Method and system for energy-carbon collaborative scheduling optimization of high-voltage insulated cable production process

Abstract

The application discloses a kind of energy-carbon collaborative scheduling optimization method and system of high-voltage insulated cable production process, method includes: obtaining the continuous production process information of high-voltage insulated cable production line, constructs directed production topology, and each connection edge is classified according to the physical characteristics between adjacent production processes;Discrete time framework is constructed, and decision variable is defined for production node and connection edge;According to the integrated energy cost and each decision variable, a target function is constructed to represent the integrated operation cost of the production line within the scheduling period;According to the type of each connection edge, material connection constraints are established respectively, and energy-carbon collaborative scheduling constraints are formed in combination with production node production collaborative constraints;With the minimum target function as the optimization goal, the decision variables of production node and connection edge are solved under the energy-carbon collaborative scheduling constraints to obtain the scheduling optimization result of the production line within the scheduling period, and the corresponding production equipment instructions are generated.The application can improve the executability of production scheduling result.

Description

Technical Field

[0001] This invention relates to the field of cable production scheduling and energy efficiency optimization technology, specifically to a method and system for energy and carbon coordinated scheduling optimization of high-voltage insulated cable production processes. Background Technology

[0002] High-voltage insulated cables are widely used in power transmission and distribution projects. Their production process typically includes multiple continuous production steps such as conductor processing, insulation extrusion, shielding processing, cabling, armoring, sheath extrusion, cooling and shaping, and winding and inspection. Because each production step has a fixed process sequence, and different production equipment requires matching production cycles, continuous material flow, and coordinated equipment operation, high-voltage insulated cable production is a typical continuous manufacturing process.

[0003] With fluctuating energy prices and increasingly stringent requirements for energy conservation and carbon reduction, high-voltage insulated cable manufacturers, while meeting order delivery requirements, also need to comprehensively consider electricity costs, equipment operating efficiency, and energy utilization levels during the production process to rationally arrange production plans in order to reduce production costs and improve production efficiency. Therefore, production scheduling has become a crucial factor affecting the economic viability and production stability of high-voltage insulated cables.

[0004] Currently, high-voltage insulated cable production lines typically formulate production plans based on production orders and equipment capacity, and organize the operation of each production piece of equipment according to a pre-set production rhythm. When changes occur during the production process, such as time-of-use electricity price fluctuations, changes in equipment operating status, or adjustments to production tasks, adjustments to the production sequence, equipment start-up and shutdown times, and production speeds are usually made manually based on experience, or only local optimizations are performed on some production equipment. While the above scheduling methods can meet basic production needs, the coordination of production rhythms between different production processes, equipment start-up and shutdown arrangements, and material flow relationships are usually considered separately, lacking a unified scheduling mechanism for the entire production line.

[0005] Furthermore, existing production scheduling methods typically focus primarily on production efficiency or production costs, lacking unified coordination of factors such as energy consumption, carbon emission costs, equipment start-up and shutdown impacts, production speed variations, and material connections between different processes. During production plan adjustments, issues such as frequent equipment start-ups and shutdowns, large fluctuations in production speed, mismatches between upstream and downstream processes, and stockpiling of intermediate materials can easily arise. This not only affects the continuous and stable operation of the production line but also makes it difficult to balance production costs, energy utilization efficiency, and production organization efficiency.

[0006] Therefore, there is an urgent need to provide a new method for scheduling the production process of high-voltage insulated cables to solve the problems of insufficient coordination in production organization, high overall operating costs, and difficulty in balancing production efficiency and energy utilization efficiency in the existing production scheduling process. Summary of the Invention

[0007] The technical problem to be solved by this invention is to provide a method and system for energy and carbon collaborative scheduling optimization of high-voltage insulated cable production processes, in order to achieve unified modeling and collaborative optimization of material connection relationships, production node operation status and energy and carbon costs of different processes, reduce the overall operating cost of the production line under the premise of meeting production process constraints, and improve the executability of production scheduling results and the level of production control automation.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A method for optimizing energy and carbon co-scheduling in the production process of high-voltage insulated cables includes: S1. Obtain the continuous production process information of the high-voltage insulated cable production line, construct a directed production topology with each continuous production process as a production node and the material connection relationship between adjacent production processes as a connection edge, and classify each connection edge according to the physical characteristics between adjacent production processes. S2, construct a discrete time frame according to a preset scheduling cycle, and define decision variables for each production node and connection edge; S3. Based on the comprehensive energy cost and various decision variables used to characterize the superposition relationship between unit electricity cost and unit carbon emission cost, construct an objective function to characterize the comprehensive operating cost of the production line within the scheduling cycle. S4. Material connection constraints are established according to the type of each connection edge, and combined with the production coordination constraints of the production nodes to form energy and carbon coordination scheduling constraints. S5, with the objective function minimization as the optimization objective, the decision variables of each production node and each connection edge are solved under the energy-carbon coordinated scheduling constraint to obtain the scheduling optimization result of the production line within the scheduling cycle, and the start-stop control command and frequency conversion speed regulation command of the corresponding production equipment are generated according to the scheduling optimization result.

[0009] Furthermore, in step S1, the connecting edges are classified according to the physical characteristics between adjacent production processes, specifically including: Based on whether adjacent production processes require direct connection within the same scheduling period, whether release is required after a process dwell time, and whether cross-period decoupling via intermediate buffering is allowed, each connection edge is divided into directly continuous edges, bufferable decoupling edges, and edges that must be delayed. The connection edge type is represented by a connection edge type parameter, expressed as follows:

[0010] In the above formula, e represents the edge number. This indicates the type parameter of the connecting edge e. These are three different parameters representing the type of the connecting edge; The continuous production process information of the high-voltage insulated cable production line includes conductor stranding, insulation extrusion, conductor shielding, cabling and filling, metal armoring, outer sheath extrusion, intermediate cooling, and take-up inspection. Based on the correspondence between adjacent production processes, corresponding connection edge type parameters are assigned to the connection edges between adjacent processes: the connection edge type parameters between conductor stranding and insulation extrusion, conductor shielding and cabling and filling, cabling and filling and metal armoring, and metal armoring and outer sheath extrusion represent bufferable decoupling edges; the connection edge type parameter between insulation extrusion and conductor shielding represents a necessary delay edge; and the connection edge type parameters between outer sheath extrusion and intermediate cooling, and between intermediate cooling and take-up inspection represent direct continuous edges.

[0011] Further, in step S2, the decision variables of the production node include one or more of the following: an operating state variable that characterizes the operating or stopping state of the production node, a speed gear selection variable that characterizes the selected speed gear of the production node, a start-up variable that characterizes the switching of the production node from the stopping state to the operating state, a stopping variable that characterizes the switching of the production node from the operating state to the stopping state, a processing length variable that characterizes the processing volume completed by the production node in the corresponding scheduling period, and a speed adjustment amplitude auxiliary variable that characterizes the speed change amplitude between adjacent scheduling periods. The decision variables of the connection edge include one or more of the following: direct flow variables that characterize the material output from the upstream production node directly entering the downstream production node; inflow variables that characterize the material output from the upstream production node entering the buffer or delay area; outflow variables that characterize the material taken from the buffer or delay area by the downstream production node for processing; and buffer or delay area inventory variables that characterize the inventory of the connection edge at the end of the corresponding scheduling period.

[0012] Further, in step S3, the objective function is constructed based on electricity cost, carbon emission cost, equipment start-up and shutdown cost, speed deviation penalty cost, speed regulation smoothing penalty cost, buffer usage cost, and direct flow coordination cost, and its expression is:

[0013] In the above formula, Let be the objective function. These represent electricity costs, carbon emission costs, equipment start-up and shutdown costs, speed deviation penalty costs, speed regulation smoothing penalty costs, buffer usage costs, and direct flow coordination costs, respectively. The electricity cost is obtained by multiplying the energy consumption of each process at each time period and at each speed level by the time-of-use electricity price for the corresponding time period, and then summing the results across all processes, time periods, and speed levels. The carbon emission cost is obtained by multiplying the electricity consumption of each process at each time period and at each speed level by the corresponding electricity carbon emission factor and carbon price, and then summing them up for all processes, time periods and speed levels. The equipment start-up and shutdown cost is obtained by summing the costs incurred when switching equipment from shutdown to operation and from operation to shutdown, respectively, for the start-up and shutdown variables of production nodes, and then accumulating these costs over all processes and time periods. The speed deviation penalty cost is obtained by calculating the squared deviation between the actual selected speed gear and the rated speed, multiplying it by the penalty imposed on the scheduling scheme that deviates from the rated operating speed, and summing it up over all processes, time periods, and speed gears. The speed adjustment smoothing penalty cost is obtained by multiplying the penalty for the speed change amplitude by the speed adjustment amplitude auxiliary variable and accumulating it over all processes and time periods; The cost of using the cache includes the processing cost of materials entering and leaving the cache or delay area, as well as the holding cost of semi-finished products occupying inventory in the cache or delay area; The direct flow coordination cost includes the coordination cost incurred when materials flow directly from upstream to downstream processes in bufferable or delayed edges.

[0014] Furthermore, the expression for the electricity cost is:

[0015] In the above formula, T represents the set of scheduling time periods; I represents the set of processes; and K represents the set of speed levels. This represents the operating power of process i at speed setting k; Indicates the duration of a single scheduling period; This represents the time-of-use electricity price for period t; This indicates whether process i selects speed gear k during scheduling period t; The expression for the carbon emission cost is:

[0016] In the above formula, This represents the carbon emission factor of electricity during time period t. Indicates the price of carbon emissions; The expression for the equipment start-up and shutdown cost is:

[0017] In the above formula, This represents the initial startup cost of process i; This represents the downtime cost of process i. This represents the starting variable for process i during scheduling period t. This represents the shutdown variable of process i during the scheduling period t; The expression for the speed deviation penalty cost is:

[0018] In the above formula, This represents the speed deviation penalty coefficient for process i; This indicates the production speed corresponding to speed setting k; Indicates the rated speed of process i; The expression for the speed regulation smoothing penalty cost is:

[0019] In the above formula, Let be the speed regulation smoothing penalty coefficient for process i. This is an auxiliary variable representing the speed adjustment range of process i during time period t; The expression for the cache usage cost is:

[0020] In the above formula, E represents the set of connecting edges; e represents the connecting edge number. This indicates the type parameter of the connecting edge e; This represents the processing cost per unit of material entering or leaving the buffer or delay area; This represents the inbound buffer or inbound delay zone traffic of connection edge e during time period t; This indicates the out-buffer or out-delay zone traffic of connection edge e during time period t; This represents the unit inventory holding cost; This represents the cache or delay zone inventory of connected edge e after time period t ends; The expression for the direct flow coordination cost is:

[0021] In the above formula, Indicates the unit direct flow coordination cost. This represents the direct flow of the connecting edge e during time period t.

[0022] Further, in step S4, before establishing material connection constraints according to the type of each connecting edge, material balance constraints between adjacent production processes are first established; the material balance constraints are used to allocate the processing length of the upstream production node as the direct flow directly entering the downstream production node and the inflow flow entering the buffer area or delay area, and to express the processing length of the downstream production node as the sum of the direct flow and the outflow, as follows:

[0023]

[0024]

[0025] In the above formula, e represents the edge connection number, and t represents the scheduling period number. Let represent the processing lengths of the upstream and downstream production nodes corresponding to edge e during scheduling period t, respectively. This represents the direct flow of connection edge e during time period t. This represents the inbound buffer or inbound delay zone traffic of connection edge e during time period t. This indicates the out-of-buffer or out-of-delay traffic of the connection edge e during time period t.

[0026] Furthermore, in step S4, establishing material connection constraints according to the type of each connection edge specifically includes: For directly continuous edges, establish direct connection constraints that prohibit caching and prohibit delay; for cacheable decoupled edges, establish dynamic caching constraints, outbound constraints, and cache capacity constraints; for edges that must be delayed, establish constraints that prohibit direct flow, dynamic delay zone constraints, delay release constraints, and delay zone capacity constraints. The direct connection constraint is used to ensure that the output materials of the upstream production node directly enter the downstream production node within the same scheduling period, and to prevent the connection edge from generating cached or delayed inventory. The expression is:

[0027]

[0028] In the above formula, This represents the direct flow of connection edge e during time period t. This represents the inbound buffer or inbound delay zone traffic of connection edge e during time period t. This indicates the out-of-buffer or out-of-delay traffic of connection edge e during time period t. This represents the cache or delay zone inventory of connected edge e after time period t ends. These represent the processing lengths of the upstream and downstream production nodes corresponding to edge e during scheduling period t, respectively. The dynamic cache constraint is used to determine the cache inventory at the end of the current scheduling period based on the inventory of the previous scheduling period, the inbound cache flow of the current scheduling period, and the outbound cache flow of the current scheduling period. The expression is:

[0029] In the above formula, This represents the cache inventory of connection edge e after the end of scheduling period t-1; The outbound constraint is used to prevent materials that enter the buffer during the current scheduling period from being released as historical buffer materials in the same scheduling period. The expression is:

[0030] The cache capacity constraint is used to limit the cache inventory from exceeding a preset cache capacity, and its expression is:

[0031] In the above formula, This indicates the maximum buffer capacity of the connected edge e; The direct flow restriction constraint is used to prevent the output materials of the upstream production node from directly entering the downstream production node in the same scheduling period. The expression is:

[0032] The delay zone dynamic constraint is used to determine the delay zone inventory at the end of the current scheduling period based on the delay zone inventory of the previous scheduling period, the inbound delay zone flow of the current scheduling period, and the outbound delay zone flow of the current scheduling period. The expression is:

[0033] The delayed release constraint is used to ensure that the flow in the delay zone comes only from historical inventory that meets the minimum process delay duration, and its expression is:

[0034]

[0035] In the above formula, This represents the initial cache inventory of the connecting edge e. This indicates that the connection edge e has passed through at least [number] times before the current scheduling period. Historical inventory for each scheduling period This represents the minimum delay time interval for connecting edge e.

