Low-carbon operation method of electricity-hydrogen comprehensive energy system based on ADMM method
By applying the low-carbon operation method based on ADMM method in an integrated energy system, a low-carbon optimization operation model is established and solved by the alternating direction multiplier method, the problems of insufficient system coordination and complex information exchange are solved, and the low-carbon optimization and reasonable resource allocation of the system are realized.
Patent Information
- Application Number
- CN202510110126.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-23
- Publication Date
- 2025-04-29
- Estimated Expiration
- 2045-01-23
AI Technical Summary
In actual operation of the integrated energy system, there are problems of insufficient coordination and complex information exchange, which affects the overall efficiency of the system and the realization of low-carbon goals.
The low-carbon operation method based on the ADMM method is adopted, and the low-carbon optimization operation model of the comprehensive energy system based on the actual carbon emissions of the system is converted into carbon emission minimization and load balance minimization problems, and the solution is made through the alternating direction multiplier method.
The operation strategy of the integrated electricity-hydrogen energy system has been optimized, the overall carbon emissions of the system have been reduced, and the inefficiency problem of resource allocation has been effectively solved, improving the low-carbon and sustainability of the system.
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Figure CN119903672A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of optimized operation of integrated energy systems, and in particular to a low-carbon operation method of an electric-hydrogen integrated energy system based on an ADMM method. Background Art
[0002] As global attention to environmental protection and sustainable development continues to increase, the optimization of low-carbon energy systems has become an important research direction in the energy field. Traditional energy systems mainly rely on fossil energy such as coal, oil and natural gas, which play an important role in electricity production and heating. However, the excessive use of fossil energy has not only brought serious environmental pollution problems, but also led to waste of energy resources and low operational efficiency. In order to meet these challenges, modern energy systems have gradually turned to integrating multiple energy forms such as renewable energy, gas-fired thermal power plants, and electric hydrogen production systems to achieve greener and more efficient energy management.
[0003] In the face of increasingly severe climate challenges, the integrated energy system, as a cutting-edge energy management model, achieves energy coordination and optimal configuration by integrating multiple energy forms such as electricity, thermal energy, and hydrogen energy. This system not only helps to improve energy utilization efficiency, but also reduces overall carbon emissions through the complementarity and cascade utilization of multiple energy forms. Despite this, the integrated energy system still faces problems such as insufficient coordination and complex information exchange in actual operation, which affect the overall efficiency of the system and the realization of low-carbon goals. Therefore, in order to promote the efficient and coordinated operation of the integrated energy system, it is necessary to fully consider the interests and operating goals of various entities in the system while achieving low-carbon goals, so as to optimize the system energy trading and cooperation mechanism. Summary of the invention
[0004] In order to overcome the deficiencies in the above-mentioned prior art, the present invention provides a low-carbon operation method for an electric-hydrogen integrated energy system based on the ADMM method, in order to optimize the operation strategy of the electric-hydrogen integrated energy system to reduce the overall carbon emissions of the system, and effectively solve the inefficiency of resource allocation within the electric-hydrogen integrated energy system.
