend the duration of the upper boundary in some time periods, allowing the quantification results to reflect the electric arc furnace's ability to absorb power fluctuations while meeting the endpoint temperature conditions.

[0060] (6) Calculate the maximum gradient The maximum upward slope rate and the maximum downward slope rate are solved according to equations (29) and (30), respectively.

[0061] The electric arc furnace exhibits a high maximum ramp rate during operation, while subsequent stages such as argon-oxygen decarburization, refining, continuous casting, and rolling primarily utilize equipment start-ups and shutdowns to provide power variations, resulting in a relatively lower maximum ramp rate. Considering the heat loss from the electric arc furnace, the model can reveal a wider range of feasible dynamic responses using temperature conditions and thermal inertia.

[0062] The final time series results consist of upper and lower power boundaries, maximum duration of upper and lower boundaries, and maximum upward and downward ramp rates. These six quantitative results are respectively attributed to the three dimensions of power boundary, flexibility duration, and ramp capability, and can serve as the basic data for analyzing the steel plant's participation in demand response, power system dispatch, and ancillary service capabilities.

Claims

1. A method for quantifying the scheduling flexibility of short-process steelmaking considering heat loss from electric arc furnaces, characterized in that, Includes the following steps: (1) Obtain steel plant production, equipment and thermal parameters: obtain candidate furnace batches, processing equipment and product resources, processing and transfer tasks, equipment power and processing time range, resource generation and consumption coefficients, maximum transfer time, steel production scheduling interval and power system reference scheduling interval; obtain scrap steel quality, solid and liquid specific heat capacity, melting point, initial melting temperature and final melting temperature, water-cooled wall area, cooling water flow rate, inlet water temperature, ambient temperature, furnace body radiation area, emissivity, Stefan-Boltzmann constant and thermal resistance parameters; (2) Construct a variable batch resource task network model for generating plant-level feasible domains: electric arc furnace, argon-oxygen decarburization unit, ladle refining unit, continuous casting machine, rolling mill and stage products are represented as resources, and the processing and transfer operations of each furnace are represented as tasks; set furnace production decision variables, task initiation variables, task execution status variables and resource status variables, and use furnace production decision variables to control whether the corresponding processing and transfer tasks enter the scheduling, so that the number of production furnaces and the task sequence are jointly determined; any resource status is updated according to the resource balance relationship; the furnace production decision and its associated tasks satisfy the activation constraint; the total transfer and waiting time between adjacent processes does not exceed the allowable value; the final product of the selected furnace is formed before the end of the scheduling cycle; for electric arc furnaces with power adjustment capability, the power and duration when performing melting tasks satisfy the upper and lower limit constraints of power and the duration constraint of task, respectively; once a task is started, it is executed continuously, and its execution status satisfies the continuity constraint; the cumulative input energy of melting tasks meets the process requirements; the above constraints, together with equipment occupancy, immediate transfer and product delivery requirements, constitute the multi-stage production feasible domain of the steel plant; (3) Establish a melting process model considering the heat loss of the electric arc furnace: The input electrical energy of the electric arc furnace in the melting task consists of two parts: the heat absorbed by the scrap steel and the heat loss of the electric arc furnace; calculate the heat absorbed by the scrap steel and the melting state: the heat absorbed by the scrap steel when it rises from the initial temperature to the melting point and continues to rise to the final melting temperature is calculated separately according to the solid-state temperature rise and the liquid-state temperature rise; set up a binary melting state variable, and judge whether it is in the solid or liquid stage according to the temperature of the scrap steel; use the big M method to rewrite the above logical relationship into a linear constraint; the melting temperature is within the range of the initial temperature and the final temperature; the temperature change only occurs when the melting task is executed; the temperature state at the end of the scheduling cycle is consistent with the temperature at the actual completion time of the melting task, and meets the specified final melting temperature; calculate the heat conduction and radiation heat loss: the total heat loss of the melting task consists of the heat conduction heat loss of the water-cooled wall and the radiation heat loss of the furnace body; the heat conduction heat loss of the water-cooled wall is calculated according to the temperature rise of the cooling water; The relationship between the representative temperature of scrap steel, the outlet temperature of cooling water and the thermal resistance is established based on the Fourier thermal conductivity relationship; the radiative heat loss of the furnace body is calculated according to the radiative heat transfer relationship; to reduce the difficulty of solving the fourth temperature term, an auxiliary variable of temperature square is introduced; the radiative heat loss is rewritten in a continuous bilinear form. The product of binary and continuous variables is reconstructed using exact linearity, and the continuous bilinear terms in the radiation model are relaxed using piecewise McCormick relaxation, so that the feasible region of the steel plant with heat loss is transformed into a solvable mixed integer linear form. (4) Map the electricity consumption of steel production to the reference dispatch period of the power system: let the reference dispatch interval of the power system contain ζ steel production dispatch intervals, and aggregate the electricity consumption of steel production in the reference period into plant-level active power; thereby constructing a flexibility index on a time scale consistent with the grid dispatch. (5) Quantification of power boundaries: Power boundaries are used to describe the maximum and minimum active power that a steel plant can achieve in each reference scheduling period under the conditions of variable batch production constraints, equipment operation constraints and electric arc furnace heat loss constraints; the upper power boundary is obtained by solving a maximization optimization problem with the plant-level active power as the objective function in that period; the lower power boundary is obtained by solving a minimization optimization problem with the plant-level active power as the objective function in that period; the above upper and lower power boundary optimization problems all use the multi-stage production feasible region and the plant-level power consumption feasible region containing heat loss as the constraint set; (6) Quantitative flexibility duration: For any reference scheduling period, the flexibility duration is represented by the number of periods during which the steel plant continuously maintains the upper or lower power boundary from the start of that period; During the maintenance process, the requirements for subsequent task execution and final product completion must still be met; the maximum duration of the upper power boundary is obtained by maximizing the number of consecutive maintenance periods of the upper boundary; the maximum duration of the lower power boundary is obtained in the same way. (7) Quantification of ramping capability: The ramping capability is represented by the maximum feasible rate of change of active power of the steel plant between adjacent reference scheduling periods; the maximum upward ramping rate is obtained by maximizing the positive power change rate between adjacent periods; the maximum downward ramping rate is obtained by maximizing the reverse power change rate between adjacent periods. (8) Output plant-level flexibility quantification results: Solve the optimization problems corresponding to power boundary, flexibility duration and ramping capability independently, and output the upper power boundary, lower power boundary, maximum duration of upper boundary, maximum duration of lower boundary, maximum upward ramping rate and maximum downward ramping rate for each reference scheduling period, and form the plant-level flexibility time series characteristics of the steel plant; The quantification results are used to characterize the adjustment range, continuous capability and dynamic response speed that the steel plant can provide, and provide a quantitative reference for subsequent power grid dispatch analysis, demand response and ancillary service capability determination; Its calculation process is not nested with specific power system dispatch models.