[0036] Furthermore, the production coordination constraints include one or more of the following: gear selection constraints, processing length constraints, strongly coupled process synchronization constraints, start-stop logic constraints, minimum continuous operation constraints, minimum continuous downtime constraints, maximum continuous downtime constraints, order output constraints, end-of-day inventory clearing constraints, and speed adjustment continuous constraints, wherein: Speed ​​selection constraint is used to ensure that each production node selects only one speed speed when it is running and does not select a speed speed when it is stopped. The processing length constraint is used to ensure that the processing length of the production node in each scheduling period is determined by the selected speed level and the length of the scheduling period; Strongly coupled synchronization constraints are used to ensure that production nodes with strong coupling relationships maintain the same operating level during the same scheduling period. End-of-day inventory clearing constraint is used to ensure that the inventory in the buffer or delay area is zero at the end of the scheduling cycle; Finished product output constraints are used to ensure that the cumulative processing length of the final production node within the scheduling cycle meets the order demand output. Start-stop logic constraints are used to ensure that start-up and stop variables are determined by changes in the operating status of adjacent scheduling periods, and that the same production node is not started and stopped at the same time in the same scheduling period; The minimum continuous running time constraint is used to ensure that the production node maintains continuous operation for no less than a preset time after startup. The minimum continuous downtime constraint is used to ensure that a production node remains continuously shut down for no less than a preset duration after it has stopped. The maximum continuous downtime constraint is used to ensure that there is at least one running scheduling period within any preset downtime window; Speed ​​regulation smoothing constraints are used to make the speed regulation amplitude auxiliary variable characterize the absolute value of the equivalent operating speed change between adjacent scheduling periods.

[0037] A co-scheduled energy and carbon scheduling optimization system for a high-voltage insulated cable production process includes a microprocessor and a memory interconnected, wherein the microprocessor is programmed or configured to execute the steps of a co-scheduled energy and carbon scheduling optimization method for the high-voltage insulated cable production process.

[0038] A computer-readable storage medium storing a computer program / instructions programmed or configured to execute, via a processor, steps of an energy-carbon co-scheduling optimization method for a high-voltage insulated cable production process.

[0039] Compared with the prior art, the advantages of the present invention are as follows: This invention constructs a directed production topology by unifying the continuous production processes of high-voltage insulated cables and the material connection relationships between adjacent processes. It classifies connection edges based on the physical characteristics of adjacent production processes, enabling the scheduling model to more accurately represent different material connection relationships between production processes. By uniformly defining the decision variables of production nodes and connection edges within a discrete time frame, it achieves a collaborative description of production equipment operation and material flow between processes. By combining unit electricity cost and unit carbon emission cost to construct a comprehensive operating cost objective function, production scheduling can simultaneously consider electricity economy and carbon emission cost. By establishing material connection constraints for different connection edges and combining them with production collaboration constraints for production nodes, it ensures that the scheduling optimization results meet the requirements of process material connection and production collaboration. Finally, by jointly solving each decision variable under constraints and transforming the scheduling optimization results into start / stop control commands and frequency conversion speed control commands for production equipment, it improves the executability of the scheduling results and the level of production control automation, thereby optimizing the comprehensive operating cost of the high-voltage insulated cable production line. Attached Figure Description

[0040] Figure 1 This is a flowchart of an energy and carbon synergistic scheduling optimization method for the production process of high-voltage insulated cables, according to an embodiment of the present invention.

[0041] Figure 2 This is a schematic diagram of the topology of a continuous cable production process in a specific application embodiment.

[0042] Figure 3 This is a schematic diagram of 24-hour time-of-use electricity price and dynamic carbon emission factor in a specific application example.

[0043] Figure 4 The above is a Gantt chart showing the operating status and speed level of each process in a specific application example.

[0044] Figure 5 This is a schematic diagram of the processing length for each process time period in a specific application embodiment.

[0045] Figure 6 This is a schematic diagram of the inventory and inflow / outflow changes of typical buffer and delay areas in a specific application embodiment, where (a), (b), (c), and (d) represent the inventory / delay area usage of connecting edges B12, B23, B34, and B56, respectively.

[0046] Figure 7 This is a schematic diagram simulating the time-period output and cumulative output of finished cables in a specific application embodiment.

[0047] Figure 8 This is a schematic diagram of the equivalent outlet temperature for a key process in cable production, as shown in a specific application example. Detailed Implementation

[0048] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0049] The key parameters of some models in this invention are defined as follows: Daily order finished product production demand, in km². In the current model:

[0050] : The kth speed gear, in km / h.

[0051] The rated speed of process i in the current model:

[0052] : Energy consumption function parameter per unit length of mechanical drive for process i.

[0053] : The heat loss coefficient of process i during temperature rise.

[0054] : Cooling energy consumption coefficient of the cooling process.

[0055] : The safe temperature threshold for process i.

[0056] Energy consumption per unit length of process i at gear k, in kWh / km.

[0057] The operating power of process i at gear k, in kW, satisfies: .

[0058] : The startup cost of process i, in yuan.

[0059] : Downtime cost for process i, in yuan.

[0060] : The minimum continuous running time of process i, in the unit of scheduling period.

[0061] : Minimum continuous downtime of process i, in scheduling time periods.

[0062] : Maximum continuous downtime of process i, in scheduling time periods.

[0063] : The maximum inventory capacity of the cache or delay area corresponding to edge e, in km.

[0064] : The initial inventory of edge e, in km.

[0065] : The minimum process delay time for edge e, in scheduling time intervals. The delay step size for E23 in the current model is: That is, at least 30 minutes must be waited after the insulation is extruded before proceeding to the next process.

[0066] : Processing cost per unit of material entering or leaving the buffer or delay area, in yuan / km.

[0067] Unit inventory holding cost, expressed in yuan / (km·time period).

[0068] Direct flow coordination cost, in yuan / km.

[0069] Speed ​​deviation penalty coefficient for process i.

[0070] : Speed ​​smoothing penalty coefficient for process i.

[0071] This invention describes a continuous production line for high-voltage insulated cables as an application example. High-voltage insulated cable production is a typical continuous manufacturing process in the process industry. During production, each process sequentially completes conductor forming, insulation manufacturing, shielding processing, cabling, armoring, sheath forming, cooling and shaping, and finished product winding, following a fixed process sequence. These processes exhibit both continuous processing relationships and different types of material connection relationships, such as process dwell times and buffer decoupling. Simultaneously, the operating power, speed levels, start-up and shutdown methods, and material flow processes of different production processes directly affect the energy consumption, carbon emission levels, and production stability of the production line. Therefore, this invention comprehensively considers production process constraints, equipment operating constraints, energy prices, and carbon emission costs, performing unified modeling and collaborative optimization of the entire production process to achieve collaborative optimization control of the start-up and shutdown states, operating speeds, and material flow processes of production equipment.

[0072] like Figure 1 As shown in the figure, this invention provides an energy-carbon coordinated scheduling optimization method for the production process of high-voltage insulated cables, comprising the following steps: Step S1: Construct production topology and establish connection edge types: Obtain continuous production process information of high-voltage insulated cable production line, construct a directed production topology with each continuous production process as production node and the material connection relationship between adjacent production processes as connection edge, and classify each connection edge according to the physical characteristics between adjacent production processes.

[0073] Specifically, the first step is to obtain the continuous production process information of the high-voltage insulated cable production line. In this embodiment, for example... Figure 2 As shown, the high-voltage insulated cable production line comprises eight continuous production processes: conductor stranding, insulation extrusion, conductor shielding, cabling and filling, metal armoring, outer sheath extrusion, intermediate cooling, and take-up inspection. Each production process sequentially completes the continuous manufacturing of the high-voltage insulated cable according to a predetermined process route. The process characteristics of each process are described below: Conductor stranding process: multiple copper wires are stranded into a round or fan-shaped conductor to ensure uniform tightness and no loose strands; the power used by the drive motor is mainly related to the speed, but the process complexity is relatively low. Insulation extrusion process: Cross-linked polyethylene insulation layer is continuously extruded on the outside of the conductor. Temperature and thickness need to be controlled. This process has the highest energy consumption and is sensitive to speed. It requires precise control to ensure insulation quality. Conductor shielding layer process: A semiconductor layer is coated on the outside of the insulating layer to improve the uniformity of the electric field and prevent partial discharge; Cable forming and filling process: multiple insulated wire cores are twisted together to form a cable, and filler material is added to maintain the structure. Metal armoring process: wrapping with steel strips or wires to enhance the cable's tensile and external force resistance; Outer sheath extrusion process: Extruding polyvinyl chloride (PVC) or low-smoke halogen-free sheath material onto the outer layer of the armor; Intermediate cooling process: The temperature of the extruded material is reduced by water or air cooling to ensure the safety of subsequent processes; energy consumption is only generated when cooling is required, and it has a significant impact on temperature control and cooling system load; Cable winding and testing process: The finished cable is wound up and necessary tests are carried out, such as pressure resistance, dimensions, conductivity and other quality tests; the energy consumption is mainly driven by mechanical drive and testing instruments, the energy consumption per unit length is relatively low and fixed.

[0074] The above-mentioned continuous production processes together form a continuous production line for high-voltage insulated cables. The process sequence is fixed, and the product processing is achieved through continuous material flow between adjacent production processes.

[0075] The production process of cross-linked polyethylene (XLPE) power cables has the following typical structural characteristics: High degree of automation: The equipment is automatically connected and transmitted through robotic arms, wire frames, traction systems and other means; Continuous operation mode: When the production line is running, materials are gradually processed from raw materials into finished products through various processes without interruption; Key process sequence: The output of each process serves as the input for the next process, reflecting a strict process sequence; Energy efficiency control depends on speed and temperature parameters: energy consumption in most processes is mainly determined by equipment operating speed and temperature control, which are key variables for optimizing scheduling.

[0076] To facilitate the establishment of a unified optimization model, the aforementioned continuous production processes are abstracted as production nodes, and the material connection relationships between adjacent production processes are abstracted as connecting edges, thereby constructing a directed production topology. Here, a production node represents the abstract object of the corresponding production process in the optimization model. Each production node corresponds to a set of independently controllable production equipment, and its operating status, operating speed, and processing volume are all used as decision objects in the optimization model. Connecting edges represent the material flow relationships between adjacent production nodes, and their direction is consistent with the material processing direction, used to describe the process of semi-finished products flowing from upstream production nodes to downstream production nodes.

[0077] Specifically, each process is represented by a production node [i]. Based on the physical connection characteristics between adjacent processes, the connecting edges are divided into direct continuous edges, bufferable decoupling edges, and necessary delay edges. For example: Necessary delay edge: [2]→[3]: After the insulation layer is extruded, it needs to go through a specified process dwell time to allow the insulation layer to complete the cross-linking reaction and temperature stabilization before it can enter the conductor shielding process; therefore, the material after the upstream process is completed cannot directly enter the next process, but enters the delay zone, and is released to the downstream process after meeting the minimum process delay time; Direct continuous edge: [6]→[7]: The outer sheath has just been formed, and the material is still in a high temperature plastic state, so it needs to be cooled and shaped in time; [7]→[8]: After cooling, the cable tension is established, and the take-up system needs to be driven stably; The above process relationships are represented by solid arrows. For direct continuous edges, the production speed of the two processes before and after must be the same, and the dwell time of the same section of conductor is short when passing through the two processes before and after, so it can be considered that they are produced in the same time step.

[0078] Decoupling is possible: [1]→[2], [3]→[4], [4]→[5], [5]→[6] allows for different production speeds. After passing through the previous process, the process can stop before the next process. This relationship can be represented by setting a small buffer inventory.

[0079] The energy consumption of each process is represented by a set of three-dimensional decision variables, and its energy consumption is: ,in , , These are the process operation status, production speed, and temperature, respectively. The process occurs over time. Internally produced materials It immediately flows to the next process or is stored in buffer inventory.

[0080] The continuity requirement of cable production lines dictates that each process must strictly adhere to the technological sequence and cannot be interrupted arbitrarily. The main connection methods include the following: Material transfer continuity: The output materials from the previous process must be transferred to the next process in a timely and efficient manner; Temperature transfer requirements: For example, the temperature output from the insulation extrusion process must meet the process requirements of the conductor shielding layer; Speed ​​coordination: can lead to synchronization or adjustment of the operating cycle of upstream and downstream processes to ensure product continuity; The timing of equipment operation: The start-up and operation time of each process must match the completion time of the preceding process to avoid idling or interruption.

[0081] Therefore, the directed production topology established in this embodiment can not only fully describe the process sequence of the entire high-voltage insulated cable production line, but also serve as the basis for establishing material flow constraints and optimization scheduling models in the future.

[0082] Because different adjacent production processes in the production of high-voltage insulated cables have different process connection methods, each connection edge is classified according to the physical characteristics between adjacent production processes.

[0083] Specifically, based on whether adjacent production processes require direct connection within the same scheduling period, whether release is required after a process dwell time, and whether cross-period decoupling via intermediate buffering is allowed, each connection edge is divided into directly continuous edges, bufferable decoupling edges, and edges that must be delayed. The connection edge type is represented by a connection edge type parameter, the expression of which is as follows:

[0084] In the above formula, e represents the edge number. This indicates the type parameter of the connecting edge e. These are three connection edge type parameters with different values; in one example, a, b, and c are 0, 1, and 2, respectively. These connection edge type parameters are used to uniformly describe the material connection methods corresponding to different connection edges, enabling the establishment of corresponding material connection constraints based on the connection edge type, and achieving unified mathematical modeling of different process relationships.