[0005] In order to achieve the above object, the technical solution adopted by the present invention is:
[0006] The present invention provides a low-carbon operation method of an electric-hydrogen integrated energy system based on the ADMM method. The electric-hydrogen integrated energy system is composed of renewable energy, an electric hydrogen production system, a gas thermal power plant and a storage battery. The low-carbon operation method comprises the following steps:
[0007] Step 1: Consider the actual carbon emissions of the electricity-hydrogen integrated energy system;
[0008] Step 1.1: Use formula (1) to obtain the actual carbon emissions of each device in the gas thermal power plant:
[0009] (1)
[0010] In formula (1): It is the carbon emission of the combined heat and power unit during CHP operation; is the carbon emissions of the gas turbine GT during operation; is the carbon emission of the gas boiler GB during operation; It is expressed as the amount of natural gas required for the operation of the cogeneration unit at time t; It is expressed as the amount of natural gas required for gas turbine operation at time t; It is expressed as the amount of natural gas required for the operation of the gas boiler at time t; is the carbon emission factor of natural gas g, T represents the total duration;
[0011] Using formula (2), we can get the total amount of natural gas required for the operation of the gas-fired thermal power plant at time t: :
[0012] (2)
[0013] Step 1.2: Use formula (3) to obtain carbon dioxide from the electricity-hydrogen integrated energy system Actual emissions ;
[0014] (3)
[0015] Step 2: Establish a low-carbon optimization operation model for the integrated energy system based on the actual carbon emissions of the system;
[0016] Step 2.1: Use formula (4) to establish the objective function J of the optimization operation model of the electricity-hydrogen integrated energy system:
[0017] (4)
[0018] In formula (4), and There are two weighting coefficients used to balance the weight between carbon emissions and energy demand; and are the actual supply and demand of the j-th load at time t respectively; Indicates the error of load balance; j is the type of load, including: electricity e, heat h, hydrogen H2;
[0019] Step 2.2, establish the constraints of the optimal operation model of the electricity-hydrogen integrated energy system;
[0020] Step 3: Solve the low-carbon optimization model of the electricity-hydrogen integrated energy system based on the ADMM method to obtain the minimum carbon emissions of the system at time t , the optimal output of renewable energy at time t , the optimal power output of the gas thermal power plant at time t and the optimal heat output of the gas-fired thermal power plant at time t .
[0021] The low-carbon operation method of the electric-hydrogen integrated energy system based on the ADMM method described in the present invention is also characterized in that the step 2.2 comprises:
[0022] Step 2.2.1: Use formula (5) to construct the power supply and demand balance constraint:
[0023] (5)
[0024] In formula (5): represents the total power generation of renewable energy at time t; represents the total power generation of the gas-fired thermal power plant at time t; It represents the demand of electric load at time t; It represents the electric energy required by the hydrogen production system at time t; represents the discharge power of the battery at time t; represents the charging power of the battery at time t;
[0025] Step 2.2.2: Use equation (6) to construct the heat energy supply and demand balance constraint:
[0026] (6)
[0027] In formula (6): It represents the total amount of heat energy produced by the gas thermal power plant at time t; It represents the demand of heat load at time t;
[0028] Step 2.2.3: Use formula (7) to construct the hydrogen energy supply and demand balance constraint:
[0029] (7)
[0030] In formula (7): It represents the amount of hydrogen produced by the electric hydrogen production system at time t; Indicates the demand for hydrogen load at time t;
[0031] Step 2.2.4: Use formula (7) to construct the equipment power generation and heating power constraints:
[0032] (8)
[0033] In formula (7): , and They are the power generation, minimum power generation and maximum power generation of renewable energy at time t respectively; , and They are the power generation, minimum power generation and maximum power generation of the gas thermal power plant at time t respectively; , and are the heat production power, minimum heat production power and maximum heat production power of the gas thermal power plant at time t respectively; and They are the hydrogen production capacity and maximum hydrogen production capacity of the electric hydrogen production system at time t respectively.
[0034] Furthermore, the step 3 comprises:
[0035] Step 3.1: Use formula (11) to construct an optimization model that considers the carbon emission part:
[0036] (11)
[0037] In formula (11), W1 represents the objective function of the optimization model considering the carbon emission part; Indicates the amount of natural gas required for the operation of equipment X at time t, the type of equipment X, including: CHP, GT, GB; Auxiliary variables representing device X at time t;
[0038] Step 3.2: Use formula (12) to construct an optimization model that considers the load balancing part:
[0039] (12)
[0040] In formula (12), W2 represents the objective function of constructing the optimization model considering the load balancing part, Auxiliary variable representing the j-th load at time t;
[0041] Step 3.3: Use the ADMM method to solve the optimization model considering the carbon emission part and the optimization model considering the load balance part.