2. The method according to claim 1, characterized in that, In step (2), any resource status is updated according to the following resource balance relationship: (1) in, For time period resources State value; Index for steel production scheduling periods; and These are the resource index and the task index, respectively. , and These are respectively the resource set, the task set, and the steel production scheduling time period set; This is a variable used to start the task; a value of 1 indicates the task is complete. During the period Startup; ν is the latency index after the task starts; For the task Duration of action; For the task After startup, resources will be processed over a period of ν time. The generation or consumption coefficient; The production decision for each furnace and its associated tasks satisfy the following: (2) in, For the candidate furnace set; For furnace number index; For the production decision variable of each furnace, a value of 1 indicates the number of furnaces to be produced. A value of 0 indicates that no batches will be produced. ; In order to be related to the furnace Associated task index; For furnace A set of associated processing and transfer tasks; The total transfer and waiting time between adjacent processes shall not exceed the allowable value: (3) in, This refers to the time interval for steel production scheduling. This is the product resource index corresponding to the termination location of the transfer task; For resources Transit time; For resources Maximum allowed transit and total waiting time; The final product of the selected furnace batch is formed before the end of the scheduling cycle: (4) in, For furnace Product resource index corresponding to the final production stage; This refers to the final period of the steel production scheduling cycle. For an electric arc furnace with power regulation capability, the power and duration for performing a melting task shall respectively satisfy: (5) in, For the task During the period The active power; This is a task execution status variable; a value of 1 indicates the task is running. During the period In the process of processing; and Tasks The lower and upper limits of power; This refers to the set of processing tasks corresponding to power-adjustable devices. (6) in, For processing tasks Subsequent transit task index; and Tasks The shortest and longest processing times; The steel production scheduling time period index used for summation; Once started, the task executes continuously, and its execution state satisfies the following: (7) The cumulative energy input for the melting task meets the process requirements: (8) in, To complete the task Minimum cumulative energy required; The aforementioned constraints, together with requirements for equipment occupancy, immediate relocation, and product delivery, constitute the multi-stage production feasible domain of the steel plant.