[0085] Subsequently, based on the correspondence between adjacent production processes in the high-voltage insulated cable production line, corresponding connection edge type parameters are assigned to each connection edge. Specifically, this includes: The connection edge type parameters between the conductor stranding process and the insulation extrusion process, between the conductor shielding process and the cabling and filling processes, between the cabling and filling processes and the metal armoring process, and between the metal armoring process and the outer sheath extrusion process represent bufferable decoupling edges. This means that these connection edges allow for the establishment of buffer zones between upstream and downstream processes. Materials processed at the upstream production node can either directly enter the downstream production node or be temporarily stored in the buffer zone and released for processing during subsequent scheduling periods. This achieves appropriate decoupling of upstream and downstream production cycles and improves the flexibility of production scheduling.

[0086] The connection edge type parameter between the insulation extrusion process and the conductor shielding process indicates that a delay edge is required. This is because the insulation layer after extrusion needs a specified process dwell time to allow the insulation material to further complete the cross-linking reaction and temperature stabilization. Therefore, the corresponding connection edge cannot be directly transferred within the same scheduling period. Materials processed at the upstream production node must enter the delay zone and can only be released to the conductor shielding process for subsequent processing after meeting the minimum process delay time.

[0087] The connection edge type parameter between the outer sheath extrusion process and the intermediate cooling process, as well as between the intermediate cooling process and the take-up inspection process, represents a direct continuous edge. This means that materials processed at the upstream production node must directly enter the downstream production node within the same scheduling period, without passing through buffer or delay areas. Specifically, after the outer sheath is extruded, it needs to immediately enter the intermediate cooling process for cooling and shaping, and after intermediate cooling, it needs to immediately enter the take-up inspection process to ensure product dimensional accuracy and continuous production stability. Therefore, the corresponding connection edges are all described as direct continuous edges.

[0088] Through the above classification method, this embodiment can simultaneously describe three different material connection relationships in a unified production topology: continuous processing, buffer decoupling, and process dwelling. This provides a unified data and model foundation for subsequently establishing material connection constraints corresponding to different types of connection edges.

[0089] In a specific application example, the optimization model set and index are first defined, as follows: Suppose that the cable production line consists of N=8 processes, and the process set is as follows:

[0090] The process includes: 1: conductor stranding, 2: insulation extrusion, 3: conductor shielding, 4: cabling and filling, 5: metal armoring, 6: outer sheath extrusion, 7: intermediate cooling, and 8: take-up and testing.

[0091] The total number of processes between adjacent steps is E=N 1 = 7 material connection edges, the edge set is as follows:

[0092] Edge e represents the material connection relationship between process e and process e+1. For example, e=2 represents the connection edge between insulation extrusion and conductor shielding, i.e., E23.

[0093] In the current model: That is, E12, E34, E45, and E56 are bufferable decoupling edges, E23 is a necessary delay edge, and E67 and E78 are direct continuous edges.

[0094] Step S2: Establish a discrete time frame and define decision variables: Construct a discrete time frame according to a preset scheduling cycle, and define decision variables for each production node and connection edge.

[0095] High-voltage insulated cable production lines are typical continuous manufacturing processes, with each production step operating continuously and their production cycles interconnected. To facilitate the transformation of the continuous production process into a mathematical model capable of unified optimization, this embodiment first discretizes the entire production scheduling cycle and establishes decision variables corresponding to each production node and connecting edge within a discrete time frame.

[0096] Specifically, the entire production scheduling cycle is divided into multiple consecutive scheduling periods of equal length. Each scheduling period serves as the basic decision unit of the model, and sets of production nodes, connecting edges, speed levels, and scheduling periods are established. The production node set represents each continuous production process, the connecting edge set represents the material connection relationships between adjacent production processes, the speed level set represents the selectable operating speed levels for each production device, and the scheduling period set represents each discrete scheduling period within the entire scheduling cycle. For example, if the scheduling cycle is 24 hours and the time step is... Then the total for the whole day is: The time set obtained from the scheduling period is: .

[0097] Within the aforementioned discrete-time framework, decision variables are defined for each production node and connecting edge. The decision variables for a production node include operating status variables, speed gear selection variables, start-up variables, shutdown variables, processing length variables, and speed adjustment range auxiliary variables. The decision variables for a connecting edge include direct flow variables, flow variables entering the buffer or delay zone, flow variables exiting the buffer or delay zone, and buffer or delay zone inventory variables. These decision variables collectively constitute the decision variable set of the optimization model, used to describe the operating status of the production node, production speed, material flow, and inventory changes.

[0098] (1) Production node decision variables: Define a running status variable for a production node during each scheduling period t, which indicates whether the corresponding production node i is in a running state during scheduling period t. Its expression is as follows:

[0099] The running state variables are used to describe the start and stop status of production equipment in each scheduling period. They are an important foundation for establishing gear selection constraints, start and stop logic constraints, and objective functions.

[0100] To represent the specific production speed level selected by production node i during scheduling period t while it is in operation, a speed level selection variable is established, and its expression is as follows:

[0101] The speed gear selection variable describes the specific operating speed adopted by the production node in its operational state, providing basic data for subsequent calculations of processing length, electricity costs, and speed smoothing costs. Simultaneously, the operational state variable and the speed gear selection variable together determine the actual operating mode of the production equipment during each scheduling period.

[0102] To further describe the changes in the operating status of production nodes, startup and shutdown variables are established. The startup variable... This represents the start-up variable for process i in time period t, indicating the transition of the production node from a stopped state to a running state. If the process transitions from a stopped state to a running state, then... Otherwise, the value is 0. This variable is mainly used to calculate the start-up and shutdown costs of equipment and to establish start-up and shutdown logic constraints.

[0103] halt variables This indicates that the production node has switched from a running state to a stopped state. If a process switches from a running state to a stopped state, then... Otherwise, the value is 0. The shutdown variable and the startup variable together describe the change process of the operating status of the production equipment throughout the entire scheduling cycle, and serve as an important basis for subsequently establishing the minimum continuous running time constraint, the minimum continuous shutdown time constraint, and the maximum continuous shutdown time constraint.

[0104] Establish processing length variable , representing the processing length of process i in time period t, in km. The processing length variable describes the actual production tasks completed by each production node within the corresponding scheduling time period, and is an important basis for subsequently establishing material balance constraints, order output constraints, and the overall cost objective function. At the same time, the processing length variable maintains a correspondence with the speed level, the specific relationship of which will be further established in the subsequent processing length constraints.

[0105] To linearize the variation in production speed between adjacent scheduling periods, an auxiliary variable for speed adjustment amplitude is established. , representing the auxiliary variable for the speed adjustment magnitude of process i in time period t, is used to linearize the absolute value of speed changes between adjacent time periods. By introducing this auxiliary variable, the originally nonlinear absolute value function can be transformed into a linear constraint form, thus facilitating a unified solution using a mixed-integer linear programming model. Simultaneously, this variable also forms an important foundation for subsequently establishing the speed adjustment smoothing penalty cost and speed adjustment smoothing constraints.

[0106] (2) Decision variables for connecting edges: After defining the decision variables for production nodes, further define the decision variables corresponding to the connecting edges to describe the material flow process between adjacent production nodes and the inventory change process in the buffer or delay area. Since this invention establishes different material connection constraints for different types of connecting edges, it is necessary to uniformly describe the material states such as direct flow, buffer storage, delayed storage, and inventory changes through the connecting edge decision variables, providing a foundation for subsequently establishing material balance constraints and constraints for different types of connecting edges.

[0107] Define the direct flow variables of the connected edges in each scheduling period. , representing the direct flow of edge e in time period t, in km. This variable indicates that the material produced by the upstream process in the current time period directly enters the downstream process and is processed in the current time period. For directly continuous edges, this variable corresponds to the entire material flow; for bufferable decoupled edges, this variable represents the portion of material that is allowed to connect directly; for edges that must be delayed, since direct flow is prohibited, this variable always remains zero and will be further limited when establishing the constraint for edges that must be delayed later. The direct flow variable can uniformly describe the process of different connected edges directly completing material transfer in the current scheduling time period.

[0108] Define the inbound buffer or inbound delay zone traffic variables of the connected edges during each scheduling period. , representing the flow rate of edge e into the buffer or delay zone during time period t, in km. This variable indicates that the material produced by the upstream process in the current time period does not directly enter the downstream, but instead enters the intermediate buffer or process delay zone. When the connecting edge is a bufferable decoupling edge, this variable represents the length of material entering the buffer zone; when the connecting edge is a necessary delay edge, this variable represents the length of material entering the delay zone waiting for process dwell; for directly continuous edges, since buffering and delay are prohibited, the corresponding flow rate into the buffer or delay zone always remains zero. This variable is mainly used to establish dynamic constraints on the buffer and delay zones, and is also an important component in calculating the cost of buffer usage.

[0109] Define the outflow variables of the buffer or outflow delay zone for each connection edge during each scheduling period. , representing the outflow from the buffer or delay zone of edge e during time period t, in km. This variable indicates that the downstream process is currently retrieving materials from historical inventory or materials that meet the delay time for processing. When the connecting edge is a bufferable decoupling edge, this variable represents the length of material released from the buffer; when the connecting edge is a necessary delay edge, this variable represents the length of material released from the delay zone to the downstream production node after meeting the minimum process delay time requirement; for directly continuous edges, since there is no buffer or delay zone, the corresponding outflow from the buffer or delay zone remains zero. This variable can accurately describe the process of releasing historical inventory to the downstream production node, providing a basis for establishing material balance constraints, buffer release constraints, and delay release constraints.

[0110] Define the cache or delay zone inventory variable for the connected edges after each scheduling period ends. , representing the cache or delay zone inventory of edge e at the end of time period t, in km. When the connecting edge is a cacheable decoupled edge, this variable represents the cache zone inventory; when the connecting edge is a required delay edge, this variable represents the delay zone inventory; for directly continuous edges, since caching and delay are prohibited, the corresponding inventory variable always remains zero. The inventory variable reflects the material accumulation between different scheduling periods and is an important basis for establishing dynamic inventory constraints, inventory capacity constraints, end-of-day inventory clearing constraints, and cache usage costs.

[0111] In summary, this embodiment establishes production node decision variables and connection edge decision variables respectively, providing a unified description of the continuous production process of high-voltage insulated cables from multiple dimensions, including production equipment operating status, operating speed, processing length, start-stop status, material flow, and inventory changes. The production node decision variables primarily describe the operational behavior of each production piece of equipment during different scheduling periods; the connection edge decision variables primarily describe the material flow relationships and inventory changes between adjacent production nodes. These decision variables collectively constitute the optimization variables of the mixed-integer linear programming model, providing a unified data foundation for subsequently establishing the comprehensive operating cost objective function and energy-carbon coordinated scheduling constraints.

[0112] Step S3: Construct the comprehensive operating cost objective function: Based on the comprehensive energy cost and various decision variables used to characterize the superposition relationship between unit electricity cost and unit carbon emission cost, construct an objective function to characterize the comprehensive operating cost of the production line within the scheduling cycle.

[0113] The overall operating cost of a high-voltage insulated cable production line includes not only the electricity consumption cost in the traditional production process, but also carbon emission costs, process recovery costs caused by equipment start-up and shutdown, and operating costs arising from frequent speed adjustments and buffer usage. Therefore, this embodiment, in establishing the objective function, not only comprehensively considers energy costs, but also further comprehensively considers production stability and process continuity, so that the optimization solution meets the process constraints while minimizing the overall operating cost of the production line.

[0114] To facilitate the subsequent establishment of a unified objective function for comprehensive operating costs, we first establish a comprehensive energy cost. The comprehensive energy cost is used to uniformly represent the superposition relationship between unit electricity cost and unit carbon emission cost, and its expression is as follows:

[0115] in, This represents the comprehensive unit energy cost for time period t. The time-of-use electricity price for period t is expressed in yuan / kWh. This indicates the price of carbon emissions, expressed in yuan / kgCO2. The electricity carbon emission factor represents the time period t, with units of kgCO2 / kWh.

[0116] The comprehensive energy cost integrates time-of-use electricity pricing and electricity carbon emission costs into a unified comprehensive cost per unit of electricity. Specifically, the time-of-use electricity price reflects the economic cost generated by production equipment consuming a unit of electricity; the electricity carbon emission factor reflects the carbon emissions per unit of electricity in the current time period; and the carbon emission price further converts carbon emissions into corresponding carbon emission costs. Therefore, the comprehensive energy cost can simultaneously reflect both energy costs and carbon emission costs, enabling the optimization model to proactively utilize low-electricity-price periods and prioritize low-carbon-emission periods during production scheduling, achieving synergistic optimization of economic benefits and carbon reduction targets.

[0117] After obtaining the comprehensive energy cost, a comprehensive operating cost objective function is established based on the decision variables of production nodes and connection edges. This comprehensive operating cost objective function is used to uniformly evaluate the comprehensive operating costs of the production line throughout the entire scheduling cycle, including electricity costs, carbon emission costs, equipment start-up and shutdown costs, speed deviation penalty costs, speed regulation smoothing penalty costs, buffer usage costs, and direct flow coordination costs. Its expression is as follows:

[0118] In the above formula, Let be the objective function for the overall operating cost of the production line throughout the entire scheduling cycle. These represent electricity costs, carbon emission costs, equipment start-up and shutdown costs, speed deviation penalty costs, speed regulation smoothing penalty costs, buffer usage costs, and direct flow coordination costs, respectively.