[0042] Further, the step 3.3 includes:
[0043] Step 3.3.1: Use formula (13) to construct the augmented Lagrangian function considering the carbon emission part :
[0044] (13)
[0045] In formula (13), is the penalty coefficient of the augmented Lagrangian function; is the Lagrange multiplier of device X;
[0046] Step 3.3.2: Use equation (13) to construct the augmented Lagrangian function considering the load balancing part :
[0047] (14)
[0048] In formula (14): is the Lagrange multiplier of the j-th load;
[0049] Step 3.3.3, define the current number of iterations as k, and initialize k=0, define the maximum number of iterations as ; Define two penalty factors as , ; Initialize the two Lagrange multipliers for the kth iteration , ; Initialize two auxiliary variables at time t for the kth iteration , ;
[0050] Step 3.3.4: Update according to equation (14) and equation (15) respectively , , thus obtaining the two auxiliary variables at time t for the k+1th iteration , :
[0051] (15)
[0052] (16)
[0053] Step 3.3.5: Update according to equation (16) and equation (17) respectively , , thus obtaining the two Lagrange multipliers of the k+1th iteration , :
[0054] (17)
[0055] (18)
[0056] Step 3.3.6: Determine whether equation (19) is true. If true, stop the iteration and output the minimum carbon emission of the system at time t. , the optimal output of renewable energy , optimal power output of gas-fired thermal power plants and optimal heat output from gas-fired thermal power plants Otherwise, assign k+1 to k and return to step 3.3.4 to execute sequentially until the maximum number of iterations is reached. until;
[0057] (19)
[0058] In formula (19), means and; is the preset threshold.
[0059] The electronic device of the present invention includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the low-carbon operation method, and the processor is configured to execute the program stored in the memory.
[0060] The present invention provides a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and the computer program executes the steps of the low-carbon operation method when executed by a processor.
[0061] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0062] 1 Aiming at the low-carbon optimization problem of the park integrated energy system, the present invention proposes a cooperative operation model of the electric-hydrogen integrated energy system considering carbon emissions to promote collaboration among different entities and improve the low-carbon nature of the system.
[0063] 2 The present invention aims at the low-carbon operation model of the electricity-hydrogen integrated energy system and proposes to convert it into the problem of carbon emission minimization and load balance minimization. By realizing the reasonable allocation of energy resources, the resource scheduling of the system is optimized and the environmental protection of the system is improved.
[0064] 3. The present invention aims at solving the optimization problem in the integrated energy system, and adopts the alternating direction multiplier method to perform distributed solution to the carbon emission minimization problem and the load balance minimization problem. Through a transparent and fair negotiation mechanism, the coordinated operation of the integrated energy system is effectively promoted. BRIEF DESCRIPTION OF THE DRAWINGS
[0065] Figure 1 It is a schematic diagram of the process of the low-carbon operation method of the present invention. DETAILED DESCRIPTION
[0066] In this embodiment, a low-carbon operation method of an electric-hydrogen integrated energy system based on the ADMM method is to establish a low-carbon optimization model of the electric-hydrogen integrated energy system by considering the actual carbon emissions of the system, and convert it into a carbon emission minimization problem and a load balance minimization problem to optimize the resource scheduling of the system and achieve a reasonable allocation of energy resources. In addition, in order to protect the privacy of the system, the alternating direction multiplier method is used to achieve an efficient solution to the cooperative operation problem of the electric-hydrogen integrated energy system, thereby optimizing the operation strategies of each subject to improve the low-carbon nature of the system. Specifically, if Figure 1 As shown, the steps are as follows:
[0067] Step 1: Consider the actual carbon emissions of the electricity-hydrogen integrated energy system;
[0068] In the integrated energy system consisting of renewable energy, electric hydrogen production system, gas-fired thermal power plant and batteries, wind power and photovoltaic power generation do not cause carbon emissions; the carbon emissions generated by gas-fired thermal power plants are related to the amount of natural gas they burn; in the process of electric hydrogen production, electricity comes from renewable energy and gas-fired thermal power plants. Since the carbon emissions of natural gas combustion in gas-fired thermal power plants have been calculated, the carbon emissions in electric hydrogen production will not be calculated again here. Therefore, in the integrated energy system, carbon emissions are only generated by gas-fired thermal power plants.
[0069] Step 1.1: Use formula (1) to obtain the actual carbon emissions of each device in the gas thermal power plant:
[0070] (1)
[0071] In formula (1): It is the carbon emission of the combined heat and power unit during CHP operation; is the carbon emissions of the gas turbine GT during operation; is the carbon emission of the gas boiler GB during operation; It is expressed as the amount of natural gas required for the operation of the cogeneration unit at time t; It is expressed as the amount of natural gas required for gas turbine operation at time t; It is expressed as the amount of natural gas required for the operation of the gas boiler at time t; is the carbon emission factor of natural gas g, and T represents the total time.