3. The method according to claim 2, characterized in that, Step (3) specifically involves: The electrical energy input of an electric arc furnace during melting consists of two parts: heat absorbed by the scrap steel and heat loss from the electric arc furnace. (9) in, For time period Internal mission The heat absorbed by scrap steel; For time period Internal mission The resulting heat loss from the electric arc furnace; (3-1) Calculate the heat absorbed by scrap steel and its melting state The amount of heat absorbed by scrap steel as it rises from its initial temperature to its melting point and then further to its final melting temperature is: (10) in, and These are the specific heat capacities of scrap steel in solid and liquid states, respectively. The quality of scrap steel per furnace batch; For binary melting state variables; For the task During the period The melting temperature of scrap steel; Set a binary melting state variable to determine whether the scrap steel is in a solid or liquid state based on its temperature: (11) in, The melting point of scrap steel; The above logical relationship can be rewritten into a linear constraint using the Big M method: (12) Where M is a sufficiently large positive number; (13) The melting temperature is within the range of initial and final temperatures: (14) in, and These are the initial melting temperature and the specified final melting temperature of scrap steel, respectively. Temperature changes only occur during the melting process: (15) The temperature at the end of the scheduling cycle remains consistent with the temperature at the actual completion time of the melting task, and meets the specified final melting temperature: (16) (17) (3-2) Calculate heat conduction and radiation heat loss The total heat loss during the melting process consists of heat loss through water-cooled walls and heat loss through furnace radiation. (18) in, and Tasks During the period The heat loss due to heat conduction from the water-cooled wall and the heat loss due to radiation from the furnace body. The heat loss of water-cooled walls is calculated based on the temperature rise of the cooling water: (19) in, This is the specific heat capacity of water; The density of water; For time period The volume of cooling water flowing through the water-cooled wall; and These are the cooling water outlet temperature and inlet temperature, respectively. Based on the Fourier thermal conductivity relation, establish the relationship between the representative temperature of scrap steel, the outlet temperature of cooling water, and the thermal resistance: (20) in, The equivalent thermal resistance between the furnace body and the water-cooled wall cooling system; Thermal resistance is calculated from the heat transfer parameters of the water-cooled wall flow and the furnace wall: (21) in, The coefficient of friction for the water-cooled wall flow; The Prandtl number of the cooling water; This refers to the wetted perimeter of the water-cooled wall. The thermal conductivity of water; The Reynolds number of the water-cooled wall; This refers to the wall thickness of the water-cooled tube. is the thermal conductivity of steel; This refers to the area of ​​the water-cooled wall; Pi; The radiative heat loss of the furnace body is calculated based on the radiative heat transfer relationship: (22) in, The emissivity of the furnace body; The outer surface radiation area of ​​the furnace body; The Stefan-Boltzmann constant; Ambient temperature; To reduce the difficulty of solving the fourth-order temperature term, an auxiliary variable of temperature square is introduced: (23) in, The square of the melting temperature is used as an auxiliary variable. Rewrite the radiative heat loss in a continuous bilinear form: (24) The product of binary and continuous variables is reconstructed using exact linearity, and the continuous bilinear terms in the radiation model are relaxed using piecewise McCormick relaxation, so that the feasible region of the steel plant with heat loss is transformed into a solvable mixed integer linear form.

4. The method according to claim 3, characterized in that, Step (4) specifically involves: Let the power system reference dispatch interval include Each steel production scheduling interval aggregates the steel electricity consumption within this reference time period into plant-level active power: (25) in, For time period The plant-level active power; To incorporate the actual power trajectory of the power-adjustable equipment, the steel mill during the time period Electricity consumption; Therefore, a flexibility index is constructed on a time scale consistent with power grid dispatch.

5. The method according to claim 4, characterized in that, In step (5), the upper power boundary is obtained by solving the following optimization problem: (26) in, For power system reference dispatch period index; For reference scheduling period The plant-level active power; To and The corresponding set of steel production scheduling time period indexes; This refers to the number of steel production dispatch intervals included in a power system reference dispatch interval. The active power at the plant level is calculated according to the following formula: (25) The lower power boundary is obtained by solving the following optimization problem: (27) The above-mentioned upper and lower power boundary optimization problems both use the multi-stage production feasible region formed in step (2) and the plant-level power consumption feasible region containing heat loss formed in step (3) as constraint sets.

6. The method according to claim 5, characterized in that, In step (6), the maximum duration of the upper power boundary is obtained through the following optimization problem: (28) in, For steel mills during the period The number of time periods during which the selected power boundary is maintained; This serves as the reference scheduling period index in the duration calculation; To maintain the state variable at the boundary, a value of 1 indicates that the steel mill is in the time period. Maintain the selected power boundary; This refers to the end of the reference scheduling period; For time period The upper power boundary; For time period The plant-level active power; Among them, the binary variable is used to identify whether the steel mill maintains the selected power boundary in the corresponding time period; the maximum duration of the lower power boundary is obtained in the same way.

7. The method according to claim 6, characterized in that, In step (7), the maximum upward climbing rate is obtained through the following optimization problem: (29) in, For time period The upward slope rate; This serves as a reference dispatch time interval for the power system. The maximum downhill ramp rate was obtained through the following optimization problem: (30) in, For time period The downward slope rate.

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