[0119] The overall operating cost objective function aims to minimize the overall operating cost over the entire scheduling cycle. Specifically, electricity cost and carbon emission cost reflect the energy consumption level of the production line; equipment start-up and shutdown costs are used to suppress frequent start-ups and shutdowns; speed deviation penalty costs limit long-term deviations from rated speeds; speed smoothing penalty costs reduce speed fluctuations between adjacent scheduling periods; buffer usage costs constrain the use of buffer resources; and direct flow coordination costs coordinate the direct flow of materials. By constructing the objective function using these various costs, the overall economic efficiency of the production line can be optimized while ensuring the continuity of the production process.

[0120] To facilitate understanding of the components in the overall operating cost objective function, the calculation methods for each cost are explained below.

[0121] (1) Electricity cost: Based on the operating power of each production node at each scheduling period and speed level, and combined with the time-of-use electricity price for the corresponding scheduling period, the electricity cost for the entire scheduling cycle is calculated. The expression is as follows:

[0122]

[0123] In the above formula, T represents the set of scheduling time periods; I represents the set of processes; and K represents the set of speed levels. This represents the operating power of process i at speed setting k; Indicates the duration of a single scheduling period; This represents the time-of-use electricity price for period t; This indicates whether process i selects speed gear k during scheduling period t; This represents the energy consumption of process i during time period t at gear k.

[0124] It is understandable that electricity costs reflect the economic cost of the actual electricity consumed by each production device throughout the entire production scheduling cycle. Electricity costs increase when production equipment operates during periods of high electricity prices and decrease during periods of low electricity prices. Therefore, by introducing electricity costs, the optimization model can be guided to rationally adjust the distribution of production tasks, increase the production ratio during periods of low electricity prices, and thus reduce the overall electricity costs for the enterprise.

[0125] (2) Carbon emission cost: To further reflect the carbon emission cost generated by electricity consumption during the production process, this embodiment establishes a carbon emission cost on top of the electricity cost. The carbon emission cost is calculated based on the electricity consumption of each production node at each scheduling period and speed level, combined with the electricity carbon emission factor and carbon emission price for the corresponding scheduling period. The expression is as follows:

[0126] It is understandable that carbon emission costs are used to quantify the economic cost of carbon emissions generated by the consumption of electricity during the operation of production equipment. Since the power grid supply structure differs across different scheduling periods, the electricity carbon emission factor also varies. When production tasks are scheduled during periods with lower carbon emission factors, lower carbon emission costs can be achieved under the same electricity consumption conditions. Therefore, by introducing carbon emission costs, the optimization model can not only utilize periods of low electricity prices to organize production, but also proactively utilize periods of low carbon emissions to schedule production tasks, achieving synergistic optimization of economic costs and carbon emission costs.

[0127] To facilitate a unified calculation of energy costs, electricity costs and carbon emission costs can be further combined into a comprehensive energy cost, the expression of which is as follows:

[0128]

[0129] It is understandable that the above-mentioned comprehensive energy cost will uniformly convert time-of-use electricity prices, electricity carbon emission factors, and carbon emission prices into a comprehensive cost per unit of electricity, providing a unified basis for subsequent comprehensive operating cost calculations.

[0130] (3) Equipment start-up and shutdown costs: Since the high-voltage insulated cable continuous production line is a continuous manufacturing production line, frequent start-up or shutdown of each production equipment will not only increase equipment wear, but also lead to additional costs such as equipment preheating, process recovery, and production switchover. Therefore, this embodiment further establishes equipment start-up and shutdown costs to constrain the frequent start-up and shutdown behavior of production equipment, and its expression is as follows:

[0131] In the above formula, This represents the initial startup cost of process i; This represents the downtime cost of process i. This represents the starting variable for process i during scheduling period t. This represents the shutdown variable of process i during the scheduling period t.

[0132] It is understandable that equipment start-up and shutdown costs reflect the comprehensive expenses incurred when switching equipment from a stopped state to an operating state and vice versa. These costs include not only energy losses during startup and shutdown but also factors such as process recovery time, equipment wear and tear, and decreased production stability. Therefore, incorporating equipment start-up and shutdown costs into the objective function can effectively reduce the frequent start-up and shutdown of equipment in the optimization model in an effort to lower electricity costs, thereby improving the stability of continuous production line operation.

[0133] (4) Speed ​​Deviation Penalty Cost: In the production process of high-voltage insulated cables, each production equipment has a corresponding rated production speed. When the production equipment deviates from the rated speed for a long period of time, it will not only affect the operating efficiency of the equipment, but may also lead to a decrease in product size consistency and process stability. Therefore, this embodiment establishes a speed deviation penalty cost to constrain the situation where the production equipment deviates from the rated speed for a long period of time. Its expression is as follows:

[0134] In the above formula, This represents the speed deviation penalty coefficient for process i; This indicates the production speed corresponding to speed setting k; This indicates the rated speed of process i.

[0135] It is understandable that the speed deviation penalty cost imposes an additional cost on scheduling schemes that deviate from the rated operating state for a long time by calculating the deviation between the actual operating speed and the rated operating speed. This guides the optimization model to prioritize the speed level that is more in line with the optimal operating conditions of the equipment, thereby improving the equipment operating efficiency and product quality stability.

[0136] (5) Speed ​​Adjustment Smoothing Penalty Cost: Adjusting production speed can improve the flexibility of production scheduling, but if the production speed changes too quickly between adjacent scheduling periods, it can easily lead to equipment shock, traction tension fluctuations, and product size changes. Therefore, this embodiment further establishes a speed adjustment smoothing penalty cost, the expression of which is as follows:

[0137] In the above formula, Let be the speed regulation smoothing penalty coefficient for process i. This is an auxiliary variable representing the speed adjustment range of process i during time period t.

[0138] It is understandable that the speed smoothing penalty cost is determined by the magnitude of speed change between adjacent scheduling periods. The more drastic the speed change, the higher the corresponding speed smoothing penalty cost, thereby guiding the optimization model to generate a smoother speed adjustment scheme, reducing equipment impact, and improving the stability of continuous production.

[0139] (6) Buffer usage cost: During the continuous production of high-voltage insulated cables, some adjacent production processes can be decoupled through buffer zones. Therefore, while using buffer resources can improve production scheduling flexibility, it also increases operating costs such as material handling, buffer management, and semi-finished product inventory. To reasonably control the use of buffer resources, this embodiment further establishes a buffer usage cost, the expression of which is as follows:

[0140] In the above formula, E represents the set of connecting edges; e represents the connecting edge number. This indicates the type parameter of the connecting edge e; This represents the processing cost per unit of material entering or leaving the buffer or delay area; This represents the inbound buffer or inbound delay zone traffic of connection edge e during time period t; This indicates the out-buffer or out-delay zone traffic of connection edge e during time period t; This represents the unit inventory holding cost; This represents the cache or delay zone inventory of the connected edge e after the end of time period t.

[0141] It is understandable that cache usage costs include two parts: the processing costs incurred when materials enter or leave the cache or delay area, and the inventory holding costs incurred while semi-finished products remain in the cache or delay area. Processing costs mainly reflect expenses such as material handling, cache equipment operation, and inventory management; inventory holding costs mainly reflect the costs incurred by semi-finished products occupying inventory space and capital. As cache flow and inventory levels increase, the corresponding cache usage costs also increase. Therefore, by introducing cache usage costs, we can avoid the optimization model from over-relying on cache resources for production scheduling, guiding production tasks to be completed as continuously as possible according to the process cycle time, and improving the overall operating efficiency of the production line. Simultaneously, for edges that must be delayed, the inventory holding portion of the cache usage cost can also reflect the occupation costs incurred by materials waiting in the delay area for process dwell, thus unifying the consideration of process dwell constraints and production costs.

[0142] (7) Direct Flow Coordination Cost: For bufferable decoupling edges, materials can achieve cycle time decoupling between upstream and downstream production processes through buffer areas. However, in actual production, if materials can directly enter downstream production processes from upstream processes, the number of material handling operations can be reduced, improving production continuity. However, the direct flow method requires good cycle time coordination between upstream and downstream production processes, thus increasing the corresponding coordination and management costs. Based on this, this embodiment further establishes the direct flow coordination cost, the expression of which is as follows:

[0143] In the above formula, Indicates the unit direct flow coordination cost. This represents the direct flow of the connecting edge e during time period t.

[0144] It is understandable that direct flow coordination cost describes the coordination cost incurred when materials flow directly from upstream production nodes to downstream production nodes in bufferable decoupled edges or edges requiring delay. For bufferable decoupled edges, increasing the proportion of direct flow can reduce buffer inventory and improve production continuity, but it requires higher operational synchronization between upstream and downstream equipment. Therefore, introducing direct flow coordination cost can achieve a balance between buffer scheduling and continuous production. For edges requiring delay, since direct flow is prohibited on the corresponding connecting edges, the corresponding direct flow will be further limited to zero when establishing material connection constraints. In this case, this part of the cost naturally does not participate in the optimization calculation. By establishing direct flow coordination cost, the optimization model can comprehensively weigh the relationship between continuous production and buffer adjustment according to different scheduling schemes, further improving the rationality of the scheduling scheme.

[0145] In summary, the comprehensive operating cost objective function established in this embodiment comprises electricity cost, carbon emission cost, equipment start-up and shutdown cost, speed deviation penalty cost, speed regulation smoothing penalty cost, buffer usage cost, and direct flow coordination cost. The objective function established in this embodiment can achieve synergistic optimization of electricity cost and carbon emission cost, while also considering production stability, process continuity, and inventory management, making the final optimized scheduling scheme more consistent with the actual operational requirements of continuous production of high-voltage insulated cables.

[0146] Step S4, Establishing Energy-Carbon Co-scheduling Constraints: After establishing the comprehensive operating cost objective function, to ensure that the solution of the objective function meets the process requirements of the continuous production of high-voltage insulated cables, it is necessary to further establish energy-carbon co-scheduling constraints. Since different connection edges in the production line correspond to different material connection methods, and the production equipment itself also needs to meet process requirements such as start-stop logic, speed matching, and continuous operation time, this embodiment establishes material connection constraints corresponding to the connection edges and production coordination constraints corresponding to the production nodes, which together form a complete energy-carbon co-scheduling constraint.

[0147] Specifically, material connection constraints are established according to the type of each connecting edge, and combined with the production coordination constraints of production nodes, energy and carbon coordinated scheduling constraints are formed. Material connection constraints include material balance constraints between adjacent processes, direct continuous edge constraints, bufferable decoupling edge constraints, and necessary delay edge constraints. Production coordination constraints include gear selection constraints, processing length constraints, synchronization constraints of strongly coupled processes, start-stop logic constraints, minimum continuous operation constraints, minimum continuous downtime constraints, maximum continuous downtime constraints, order output constraints, end-of-day inventory clearing constraints, and speed smoothing constraints. All these constraints work together to ensure that the optimization solution meets the requirements of the high-voltage insulated cable production process.

[0148] (1) Establish material balance constraints between adjacent production processes: Before establishing material connection constraints according to the connection edge type, first establish material balance constraints between adjacent production processes.

[0149] Because the continuous production of high-voltage insulated cables involves continuous material transfer between production processes, for any given connection edge, all materials processed by the upstream production node must flow to the downstream production node; unauthorized increases or decreases in material are not permitted. Furthermore, the materials processed by the downstream production node may originate from materials directly transferred from the upstream production node during the current scheduling period, or from historical materials released from the buffer or delay zone. Therefore, it is necessary to first establish a unified material balance relationship to provide a foundation for subsequently establishing constraints for different types of connection edges.

[0150] In this embodiment, the material balance constraint allocates the processing length of the upstream production node as the direct flow directly into the downstream production node and the inflow flow into the buffer or delay area, and expresses the processing length of the downstream production node as the sum of the direct flow and the outflow, as follows: (Upstream process) (Downstream processes) (Non-negative flow) In the above formula, e represents the edge connection number, and t represents the scheduling period number. Let represent the processing lengths of the upstream and downstream production nodes corresponding to edge e during scheduling period t, respectively. This represents the direct flow of connection edge e during time period t. This represents the inbound buffer or inbound delay zone traffic of connection edge e during time period t. This indicates the out-of-buffer or out-of-delay traffic of the connection edge e during time period t.

[0151] The aforementioned material balance constraints have two meanings: First, all processing lengths completed by upstream production nodes during the current scheduling period need to be allocated. The materials can only be allocated in two parts: one part directly enters the downstream production node for processing, and the other part enters the buffer or delay area to await subsequent release. Therefore, the processing length of the upstream production node equals the sum of direct flow and inflow. Second, the processing length completed by downstream production nodes during the current scheduling period comes from two parts: one part comes from materials directly transferred by upstream production nodes during the current scheduling period, and the other part comes from historical inventory released from the buffer or delay area. Therefore, the processing length of the downstream production node equals the sum of direct flow and outflow.

[0152] Material balance constraints establish a one-to-one correspondence between the processing length of production nodes and the material flow of connecting edges, ensuring that the material flow process throughout the production topology always satisfies the principle of mass conservation. This also provides a unified mathematical foundation for establishing constraints on different types of connecting edges. Regardless of whether a connecting edge is a directly continuous edge, a bufferable decoupling edge, or an edge that must be delayed, it must first satisfy the aforementioned material balance relationship. Then, corresponding material connection constraints are established according to different edge types, thereby ensuring that the entire scheduling model has a unified data interface and good scalability.