[0072] Using formula (2), we can get the total amount of natural gas required for the operation of the gas-fired thermal power plant at time t: :
[0073] (2)
[0074] Step 1.2: Use formula (3) to obtain carbon dioxide from the electricity-hydrogen integrated energy system Actual emissions ;
[0075] (3).
[0076] Step 2: Establish a low-carbon optimization operation model for the integrated energy system based on the actual carbon emissions of the system;
[0077] Step 2.1: Use formula (4) to establish the objective function J of the optimization operation model of the electricity-hydrogen integrated energy system:
[0078] (4)
[0079] In formula (4), and There are two weighting coefficients used to balance the weight between carbon emissions and energy demand; and are the actual supply and demand of the j-th load at time t respectively; Indicates the error of load balance; j is the type of load, including: electricity e, heat h, hydrogen H2.
[0080] Step 2.2: Establish the constraints of the optimal operation model of the electricity-hydrogen integrated energy system
[0081] Step 2.2.1: Use formula (5) to construct the power supply and demand balance constraint:
[0082] (5)
[0083] In formula (5): represents the total power generation of renewable energy at time t; represents the total power generation of the gas-fired thermal power plant at time t; It represents the demand of electric load at time t; It represents the electric energy required by the hydrogen production system at time t; represents the discharge power of the battery at time t; Represents the charging power of the battery at time t.
[0084] Step 2.2.2: Use equation (6) to construct the heat energy supply and demand balance constraint:
[0085] (6)
[0086] In formula (6): It represents the total amount of heat energy produced by the gas thermal power plant at time t; Represents the heat load demand at time t.
[0087] Step 2.2.3: Use formula (7) to construct the hydrogen energy supply and demand balance constraint:
[0088] (7)
[0089] In formula (7): It represents the amount of hydrogen produced by the electric hydrogen production system at time t; Represents the hydrogen load demand at time t.
[0090] Step 2.2.4: Use formula (7) to construct the equipment power generation and heating power constraints:
[0091] (8)
[0092] In formula (7): , and They are the power generation, minimum power generation and maximum power generation of renewable energy at time t respectively; , and They are the power generation, minimum power generation and maximum power generation of the gas thermal power plant at time t respectively; , and are the heat production power, minimum heat production power and maximum heat production power of the gas thermal power plant at time t respectively; and They are the hydrogen production capacity and maximum hydrogen production capacity of the electric hydrogen production system at time t respectively.
[0093] Step 3: Solve the low-carbon optimization model of the electricity-hydrogen integrated energy system based on the ADMM method to obtain the minimum carbon emissions of the system at time t , the optimal output of renewable energy at time t , the optimal power output of the gas thermal power plant at time t and the optimal heat output of the gas-fired thermal power plant at time t ;
[0094] The equipment carbon emissions and load scheduling are introduced into auxiliary variables to deal with the carbon emission part and the load balance part respectively. At the same time, the carbon emission minimization and load balance minimization optimization models are constructed.
[0095] Step 3.1: Use formula (11) to construct an optimization model that considers the carbon emission part:
[0096] (11)
[0097] In formula (11), W1 represents the objective function of the optimization model considering the carbon emission part; Indicates the amount of natural gas required for the operation of equipment X at time t, the type of equipment X, including: CHP, GT, GB; Auxiliary variables representing device X at time t.
[0098] Step 3.2: Use formula (12) to construct an optimization model that considers the load balancing part:
[0099] (12)
[0100] In formula (12), W2 represents the objective function of constructing the optimization model considering the load balancing part, Auxiliary variable representing the j-th load at time t.