[0153] Furthermore, after establishing unified material balance constraints, direct continuous edge constraints, cacheable decoupling edge constraints, and mandatory delayed edge constraints are established according to the connection edge type parameters to further reflect the material flow mode corresponding to different physical processes.

[0154] For direct continuous edges, since there is no buffer or process dwell between adjacent production processes, the materials processed by the upstream production node must immediately enter the downstream production node for processing within the same scheduling period, and storage across scheduling periods through the buffer or delay area is not allowed.

[0155] In this embodiment, the connection points between the outer sheath extrusion process and the intermediate cooling process, as well as between the intermediate cooling process and the take-up inspection process, are all direct continuous edges, based on the high-voltage insulated cable manufacturing process. This is because the sheath material after extrusion is still in a high-temperature plastic state and needs to immediately enter the intermediate cooling process for cooling and shaping. After intermediate cooling, to ensure stable cable tension and take-up quality, it needs to immediately enter the take-up inspection process. Therefore, no buffers or delays can be set between these two types of processes; otherwise, product quality and continuous production stability will be affected.

[0156] To accurately describe the aforementioned continuous processing relationship, this embodiment establishes a direct connection constraint for directly continuous edges. The direct connection constraint ensures that the output materials from the upstream production node directly enter the downstream production node within the same scheduling period, and prevents the connection edge from generating cached or delayed inventory. Its expression is as follows:

[0157]

[0158] In the above formula, This represents the direct flow of connection edge e during time period t. This represents the inbound buffer or inbound delay zone traffic of connection edge e during time period t. This indicates the out-of-buffer or out-of-delay traffic of connection edge e during time period t. This represents the cache or delay zone inventory of connected edge e after time period t ends. These represent the processing lengths of the upstream and downstream production nodes corresponding to edge e during the scheduling period t, respectively.

[0159] The aforementioned direct connection constraints include two aspects: First, for directly continuous edges, buffer zones or delay zones are not allowed. Therefore, the material flow entering or leaving the buffer or delay zone during the current scheduling period, the material flow released from the buffer or delay zone, and the inventory at the end of the scheduling period all remain zero. That is, no flow enters or leaves the buffer or delay zone; no flow leaves the buffer or delay zone; and no inventory is retained in the buffer or delay zone. Therefore, all materials on the connection edge are transferred through direct flow. Second, since there is no buffering or delay process, all materials processed by the upstream production node during the current scheduling period must immediately enter the downstream production node and complete processing within the same scheduling period. That is, the processing length of the upstream production node is consistent with the processing length of the downstream production node, achieving true continuous production.

[0160] Direct connection constraints ensure that the upstream and downstream production processes corresponding to directly continuous edges always maintain a continuous processing state, avoiding problems such as sheath deformation, insufficient cooling, or tension imbalance caused by human-induced buffering or delays, thus guaranteeing the requirements of continuous production processes. Simultaneously, since directly continuous edges never have inventory, the corresponding connecting edges do not participate in dynamic buffering calculations or buffer usage cost calculations, further reducing model complexity and clearly distinguishing directly continuous edges from bufferable decoupled edges and edges that must be delayed.

[0161] For cacheable decoupling edges, establish dynamic cache constraints, outbound constraints, and cache capacity constraints. Cacheable decoupling edges allow a portion of the materials processed by the upstream production node in the current scheduling period to directly enter the downstream production node, while allowing the remaining materials to enter the cache area and be released from the cache area in subsequent scheduling periods, thereby achieving cross-time decoupling between adjacent production processes.

[0162] In this embodiment, the connecting edges between the conductor stranding process and the insulation extrusion process, between the conductor shielding process and the cabling and filling process, between the cabling and filling process and the metal armoring process, and between the metal armoring process and the outer sheath extrusion process are bufferable decoupling edges. These adjacent production processes may differ in equipment capacity, production cycle time, or operating speed. Semi-finished products completed at the upstream production node can temporarily remain before the downstream production node, and production cycle time can be adjusted through a buffer zone with limited capacity. For example, connecting edges E12, E34, E45, and E56 are set as bufferable decoupling edges.

[0163] When the connection edge type parameter When, it indicates that the connecting edge e is a cacheable decoupling edge; in a specific embodiment using a numerical connecting edge type parameter, it can be set to... This indicates a cacheable decoupling edge. Cacheable decoupling edges still satisfy the aforementioned material balance constraints between adjacent production processes, meaning that the processing length of the upstream production node is allocated jointly by the direct flow and the inbound buffer flow, while the processing length of the downstream production node is provided jointly by the direct flow and the outbound buffer flow.

[0164] The cache dynamic constraint determines the cache inventory at the end of the current scheduling period based on the cache inventory at the end of the previous scheduling period, the inbound cache traffic in the current scheduling period, and the outbound cache traffic in the current scheduling period.

[0165] For the second and subsequent scheduling periods, the expression for the cache dynamic constraint is:

[0166] In the above formula, This represents the cache inventory of edge e at the end of scheduling period t-1. That is, the cache inventory at the end of the current scheduling period equals the cache inventory at the end of the previous scheduling period plus the amount of material entering the cache during the current scheduling period minus the amount of material released from the cache during the current scheduling period. By recursively updating the cache inventory for each scheduling period, the material changes in the cache corresponding to each cacheable decoupling edge can be continuously recorded throughout the entire scheduling cycle.

[0167] For the first scheduling period within a scheduling cycle, since there is no previous scheduling period, the cache inventory is updated based on the pre-given initial cache inventory, and the expression is as follows:

[0168] in This represents the initial cache inventory of edge e before the start of the scheduling period; This represents the cache inventory of connected edge e after the first scheduling period ends; This represents the inbound buffer traffic of connection edge e during the first scheduling period; This represents the out-of-buffer traffic of connection edge e during the first scheduling period.

[0169] The initial buffer inventory can be determined based on the actual inventory status at the end of the previous scheduling cycle, the results of the production line inventory count, or the quantity of semi-finished products prepared in advance before the start of the scheduling cycle. When the production line starts scheduling with an empty buffer, it can... Set to zero.

[0170] To prevent materials entering the cache during the current scheduling period from being immediately released as historical cached materials within the same scheduling period, an outbound constraint is established to ensure that the outbound cache flow during the current scheduling period does not exceed the cached inventory that already existed after the end of the previous scheduling period.

[0171] For the second and subsequent scheduling periods, the expression for the outbound constraint is:

[0172] This constraint ensures that materials exiting the cache during the current scheduling period can only originate from materials already in the cache before the start of the current scheduling period, and not from materials that have just entered the cache during the current scheduling period. This avoids the false decoupling result of "immediately exiting the cache after entering it" within the same scheduling period in the optimization model, giving the caching process a clear cross-time period attribute.

[0173] For the first scheduling period, the outflow from the cache is limited by the initial cache inventory, and its expression is:

[0174] in, This indicates the length of material released from the buffer during the first scheduling period. When the initial buffer inventory is zero, no material can be released from the buffer during the first scheduling period, and the incoming materials to downstream production nodes during this scheduling period can only be provided by the direct flow from upstream production nodes.

[0175] Outbound constraints and cache dynamic constraints together establish a time-recursive relationship for cached inventory, ensuring that the time sequence of materials entering and leaving the cache area is consistent, thus avoiding scheduling results that only mathematically satisfy material balance but do not conform to the actual logistics process.

[0176] Since the buffer zone in the actual production site has limited storage capacity, a further buffer capacity constraint is established to ensure that the buffer inventory at the end of any scheduling period does not exceed the maximum buffer capacity of the corresponding buffer zone. The expression for this constraint is:

[0177] In the above formula, This represents the maximum buffer capacity of connection edge e. The maximum buffer capacity can be determined based on the actual mechanical capacity of the buffer equipment, the capacity of the semi-finished product trays, the production area space, and the allowable dwell conditions for semi-finished products. By setting buffer capacity constraints, the optimization model can be prevented from accumulating semi-finished products indefinitely to reduce production load during periods of high electricity prices or high carbon emissions, ensuring that the obtained scheduling optimization results can be executed on actual production equipment.

[0178] It is understandable that by using dynamic constraints, outbound constraints, and cache capacity constraints, cacheable decoupling edges can achieve cross-time adjustment of upstream and downstream production nodes based on material conservation: when the processing length of the upstream production node exceeds the current processing demand of the downstream production node, some materials enter the cache area; when the processing demand of the downstream production node exceeds the current direct supply of materials from the upstream production node, materials can be released from historical cache inventory to replenish incoming materials. Thus, without changing the production process sequence, upstream and downstream production nodes can adopt different production rhythms based on time-of-use electricity prices, electricity carbon emission factors, and equipment operating status, improving the flexibility of energy and carbon coordinated scheduling of the production line.

[0179] For edges requiring delay, the caching model corresponding to cacheable decoupling edges cannot be directly applied due to the explicit process dwell requirements between adjacent production processes. Edges requiring delay not only require materials to be temporarily stored but also require materials to meet a preset minimum process delay time before entering downstream production nodes. Only materials that meet the process dwell requirements can be released to downstream production nodes for further processing. Therefore, this embodiment establishes prohibition of direct flow constraints, delay region dynamic constraints, delay release constraints, and delay region capacity constraints for edges requiring delay to accurately describe the process dwell process.

[0180] In this embodiment, the connecting edge between the insulation extrusion process and the conductor shielding process is a mandatory delay edge. After the insulation extrusion is completed, the insulation layer is still at a high temperature and needs a certain amount of time to complete the cross-linking reaction and temperature equalization before it can enter the conductor shielding process for the next step of processing. Therefore, this connecting edge does not allow the material to directly enter the downstream production node from the upstream production node, but must first enter the delay zone and be released only after the minimum process delay time is met.

[0181] When the connection edge type parameter When, it indicates that the connecting edge e is a necessary delay edge; in a specific embodiment using a numerical connecting edge type parameter, it can be set to... This indicates that the edge must be delayed.

[0182] To ensure that materials must undergo the process dwell period, a no-direct-flow constraint is first established. The no-direct-flow constraint ensures that the direct flow of the connected edge corresponding to the required delay edge remains zero at all times; its expression is as follows:

[0183] This constraint stipulates that for edges requiring delay, materials processed by upstream production nodes cannot directly enter downstream production nodes during the current scheduling period. Instead, they must first enter the delay area to await subsequent release. Therefore, compared to direct continuous edges and cacheable decoupled edges, edges requiring delay completely prohibit direct flow, ensuring that process residency requirements are met from the source.

[0184] After establishing the direct flow prohibition constraint, a dynamic constraint for the delay zone is further established to describe the change of delay zone inventory over time. The dynamic constraint updates the delay zone inventory at the end of the current scheduling period based on the delay zone inventory at the end of the previous scheduling period, the materials entering the delay zone in the current scheduling period, and the materials released in the current scheduling period. Its expression is as follows:

[0185] For the first scheduling period, the delay zone inventory is updated based on the initial delay inventory, and its calculation method is similar to that of the buffer zone. .

[0186] The dynamic constraints of the delay zone and the dynamic constraints of the buffer have the same inventory recursion form, but their physical meanings are different. The buffer is used to adjust the production cycle time, while the delay zone is used to ensure that materials meet the process residence time. Therefore, although both use an inventory recursion model, the subsequent release conditions are completely different.

[0187] To ensure that materials meet the minimum process delay time, a delayed release constraint is established. The delayed release constraint restricts the materials that can be released during the current scheduling period to only those from historical inventory that meet the minimum process delay time requirement. Its expression is as follows: (like To minimize the number of delay periods, then the previous (Only the initial inventory can be released during each time period) (when At that time, outbound flow can only come from areas that have already been congested. Historical inventory for each time period In the above formula, This represents the initial cache inventory of the connecting edge e. This indicates that the connection edge e has passed through at least [number] times before the current scheduling period. Historical inventory for each scheduling period This represents the minimum delay time interval for connecting edge e.

[0188] The purpose of the delayed release constraint is to establish the correspondence between the time when materials enter the delay zone and the allowed release time. Only materials that have stayed in the delay zone for no less than the minimum process delay time can be included in the current scheduling period's outflow from the delay zone and enter the conductor shielding process for processing. This constraint effectively prevents the optimization model from prematurely releasing semi-finished products that have not yet completed the cross-linking or cooling process in order to reduce overall operating costs, ensuring that the resulting scheduling scheme meets the actual manufacturing process requirements of high-voltage insulated cables.

[0189] To ensure that the inventory in the delay zone does not exceed the temporary storage capacity allowed by the actual production site, a delay zone capacity constraint is established. The delay zone capacity constraint is used to ensure that the inventory in the delay zone remains within the allowable range after each scheduling period ends, and its expression is as follows:

[0190] The lower limit of inventory in the delayed zone is zero, and the upper limit is... The capacity of the delay zone is determined by the allowable capacity of the actual process. This capacity can be determined based on the length of the crosslinking process buffer, the allowed temporary storage time, and the production site layout. By limiting the inventory capacity of the delay zone, the optimization model can be prevented from extending the material residence time indefinitely, allowing the obtained scheduling results to be directly applied to the actual production site.

[0191] Since the high-voltage insulated cable production line is a continuous manufacturing line, each production node not only needs to meet the requirements of continuous material flow, but also needs to meet the production process requirements such as equipment operation mode, production speed, start-stop logic, and order delivery. Therefore, this embodiment further establishes production coordination constraints to coordinate the operating status of production nodes with the material flow process, jointly ensuring that the optimization solution meets the actual production requirements.

[0192] Specifically, production coordination constraints include gear selection constraints, processing length constraints, strong coupling synchronization constraints, end-of-day inventory clearing constraints, finished product output constraints, start-stop logic constraints, minimum continuous running time constraints, minimum continuous downtime constraints, maximum continuous downtime constraints, and speed regulation smoothing constraints. These constraints, respectively, constrain the optimization model from aspects such as equipment operating status, processing capacity, production continuity, and order completion status, collectively constraining the coordination mechanism at the production node level.

[0193] 1. Speed ​​Gear Selection Constraint: When the production equipment is running, only one speed gear can be selected; when the production equipment is stopped, no speed gear should be selected. Therefore, a speed gear selection constraint needs to be established to ensure that the operating state of the production node is consistent with the speed gear selection. The speed gear selection constraint is used to ensure that each production node selects only one speed gear when it is running, and does not select a speed gear when it is stopped. Its expression is as follows:

[0194] Each process has K=3 discrete operating positions, and the set of positions is as follows: The corresponding speed is: , where 4km / h is the rated operating speed.

[0195] The above constraints establish the correspondence between the operating state variables and the speed gear selection variables. When the production node is in the running state, only one speed gear is allowed to be selected; when the production node is in the stopped state, all speed gear selection variables remain at zero, thereby avoiding the situation where the optimization model selects multiple speed gears at the same time or where production speed still exists in the stopped state.

[0196] 2. Processing Length Constraint: Since production nodes have different processing capacities at different speed levels, a processing length constraint is established so that the processing length completed by a production node in each scheduling period is determined by the corresponding speed level and the length of the scheduling period. The processing length constraint is used to establish the correspondence between the processing length variable and the speed level, and its expression is as follows: ,

[0197] in, This represents the processing length of production node i during scheduling period t; This represents the production speed corresponding to speed setting k. The processing length constraint ensures that the processing capacity of the production node remains consistent with the equipment's operating speed. When a production node selects different speed settings, its corresponding processing length automatically changes, thus achieving a unified description between equipment operating speed and production capacity.

[0198] 3. Strong Coupling Synchronization Constraint: For production processes with strong coupling relationships, since upstream and downstream production equipment cannot adjust their cycle time through buffering or process dwell, they need to maintain synchronized operation. If the operating speeds of upstream and downstream production nodes differ, it can easily lead to material accumulation, tension fluctuations, or a decline in product quality. For example, in the current model, the strongly coupled processes are (6,7) and (7,8), i.e., the outer sheath extrusion, intermediate cooling, and take-up detection must maintain synchronized operation. Since E23 is set as a necessary delay edge, P2 and P3 are no longer forced to synchronize, otherwise it would conflict with the delay logic. Therefore, a strong coupling synchronization constraint is established. The strong coupling synchronization constraint is used to ensure that production nodes with strong coupling relationships maintain the same operating speed during the same scheduling period. Let the set of strong couplings be: Then we have: .

[0199] In this embodiment, the outer sheath extrusion process, the intermediate cooling process, and the take-up inspection process are strongly coupled. Therefore, the corresponding production nodes need to maintain the same operating speed to achieve continuous synchronous production. By establishing strong coupling synchronization constraints, it can be ensured that the production rhythm between the strongly coupled processes remains consistent, thereby improving the stability of continuous production.

[0200] 4. End-of-Day Inventory Clearance Constraint: To ensure that semi-finished products entering the buffer or delay area on the same day complete subsequent processing within the scheduling cycle, an end-of-day inventory clearance constraint is established to prevent the optimizer from falsely reducing daily costs by retaining a large number of semi-finished products. The end-of-day inventory clearance constraint is used to restore the inventory of each buffer and delay area to a predetermined state at the end of the scheduling cycle. Its expression is as follows:

[0201] in, This represents the inventory corresponding to edge e at the end of the scheduling cycle. This constraint ensures that after the entire scheduling cycle ends, the materials in each buffer and delay area are properly processed, and the production arrangement of the next scheduling cycle will not be affected by long-term inventory backlog, thus ensuring the independence and continuous execution between scheduling cycles.

[0202] 5. Finished Product Output Constraint: To ensure that production scheduling results meet order delivery requirements, a finished product output constraint is established. The finished product output constraint ensures that the cumulative processing length completed by the final production node throughout the entire scheduling cycle meets order requirements. Its expression is as follows:

[0203] in, Indicates the required production volume based on orders; This represents the processing length completed by the final production node during scheduling period t. An equality constraint is used here, meaning that the daily production plan has a fixed order quantity, and the optimizer cannot change the objective function structure by increasing production. By establishing finished product output constraints, the number of products completed throughout the scheduling cycle meets order requirements. This ensures timely completion of production tasks while guaranteeing process constraints and energy and carbon optimization objectives, avoiding insufficient order delivery due to over-optimization of energy costs.

[0204] 6. Start-Stop Logic Constraints: The changes in the operating state of production equipment between adjacent scheduling periods should be consistent with the start and stop variables. When a production node switches from a stopped state to a running state, the corresponding start variable takes a value of 1; when a production node switches from a running state to a stopped state, the corresponding stop variable takes a value of 1; if the operating state of the production node remains unchanged, both the start and stop variables remain 0. Therefore, start-stop logic constraints need to be established to uniformly describe the state transition process of production nodes between adjacent scheduling periods. Start-stop logic constraints are used to ensure that the start and stop variables are determined by the relationship between the changes in the operating state of production nodes in adjacent scheduling periods, and to ensure that the same production node will not start and stop simultaneously within the same scheduling period. The start and stop variables are determined by the changes in the operating state in adjacent periods. Let... Given the initial running state:

[0205]

[0206] The same process cannot be started and stopped simultaneously at the same time: ; If we consider the initial shutdown state, then: ; If the system transitions from an initial shutdown state to a running state during the first time period, the startup cost will be included.

[0207] The aforementioned start-stop logic constraints include two aspects: First, by accurately describing the state changes of production nodes between adjacent scheduling periods through the logical relationship between operating state variables and start and stop variables. When a production node switches from a stopped state to an operating state, only the start variable takes a value of 1; when a production node switches from an operating state to a stopped state, only the stop variable takes a value of 1; if the operating state remains unchanged, both the start and stop variables remain 0. Second, mutual exclusion constraints ensure that the same production node cannot be started and stopped simultaneously within the same scheduling period, thereby avoiding state transition results that do not conform to the actual production process. By establishing start-stop logic constraints, the process of equipment operating state changes can be made to conform to actual production laws, and a foundation can be provided for subsequent calculation of equipment start-stop costs and continuous operating time constraints.

[0208] 7. Minimum Continuous Operating Time Constraint: High-voltage insulated cable production equipment typically involves a long preheating, stable operation, and process setup process. If the equipment is shut down immediately after startup, it will not only result in significant energy waste but also negatively impact product quality and equipment lifespan. Therefore, a minimum continuous operating time constraint needs to be established. This constraint ensures that production nodes maintain continuous operation for at least a preset time after startup. If process i starts during time period t, it must subsequently operate continuously for at least [a certain duration]. Time period:

[0209] in: This represents the minimum allowed continuous running time for a production node. The minimum continuous running time constraint stipulates that once a production node starts, it must remain operational for a consecutive number of scheduling periods, and cannot be shut down again before reaching the minimum continuous running time. This constraint effectively prevents the optimization model from frequently starting and stopping equipment in pursuit of local optima, thus improving the operational stability of production equipment.

[0210] 8. Minimum Continuous Downtime Constraint: Similar to the minimum continuous running time, after production equipment completes a shutdown, it also needs to maintain a certain continuous downtime to avoid immediate restarting. Therefore, a minimum continuous downtime constraint is established. This constraint ensures that after a production node stops, it maintains continuous downtime for at least a preset duration. If process i stops during time period t, then it must subsequently maintain continuous downtime for at least [a certain duration]. Time period:

[0211] in: This represents the minimum allowed consecutive downtime for a production node. The model uses... This constraint is established with the state variables within the subsequent shutdown window. This constraint ensures that the equipment cannot be restarted after it has completed shutdown until the minimum continuous shutdown time is reached, thereby avoiding repeated start-stop cycles in a short period of time, improving equipment operational reliability, and reducing equipment startup energy consumption.

[0212] 9. Maximum Continuous Downtime Constraint: Optimization models may tend to schedule some production equipment downtime during periods of high electricity prices to reduce overall operating costs. However, excessive downtime can lead to insufficient production capacity and affect on-time order completion. Therefore, a maximum continuous downtime constraint needs to be established. This constraint limits the continuous downtime of production nodes to a preset upper limit. Specifically, to avoid the model simply adopting long periods of continuous downtime, a maximum continuous downtime constraint is set. Let... Let be the maximum number of consecutive downtime periods allowed for process i, then any length is... At least one time period must be active within the sliding window:

[0213] This constraint requires that within any consecutive downtime window, production nodes must be operational for at least one scheduling period, thus preventing insufficient production capacity or failure to complete production plans due to prolonged equipment downtime. Simultaneously, this constraint makes scheduling results rely more on speed adjustments, buffer releases, and process delays, rather than simply on long-term downtime for peak shaving. This constraint, in conjunction with the order output constraint, enables the optimization model to achieve a balance between reducing overall operating costs and ensuring production capacity.

[0214] 10. Speed ​​Smoothing Constraint: Significant speed changes in production equipment between adjacent scheduling periods can lead to fluctuations in traction tension, changes in product dimensions, and mechanical shock to the equipment. Therefore, a speed smoothing constraint is needed to limit the magnitude of production speed changes. The speed smoothing constraint is used to make the speed adjustment amplitude auxiliary variable characterize the absolute value of the equivalent operating speed change between adjacent scheduling periods.

[0215] Specifically, the equivalent running speed of process i in time period t is defined as: Speed ​​adjustment amplitude variable Used to linearize the absolute value of velocity changes between adjacent time periods:

[0216]

[0217]

[0218] in, An auxiliary variable representing the speed adjustment magnitude of production node i during scheduling period t; , These represent the equivalent running speeds of production node i during scheduling periods t and t-1, respectively.

[0219] The speed regulation smoothing constraint uses the speed regulation amplitude auxiliary variable to linearize the absolute value of the speed change between adjacent scheduling periods, enabling the mixed-integer linear programming model to be solved directly. Simultaneously, the speed regulation smoothing penalty cost in the objective function, working in conjunction with this constraint, can prevent drastic fluctuations in the operating speed of production equipment, thus improving the stability of the continuous production process.

[0220] In summary, this embodiment establishes constraints for gear selection, processing length, strong coupling synchronization, end-of-day inventory clearing, finished product output, start / stop logic, minimum continuous running time, minimum continuous downtime, maximum continuous downtime, and speed regulation smoothing. These, together with the aforementioned material connection constraints, constitute a complete energy-carbon coordinated scheduling constraint system. This constraint system not only ensures that the production scheduling scheme meets the continuous production process requirements of high-voltage insulated cables, but also, together with the comprehensive operating cost objective function, forms a complete mixed-integer linear programming model, providing constraints for subsequent optimization solutions.

[0221] Step S5: Optimization and Control Command Generation: With the objective function minimization as the optimization goal, the decision variables of each production node and each connection edge are solved under the energy and carbon coordinated scheduling constraint to obtain the scheduling optimization results of the production line within the scheduling cycle. Based on the scheduling optimization results, start-stop control commands and frequency conversion speed regulation commands for the corresponding production equipment are generated.

[0222] After establishing the overall operating cost objective function and energy-carbon coordinated scheduling constraints, the energy-carbon coordinated scheduling model for the entire high-voltage insulated cable production process can be uniformly represented as a mixed-integer linear programming (MILP) model. In this model, the operating status variables of production nodes, speed range selection variables, start-up variables, and shutdown variables are all integer decision variables; the processing length variables, direct flow variables, flow variables entering the buffer or delay zone, flow variables exiting the buffer or delay zone, buffer or delay zone inventory variables, and speed adjustment amplitude auxiliary variables are continuous decision variables. The entire model uses the minimum overall operating cost as the optimization objective and satisfies all the aforementioned material connection constraints and production coordination constraints.

[0223] Specifically, the following optimization model is established:

[0224] Where J represents the comprehensive operating cost objective function established in step S3; the constraints include all material connection constraints and production coordination constraints established in step S4; and the variable value constraints are used to limit the value range of each integer variable and continuous variable.

[0225] The aforementioned optimization model integrates the comprehensive operating cost objective function and the energy-carbon coordinated scheduling constraint into the same mathematical model, enabling the production scheduling problem to be transformed into a standard mixed-integer linear programming problem, which can then be solved uniformly using a mature optimization solver.

[0226] In this embodiment, the above-described mixed-integer linear programming model is input into an optimization solver for solving to obtain the optimal decision variables corresponding to each production node and each connection edge throughout the entire scheduling cycle. Preferably, the above optimization model can be solved using a CPLEX solver, a Gurobi solver, or other optimization solvers that support mixed-integer linear programming.

[0227] During the solution process, the comprehensive operating cost objective function established in step S3 is used as the optimization objective, while simultaneously satisfying all the constraints established in step S4. The optimization solver performs joint optimization on all decision variables based on input parameters such as the operating parameters of each production node equipment, time-of-use electricity price, electricity carbon emission factor, order demand, and buffer capacity, and finally outputs the scheduling optimization result that satisfies all process constraints and minimizes the comprehensive operating cost.

[0228] Since the objective function comprehensively considers electricity costs, carbon emission costs, equipment start-up and shutdown costs, speed deviation penalty costs, speed regulation smoothing penalty costs, buffer usage costs, and direct flow coordination costs, the resulting scheduling optimization can reduce energy costs and carbon emission costs while taking into account equipment operation stability, process continuity, and inventory management requirements, thus achieving energy and carbon synergistic optimization in the high-voltage insulated cable production process.