[0101] Step 3.3, using ADMM method to solve the optimization model considering the carbon emission part and the optimization model considering the load balance part;
[0102] Step 3.3.1: Use formula (13) to construct the augmented Lagrangian function considering the carbon emission part :
[0103] (13)
[0104] In formula (13), is the penalty coefficient of the augmented Lagrangian function; is the Lagrange multiplier of device X;
[0105] Step 3.3.2: Use equation (13) to construct the augmented Lagrangian function considering the load balancing part :
[0106] (14)
[0107] In formula (14): is the Lagrange multiplier of the j-th load;
[0108] Step 3.3.3, define the current number of iterations as k, and initialize k=0, define the maximum number of iterations as ; Define two penalty factors as , ; Initialize the two Lagrange multipliers for the kth iteration , ; Initialize two auxiliary variables at time t for the kth iteration , .
[0109] Step 3.3.4: Update according to equation (14) and equation (15) respectively , , thus obtaining the two auxiliary variables at time t for the k+1th iteration , :
[0110] (15)
[0111] (16)
[0112] Step 3.3.5: Update according to equation (16) and equation (17) respectively , , thus obtaining the two Lagrange multipliers of the k+1th iteration , :
[0113] (17)
[0114] (18)
[0115] Step 3.3.6: Determine whether equation (19) is true. If true, stop the iteration and output the minimum carbon emission of the system at time t. , the optimal output of renewable energy , optimal power output of gas-fired thermal power plants and optimal heat output from gas-fired thermal power plants Otherwise, k+1 is assigned to k, which means the value of the kth iteration is updated and the auxiliary variable obtained in the k+1th iteration is assigned , , return to step 3.3.4 and execute sequentially until the maximum number of iterations is reached until;
[0116] (19)
[0117] In formula (19), means and; is the preset threshold.
[0118] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.
[0119] In this embodiment, a computer-readable storage medium stores a computer program on the computer-readable storage medium, and the computer program executes the steps of the above method when executed by a processor.
[0120] In summary, by considering the carbon emissions of IES, the present invention can not only improve the low-carbon nature of the system, but also promote the utilization of renewable energy in the system and efficient collaboration with the system, thereby improving the sustainability of the integrated energy system; subsequently, in view of the optimal operation problem of the integrated energy system in the park, an optimal operation model of the electric-hydrogen integrated energy system is proposed, and it is converted into the problem of minimizing carbon emissions and minimizing load balance. At the same time, the solution based on the alternating direction multiplier method has good stability, and the low-carbon optimized operation of the system is achieved while protecting the privacy information of the system.
Claims
1. A low-carbon operation method of an electric-hydrogen integrated energy system based on the ADMM method, wherein the electric-hydrogen integrated energy system is composed of renewable energy, an electric hydrogen production system, a gas-fired thermal power plant and a battery, characterized in that: The low-carbon operation method comprises the following steps: Step 1: Consider the actual carbon emissions of the electricity-hydrogen integrated energy system; Step 1.1: Use formula (1) to obtain the actual carbon emissions of each device in the gas thermal power plant: (1) In formula (1): It is the carbon emission of the combined heat and power unit during CHP operation; is the carbon emissions of the gas turbine GT during operation; is the carbon emission of the gas boiler GB during operation; It is expressed as the amount of natural gas required for the operation of the cogeneration unit at time t; It is expressed as the amount of natural gas required for gas turbine operation at time t; It is expressed as the amount of natural gas required for the operation of the gas boiler at time t; is the carbon emission factor of natural gas g, T represents the total duration; Using formula (2), we can get the total amount of natural gas required for the operation of the gas-fired thermal power plant at time t: : (2) Step 1.2: Use formula (3) to obtain carbon dioxide from the electricity-hydrogen integrated energy system Actual emissions ; (3) Step 2: Establish a low-carbon optimization operation model for the integrated energy system based on the actual carbon emissions of the system; Step 2.1: Use formula (4) to establish the objective function J of the optimization operation model of the electricity-hydrogen integrated energy system: (4) In formula (4), and There are two weighting coefficients used to balance the weight between carbon emissions and energy demand; and are the actual supply and demand of the j-th load at time t respectively; Indicates the error of load balance; j is the type of load, including: electricity e, heat h, hydrogen H2; Step 2.2, establish the constraints of the optimal operation model of the electricity-hydrogen integrated energy system; Step 3: Solve the low-carbon optimization model of the electricity-hydrogen integrated energy system based on the ADMM method to obtain the minimum carbon emissions of the system at time t , the optimal output of renewable energy at time t , the optimal power output of the gas thermal power plant at time t and the optimal heat output of the gas-fired thermal power plant at time t .