[0229] After optimization, the scheduling optimization results for each production node and each connection edge throughout the entire scheduling cycle can be obtained. The scheduling optimization results for each production node include: the operating status, speed level, processing length, start-up and shutdown times of each production node in each scheduling period. The scheduling optimization results for each connection edge include: the direct traffic, traffic entering the buffer or delay zone, traffic exiting the buffer or delay zone, and the inventory changes in the buffer or delay zone.

[0230] The above scheduling optimization results can fully reflect the changes in the operating status of production equipment and the material flow process throughout the entire scheduling cycle, providing a basis for generating subsequent equipment control commands.

[0231] Based on the production node operating status variables, start-up variables, and stop-down variables obtained from the optimization solution, start-up and stop control commands corresponding to each production device are further generated.

[0232] Specifically, the operating status of the corresponding production equipment is determined based on the operating status variables of each production node in each scheduling period. When the operating status variable changes from 0 to 1, a start control command for the corresponding production equipment is generated to control the corresponding production equipment to complete the start-up process. When the operating status variable remains at 1, the corresponding production equipment continues to run. When the operating status variable changes from 1 to 0, a stop control command for the corresponding production equipment is generated to control the corresponding production equipment to complete the stop-up process according to the process requirements.

[0233] Since the start-stop control commands are derived from the unified solution results of the optimization model, the start-stop sequence of each production equipment can meet the requirements of material connection relationship and production coordination constraints, and there will be no mismatch in the operating status of upstream and downstream equipment or material interruption, thereby ensuring continuous and stable production operation.

[0234] After generating start-stop control commands, the variable selection based on the speed gear obtained from the optimization solution is used to further generate frequency conversion speed control commands for each production equipment.

[0235] Specifically, the target operating speed of the production equipment for the current scheduling period is determined by selecting variables based on the speed level of each production node in each scheduling period.

[0236] Subsequently, a frequency converter control command is generated based on the frequency parameters corresponding to the target operating speed and sent to the frequency converter controller of the corresponding production equipment to control the production equipment to adjust its operating speed.

[0237] For strongly coupled production nodes that need to maintain synchronous operation, since the strong coupling synchronization constraint has ensured that each production node has a consistent speed level, the generated frequency conversion speed control command can ensure that the corresponding production equipment maintains synchronous operation, avoiding material accumulation, tension fluctuation or product quality degradation due to speed differences.

[0238] Meanwhile, since the speed regulation smoothing constraint has limited the speed change range between adjacent scheduling periods, the speed adjustment process corresponding to the frequency conversion speed regulation command is more stable, which can effectively reduce the mechanical shock of the equipment and improve the long-term operational reliability of the production line.

[0239] After receiving the start / stop control commands and frequency conversion speed control commands, the production control system will send the corresponding control commands to the control units of each production equipment.

[0240] Each production equipment completes equipment start-up, equipment shutdown, and running speed adjustment according to the received control commands, and at the same time completes material processing and material flow according to the optimization solution results.

[0241] As the production process continues, the latest order information, time-of-use electricity price, electricity carbon emission factor and equipment operating status can be obtained again according to the preset rolling scheduling cycle, and steps S1 to S5 can be repeated to optimize the subsequent scheduling cycle, thereby forming a rolling optimization scheduling mechanism, so that the high-voltage insulated cable production line can continuously maintain a better energy and carbon synergy operation state.

[0242] It is understood that this embodiment achieves coordinated optimization of the operating status of production equipment, production speed and material flow process in the continuous production of high-voltage insulated cables by constructing a comprehensive operating cost objective function, establishing energy and carbon coordinated scheduling constraints and uniformly performing mixed integer linear programming solution. Under the premise of meeting the production process requirements and order delivery requirements, it effectively reduces the comprehensive operating cost of the production line and improves energy utilization efficiency and production stability.

[0243] To further illustrate the specific implementation process of the energy-carbon coordinated scheduling optimization method for the high-voltage insulated cable production process of this invention, the following section uses a 110kV cross-linked polyethylene (XLPE) high-voltage insulated cable continuous production line as an example. Based on the MATLAB platform, the model is numerically solved, and the scheduling results are systematically analyzed under a given production structure, energy consumption parameters, and electricity pricing mechanism. This application example is only used to illustrate the technical solution of this invention and is not intended to limit the scope of protection of this invention.

[0244] 1. Initialization parameter settings 1.1 Production System Structure Setting Consider a typical cable production line consisting of 8 consecutive processes, represented as: The processes are as follows: conductor stranding, insulation extrusion, conductor shielding, cabling and filling, metal armoring, outer sheath extrusion, intermediate cooling, and winding and testing.

[0245] The scheduling cycle is set to 24 hours, with time discrete into equally spaced time periods: Each process is set with 3 discrete operating levels: The corresponding processing speeds are 2km / h, 4km / h and 6km / h, respectively, where 4km / h is the rated speed.

[0246] 1.2. Electricity Price and Carbon Emission Parameters Considering the time-of-use pricing mechanism, the electricity price function It varies according to time period. At the same time, an electricity carbon emission factor is introduced. With carbon price Construct a comprehensive energy cost: ; in, For time period Electricity price (yuan / kWh); Carbon emission factor (kgCO2 / kWh); Carbon price (yuan / kgCO2): Carbon emission factor: 0.7kkgCO2 / kWh; Carbon price: 0.05 yuan / kgCO2.

[0247] For details regarding the relevant 24-hour time-of-use electricity price and dynamic carbon emission factor, please refer to [link / reference]. Figure 3 Electricity prices are low in the early morning and at night, with significant peaks in the morning and evening; carbon emission factors show a trend of first decreasing and then increasing. Together, these factors constitute the external cost signal for production scheduling. Since the objective function considers both electricity costs and carbon emission costs, the optimization model tends to increase production line load during periods of low electricity prices and low carbon emission factors, while reducing production intensity during periods of high electricity prices or high carbon emission factors, thereby achieving a comprehensive optimization of both economic efficiency and low carbon emissions.

[0248] 1.3. Setting Production Requirements and Process Constraints The daily production requirement is set as follows: The material connection relationships between processes are categorized into three types: bufferable edges (allowing inventory adjustments), mandatory delay edges (indicating process waiting time), and direct continuous edges (requiring synchronous processing). Specifically, the section between insulation extrusion and conductor shielding is designated as a mandatory delay edge, with a minimum delay of one time period. Outer sheath extrusion, intermediate cooling, and take-up inspection constitute a strongly coupled process group.

[0249] 1.4. Baseline Scene Setup The baseline scenario is set to have no adjustability between production processes, running at a fixed speed of 4km / h without frequency conversion speed regulation, and each process is organized to produce continuously according to the predetermined production sequence without scheduling optimization.

[0250] 2. Optimization Results and Analysis Based on the above parameters, the constructed mixed-integer optimization model was solved using MATLAB to obtain the optimal scheduling scheme. The results are analyzed from multiple dimensions below.

[0251] 2.1. Overall Situation Analysis The results of the baseline and optimized schemes are shown in Table 1. The results show that the actual cost of the optimized scheme decreased from RMB 15,134.4452 to RMB 13,212.2340, a reduction of 12.70%. The model can effectively reduce production operating costs by adjusting the running time and speed of each process.

[0252] In terms of total energy consumption, the optimized scheme increased slightly from 16333.5060kWh to 16403.4514kWh, an increase of only 0.43%. The cost reduction was not achieved by significantly reducing energy consumption, but mainly by optimizing the transfer of production load between different time periods.

[0253] In terms of total carbon emissions, the optimized scheme reduced CO2 from 9325.0708 kg CO2 to 8714.3028 kg CO2, a decrease of 6.55%. This indicates that optimized scheduling can allocate some production tasks to periods with low carbon emission factors, achieving carbon reduction while lowering costs.

[0254] Table 1. Comparison and Analysis of the Operating Results of the Baseline and Optimized Schemes index benchmark scheme Optimization plan Change rate of change Actual cost / yuan 15134.4452 13212.2340 -1922.2111 -12.70% Total energy consumption / kWh 16333.5060 16403.4514 69.9454 0.43% <![CDATA[Total carbon emission / kgCO2]]> 9325.0708 8714.3028 -610.7680 -6.55% 2.2. Analysis of scheduling results for each time period 2.2.1. Gantt chart of process operation status and speed gear Figure 4 The diagram illustrates the operational status and speed levels of each process throughout the day. As shown, the production line does not operate continuously at its rated speed, but rather switches speed levels at different times. During low-cost periods, some processes select a high speed of 5 km / h to increase output; during periods of higher electricity prices, some processes switch to 3 km / h or 4 km / h to reduce electricity load. Meanwhile, the diagram does not show any large-scale, long-term shutdowns, indicating that the model does not simply rely on shutdowns to avoid peak electricity price / carbon emission factor periods, but rather achieves flexible scheduling through speed adjustment while meeting continuous production and minimum start-stop constraints.

[0255] From the perspective of inter-process coordination, the strongly coupled processes such as outer sheath extrusion, intermediate cooling, take-up, and inspection exhibit a relatively consistent operating rhythm in the diagram. The production process can maintain speed synchronization between strongly coupled processes, avoiding unreasonable working conditions such as the outer sheath not being able to cool in time after forming or the take-up not being able to be completed in time after cooling due to inconsistent speeds between upstream and downstream processes.

[0256] 2.2.2. Cable processing length at different times Figure 5 The changes in processing length for each process over a 24-hour period are presented. It can be seen that the processing length of each process does not remain at a constant rated level, but rather dynamically adjusts according to electricity price, carbon emission factor, and process connection constraints. During periods of low electricity price, the processing length of some processes increases, corresponding to high-speed operation; during periods of high electricity price, the processing length decreases, indicating that the model can proactively reduce production load during high-cost periods. There are certain differences in the changes in processing length between different processes. This is due to the combined effect of bufferable edges, delayed edges, and strongly coupled edges, which allow upstream and downstream processes to avoid complete synchronization, thereby improving the flexibility of production line scheduling.

[0257] 2.2.3. Inventory / Delay Zone Usage Figure 6 The data presents the inventory and inflow / outflow changes for typical buffer and delay areas. It can be seen that there are significant differences in buffer usage across different edges. For bufferable decoupling edges, inventory is mainly generated when upstream and downstream processes have inconsistent speeds or when operating rhythms switch, serving to buffer production differences between processes. For edges requiring delay, inventory reflects the process dwell time, where materials need a certain delay before entering the downstream process.

[0258] Among them, (a) shows the inventory / delay zone usage of connecting edge B12, which shows that the inventory remains at 0, with no material buffering or delay. (b) shows the inventory / delay zone usage of the necessary delay edge B23, which shows that materials continuously enter and exit the delay zone, maintaining a certain amount of delayed inventory to meet process dwell requirements. (c) shows the inventory / delay zone usage of connecting edge B34, which shows that there are material entry and exit processes during production, and the upstream and downstream process rhythm is coordinated through inventory changes. (d) shows the inventory / delay zone usage of connecting edge B56, which shows that only a small amount of material buffering occurs in local periods, followed by timely release, buffering short-term production rhythm fluctuations. The results indicate that intermediate buffering and process delay optimization scheduling play a role in decoupling upstream and downstream processes and improving production line flexibility.

[0259] 2.2.4. Output of finished cables Figure 7Let represent the time-period output and cumulative output of finished cables. It can be seen that the time-period output fluctuates with changes in operating speed and process status, but the cumulative output maintains a monotonically increasing trend and reaches order demand at the end of the scheduling cycle. The results demonstrate that the model reallocates production load across time periods while satisfying daily order constraints.

[0260] 2.2.5. Temperature Changes in Key Processes Figure 8 The equivalent outlet temperatures for key processes such as insulation extrusion, outer sheath extrusion, and intermediate cooling are presented. As shown in the figure, the temperatures of each key process fluctuate with the speed setting, but overall remain within their corresponding safety threshold ranges. The temperature changes in the insulation and outer sheath extrusion processes reflect the increased heat load during high-speed operation and the decreased heat load during low-speed operation; the intermediate cooling process regulates the temperature changes in the upstream extrusion process. The results demonstrate that while reducing operating costs, the temperature safety requirements of key processes can still be met, avoiding the compromise of cable production quality due to excessive pursuit of economic efficiency.

[0261] Compared with the prior art, the present invention has the following beneficial effects: This invention abstracts the continuous production process of high-voltage insulated cables into a directed production topology composed of production nodes and connecting edges. Based on the actual physical connection relationship between different processes, different types of connecting edge models are established. This allows the production topology to accurately reflect different production relationships such as continuous processing, buffer decoupling, and process dwell, thereby improving the consistency between the production scheduling model and the actual production process.

[0262] This invention establishes material connection constraints for direct continuous edges, bufferable decoupling edges, and edges that must be delayed, so that different process requirements correspond to different material flow methods. While ensuring material conservation, it also takes into account continuous processing, buffer adjustment, and process dwell requirements, avoiding the problem of inconsistency between scheduling results and actual production processes caused by using a unified material flow model, and improving the executability of scheduling results.

[0263] This invention incorporates comprehensive energy costs, along with production operation factors such as equipment start-up and shutdown, speed adjustment, and material buffering, into the comprehensive operating cost objective function. It also combines these factors with production coordination constraints for unified optimization. This allows for coordinated optimization of the operating status, operating speed, and material flow of production equipment. Under the premise of meeting order production needs and process constraints, it achieves a reduction in the comprehensive operating cost of the production line and an improvement in energy utilization efficiency and carbon emission control.