2. According to claim 1, a low-carbon operation method of an electric-hydrogen integrated energy system based on the ADMM method is characterized in that: The step 2.2 comprises: Step 2.2.1: Use formula (5) to construct the power supply and demand balance constraint: (5) In formula (5): represents the total power generation of renewable energy at time t; represents the total power generation of the gas-fired thermal power plant at time t; It represents the demand of electric load at time t; It represents the electric energy required by the hydrogen production system at time t; represents the discharge power of the battery at time t; represents the charging power of the battery at time t; Step 2.2.2: Use equation (6) to construct the heat energy supply and demand balance constraint: (6) In formula (6): It represents the total amount of heat energy produced by the gas thermal power plant at time t; It represents the demand of heat load at time t; Step 2.2.3: Use formula (7) to construct the hydrogen energy supply and demand balance constraint: (7) In formula (7): It represents the amount of hydrogen produced by the electric hydrogen production system at time t; Indicates the demand for hydrogen load at time t; Step 2.2.4: Use formula (7) to construct the equipment power generation and heating power constraints: (8) In formula (7): , and They are the power generation, minimum power generation and maximum power generation of renewable energy at time t respectively; , and They are the power generation, minimum power generation and maximum power generation of the gas thermal power plant at time t respectively; , and are the heat production power, minimum heat production power and maximum heat production power of the gas thermal power plant at time t respectively; and They are the hydrogen production capacity and maximum hydrogen production capacity of the electric hydrogen production system at time t respectively.
3. A low-carbon operation method of an electric-hydrogen integrated energy system based on the ADMM method according to claim 2, characterized in that: The step 3 comprises: Step 3.1: Use formula (11) to construct an optimization model that considers the carbon emission part: (11) In formula (11), W1 represents the objective function of the optimization model considering the carbon emission part; Indicates the amount of natural gas required for the operation of equipment X at time t, the type of equipment X, including: CHP, GT, GB; Auxiliary variables representing device X at time t; Step 3.2: Use formula (12) to construct an optimization model that considers the load balancing part: (12) In formula (12), W2 represents the objective function of constructing the optimization model considering the load balancing part, Auxiliary variable representing the j-th load at time t; Step 3.3: Use the ADMM method to solve the optimization model considering the carbon emission part and the optimization model considering the load balance part.
4. A low-carbon operation method for an electric-hydrogen integrated energy system based on the ADMM method according to claim 3, characterized in that: The step 3.3 comprises: Step 3.3.1: Use formula (13) to construct the augmented Lagrangian function considering the carbon emission part : (13) In formula (13), is the penalty coefficient of the augmented Lagrangian function; is the Lagrange multiplier of device X; Step 3.3.2: Use equation (13) to construct the augmented Lagrangian function considering the load balancing part : (14) In formula (14): is the Lagrange multiplier of the j-th load; Step 3.3.3, define the current number of iterations as k, and initialize k=0, define the maximum number of iterations as ; Define two penalty factors as , ; Initialize the two Lagrange multipliers for the kth iteration , ; Initialize two auxiliary variables at time t for the kth iteration , ; Step 3.3.4: Update according to equation (14) and equation (15) respectively , , thus obtaining the two auxiliary variables at time t for the k+1th iteration , : (15) (16) Step 3.3.5: Update according to equation (16) and equation (17) respectively , , thus obtaining the two Lagrange multipliers of the k+1th iteration , : (17) (18) Step 3.3.6: Determine whether equation (19) is true. If true, stop the iteration and output the minimum carbon emission of the system at time t. , the optimal output of renewable energy , optimal power output of gas-fired thermal power plants and optimal heat output from gas-fired thermal power plants Otherwise, assign k+1 to k and return to step 3.3.4 to execute sequentially until the maximum number of iterations is reached. until; (19) In formula (19), means and; is the preset threshold.
5. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports a processor to execute the low-carbon operation method according to any one of claims 1 to 4, and the processor is configured to execute the program stored in the memory.
6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the low-carbon operation method according to any one of claims 1 to 4 are executed.
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