[0264] This invention directly generates start-stop control commands and frequency conversion speed regulation commands for production equipment by uniformly solving the decision variables of production nodes and connection edges. This allows the scheduling optimization results to be directly applied to the continuous production control process of high-voltage insulated cables, reducing the reliance of manual scheduling on production planning and improving the automation level of production scheduling and the stability of production operation.

[0265] The system and medium of the present invention, corresponding to the methods described above, also have the advantages described above.

[0266] The present invention can implement all or part of the processes in the methods of the above embodiments, or it can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, it can implement the steps of the above method embodiments. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or some intermediate form. Computer-readable media include: any entity or device capable of carrying computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. The memory is used to store computer programs and / or modules. The processor implements various functions by running or executing the computer programs and / or modules stored in the memory, and by calling data stored in the memory. The memory may include high-speed random access memory, as well as non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart media cards (SMC), secure digital (SD) cards, flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0267] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for optimizing energy and carbon co-scheduling in the production process of high-voltage insulated cables, characterized in that, include: S1. Obtain the continuous production process information of the high-voltage insulated cable production line, construct a directed production topology with each continuous production process as a production node and the material connection relationship between adjacent production processes as a connection edge, and classify each connection edge according to the physical characteristics between adjacent production processes. S2, construct a discrete time frame according to a preset scheduling cycle, and define decision variables for each production node and connection edge; S3. Based on the comprehensive energy cost and various decision variables used to characterize the superposition relationship between unit electricity cost and unit carbon emission cost, construct an objective function to characterize the comprehensive operating cost of the production line within the scheduling cycle. S4. Material connection constraints are established according to the type of each connection edge, and combined with the production coordination constraints of the production nodes to form energy and carbon coordination scheduling constraints. S5, with the objective function minimization as the optimization objective, the decision variables of each production node and each connection edge are solved under the energy-carbon coordinated scheduling constraint to obtain the scheduling optimization result of the production line within the scheduling cycle, and the start-stop control command and frequency conversion speed regulation command of the corresponding production equipment are generated according to the scheduling optimization result.

2. The energy and carbon synergistic scheduling optimization method for high-voltage insulated cable production processes according to claim 1, characterized in that, In step S1, the connecting edges are classified according to the physical characteristics between adjacent production processes, specifically including: Based on whether adjacent production processes require direct connection within the same scheduling period, whether release is required after a process dwell time, and whether cross-period decoupling via intermediate buffering is allowed, each connection edge is divided into directly continuous edges, bufferable decoupling edges, and edges that must be delayed. The connection edge type is represented by a connection edge type parameter, expressed as follows: In the above formula, e represents the edge number. This indicates the type parameter of the connecting edge e. These are three different parameters representing the type of the connecting edge; The continuous production process information of the high-voltage insulated cable production line includes conductor stranding, insulation extrusion, conductor shielding, cabling and filling, metal armoring, outer sheath extrusion, intermediate cooling, and take-up inspection. Based on the correspondence between adjacent production processes, corresponding connection edge type parameters are assigned to the connection edges between adjacent processes: the connection edge type parameters between conductor stranding and insulation extrusion, conductor shielding and cabling and filling, cabling and filling and metal armoring, and metal armoring and outer sheath extrusion represent bufferable decoupling edges; the connection edge type parameter between insulation extrusion and conductor shielding represents a necessary delay edge; and the connection edge type parameters between outer sheath extrusion and intermediate cooling, and between intermediate cooling and take-up inspection represent direct continuous edges.

3. The energy and carbon synergistic scheduling optimization method for the high-voltage insulated cable production process according to claim 1, characterized in that, In step S2, the decision variables of the production node include one or more of the following: operating state variable to characterize the operating or stopping state of the production node, speed gear selection variable to characterize the selected speed gear of the production node, start-up variable to characterize the production node switching from the stopping state to the operating state, stopping variable to characterize the production node switching from the operating state to the stopping state, processing length variable to characterize the processing volume completed by the production node in the corresponding scheduling period, and speed adjustment amplitude auxiliary variable to characterize the speed change amplitude between adjacent scheduling periods. The decision variables of the connection edge include one or more of the following: direct flow variables that characterize the material output from the upstream production node directly entering the downstream production node; inflow variables that characterize the material output from the upstream production node entering the buffer or delay area; outflow variables that characterize the material taken from the buffer or delay area by the downstream production node for processing; and buffer or delay area inventory variables that characterize the inventory of the connection edge at the end of the corresponding scheduling period.

4. The energy and carbon synergistic scheduling optimization method for high-voltage insulated cable production processes according to claim 1, characterized in that, In step S3, the objective function is constructed based on electricity cost, carbon emission cost, equipment start-up and shutdown cost, speed deviation penalty cost, speed regulation smoothing penalty cost, buffer usage cost, and direct flow coordination cost, and its expression is: In the above formula, Let be the objective function. These represent electricity costs, carbon emission costs, equipment start-up and shutdown costs, speed deviation penalty costs, speed regulation smoothing penalty costs, buffer usage costs, and direct flow coordination costs, respectively. The electricity cost is obtained by multiplying the energy consumption of each process at each time period and at each speed level by the time-of-use electricity price for the corresponding time period, and then summing the results across all processes, time periods, and speed levels. The carbon emission cost is obtained by multiplying the electricity consumption of each process at each time period and at each speed level by the corresponding electricity carbon emission factor and carbon price, and then summing them up for all processes, time periods and speed levels. The equipment start-up and shutdown cost is obtained by summing the costs incurred when switching equipment from shutdown to operation and from operation to shutdown, respectively, for the start-up and shutdown variables of production nodes, and then accumulating these costs over all processes and time periods. The speed deviation penalty cost is obtained by calculating the squared deviation between the actual selected speed gear and the rated speed, multiplying it by the penalty imposed on the scheduling scheme that deviates from the rated operating speed, and summing it up over all processes, time periods, and speed gears. The speed adjustment smoothing penalty cost is obtained by multiplying the penalty for the speed change amplitude by the speed adjustment amplitude auxiliary variable and accumulating it over all processes and time periods; The cost of using the cache includes the processing cost of materials entering and leaving the cache or delay area, as well as the holding cost of semi-finished products occupying inventory in the cache or delay area; The direct flow coordination cost includes the coordination cost incurred when materials flow directly from upstream to downstream processes in bufferable or delayed edges.

5. The energy and carbon synergistic scheduling optimization method for the high-voltage insulated cable production process according to claim 4, characterized in that, The expression for the electricity cost is: In the above formula, T represents the set of scheduling time periods; I represents the set of processes; and K represents the set of speed levels. This represents the operating power of process i at speed setting k; Indicates the duration of a single scheduling period; This represents the time-of-use electricity price for period t; This indicates whether process i selects speed gear k during scheduling period t; The expression for the carbon emission cost is: In the above formula, This represents the carbon emission factor of electricity during time period t. Indicates the price of carbon emissions; The expression for the equipment start-up and shutdown cost is: In the above formula, This represents the initial startup cost of process i; This represents the downtime cost of process i. This represents the starting variable for process i during scheduling period t. This represents the shutdown variable of process i during the scheduling period t; The expression for the speed deviation penalty cost is: In the above formula, This represents the speed deviation penalty coefficient for process i; This indicates the production speed corresponding to speed setting k; Indicates the rated speed of process i; The expression for the speed regulation smoothing penalty cost is: In the above formula, Let be the speed regulation smoothing penalty coefficient for process i. This is an auxiliary variable representing the speed adjustment range of process i during time period t; The expression for the cache usage cost is: In the above formula, E represents the set of connecting edges; e represents the connecting edge number. This indicates the type parameter of the connecting edge e; This represents the processing cost per unit of material entering or leaving the buffer or delay area; This represents the inbound buffer or inbound delay zone traffic of connection edge e during time period t; This indicates the out-buffer or out-delay zone traffic of connection edge e during time period t; This represents the unit inventory holding cost; This represents the cache or delay zone inventory of connected edge e after time period t ends; The expression for the direct flow coordination cost is: In the above formula, Indicates the unit direct flow coordination cost. This represents the direct flow of the connecting edge e during time period t.

6. The energy and carbon synergistic scheduling optimization method for high-voltage insulated cable production processes according to claim 1, characterized in that, In step S4, before establishing material connection constraints according to the type of each connection edge, material balance constraints between adjacent production processes are first established. These material balance constraints are used to allocate the processing length of the upstream production node as the direct flow directly into the downstream production node and the inflow flow into the buffer or delay area. The processing length of the downstream production node is expressed as the sum of the direct flow and the outflow, as shown in the expression: In the above formula, e represents the edge connection number, and t represents the scheduling period number. Let represent the processing lengths of the upstream and downstream production nodes corresponding to edge e during scheduling period t, respectively. This represents the direct flow of connection edge e during time period t. This represents the inbound buffer or inbound delay zone traffic of connection edge e during time period t. This indicates the out-of-buffer or out-of-delay traffic of the connection edge e during time period t.

7. The energy and carbon synergistic scheduling optimization method for high-voltage insulated cable production processes according to claim 1, characterized in that, In step S4, establishing material connection constraints according to the type of each connection edge specifically includes: For directly continuous edges, establish direct connection constraints that prohibit caching and prohibit delay; for cacheable decoupled edges, establish dynamic caching constraints, outbound constraints, and cache capacity constraints; for edges that must be delayed, establish constraints that prohibit direct flow, dynamic delay zone constraints, delay release constraints, and delay zone capacity constraints. The direct connection constraint is used to ensure that the output materials of the upstream production node directly enter the downstream production node within the same scheduling period, and to prevent the connection edge from generating cached or delayed inventory. The expression is: In the above formula, This represents the direct flow of connection edge e during time period t. This represents the inbound buffer or inbound delay zone traffic of connection edge e during time period t. This indicates the out-of-buffer or out-of-delay traffic of connection edge e during time period t. This represents the cache or delay zone inventory of connected edge e after time period t ends. These represent the processing lengths of the upstream and downstream production nodes corresponding to edge e during scheduling period t, respectively. The dynamic cache constraint is used to determine the cache inventory at the end of the current scheduling period based on the inventory of the previous scheduling period, the inbound cache flow of the current scheduling period, and the outbound cache flow of the current scheduling period. The expression is: In the above formula, This represents the cache inventory of connection edge e after the end of scheduling period t-1; The outbound constraint is used to prevent materials that enter the buffer during the current scheduling period from being released as historical buffer materials in the same scheduling period. The expression is: The cache capacity constraint is used to limit the cache inventory from exceeding a preset cache capacity, and its expression is: In the above formula, This indicates the maximum buffer capacity of the connected edge e; The direct flow restriction constraint is used to prevent the output materials of the upstream production node from directly entering the downstream production node in the same scheduling period. The expression is: The delay zone dynamic constraint is used to determine the delay zone inventory at the end of the current scheduling period based on the delay zone inventory of the previous scheduling period, the inbound delay zone flow of the current scheduling period, and the outbound delay zone flow of the current scheduling period. The expression is: The delayed release constraint is used to ensure that the flow in the delay zone comes only from historical inventory that meets the minimum process delay duration, and its expression is: In the above formula, This represents the initial cache inventory of the connecting edge e. This indicates that the connection edge e has passed through at least [number] times before the current scheduling period. Historical inventory for each scheduling period This represents the minimum delay time interval for connecting edge e.

8. The energy and carbon synergistic scheduling optimization method for high-voltage insulated cable production processes according to claim 1, characterized in that, The production coordination constraints include one or more of the following: gear selection constraints, processing length constraints, strongly coupled process synchronization constraints, start / stop logic constraints, minimum continuous operation constraints, minimum continuous downtime constraints, maximum continuous downtime constraints, order output constraints, end-of-day inventory clearing constraints, and speed adjustment continuous constraints, wherein: Speed ​​selection constraint is used to ensure that each production node selects only one speed speed when it is running and does not select a speed speed when it is stopped. The processing length constraint is used to ensure that the processing length of the production node in each scheduling period is determined by the selected speed level and the length of the scheduling period; Strongly coupled synchronization constraints are used to ensure that production nodes with strong coupling relationships maintain the same operating level during the same scheduling period. End-of-day inventory clearing constraint is used to ensure that the inventory in the buffer or delay area is zero at the end of the scheduling cycle; Finished product output constraints are used to ensure that the cumulative processing length of the final production node within the scheduling cycle meets the order demand output. Start-stop logic constraints are used to ensure that start-up and stop variables are determined by changes in the operating status of adjacent scheduling periods, and that the same production node is not started and stopped at the same time in the same scheduling period; The minimum continuous running time constraint is used to ensure that the production node maintains continuous operation for no less than a preset time after startup. The minimum continuous downtime constraint is used to ensure that a production node remains continuously shut down for no less than a preset duration after it has stopped. The maximum continuous downtime constraint is used to ensure that there is at least one running scheduling period within any preset downtime window; Speed ​​regulation smoothing constraints are used to make the speed regulation amplitude auxiliary variable characterize the absolute value of the equivalent operating speed change between adjacent scheduling periods.

9. An energy-carbon coordinated scheduling optimization system for a high-voltage insulated cable production process, comprising a microprocessor and a memory interconnected, characterized in that, The microprocessor is programmed or configured to execute the steps of the energy-carbon coordinated scheduling optimization method for the high-voltage insulated cable production process as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program / instructions, characterized in that, The computer program / instructions are programmed or configured to execute, via a processor, the steps of the energy-carbon coordinated scheduling optimization method for the high-voltage insulated cable production process as described in any one of claims 1 to 8.

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