A method for optimizing operation and control of integrated energy system considering carbon emission cost

By constructing a system computation model that includes an objective function and constraints on carbon emission costs, and using particle swarm optimization to optimize equipment output, the problem of combining economic efficiency and low-carbon operation in existing technologies has been solved. This has enabled the economic efficiency and low-carbon operation of integrated energy systems, and improved the absorption of renewable energy and demand-side response.

CN116131252BActive Publication Date: 2026-11-06JIANGSU INST OF URBAN PLANNING & DESIGN
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Patent Information

Application Number
CN202211596876.8
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-12-12
Publication Date
2026-11-06
Estimated Expiration
2042-12-12

AI Technical Summary

Technical Problem

Existing integrated energy system optimization and operation control methods fail to effectively combine economic efficiency and low-carbon operation, fail to fully consider the absorption of renewable energy and demand-side impacts, and have shortcomings in carbon emission control.

Method used

By constructing a system computational model that includes an objective function and constraints on carbon emission costs, and using particle swarm optimization to optimize equipment output, combined with wind and solar curtailment penalties and demand response compensation costs, the system's economic efficiency and low-carbon operation are ensured to meet regional carbon emission requirements.

Benefits of technology

This has enabled the improvement of renewable energy consumption and demand-side response while ensuring economic operation, meeting regional carbon emission targets, and optimizing the operation of the integrated energy system.

✦ Generated by Eureka AI based on patent content.

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Abstract

The application discloses a kind of carbon emission cost comprehensive energy system optimization operation control method, including the following steps, S1, the basic data of the comprehensive energy system needing optimization operation is collected;S2, the objective function of the optimization operation of comprehensive energy system is established, with the minimum system operation cost as target, the influence of operation maintenance, energy interaction, abandoned wind and light, carbon emission, demand response and other factors on system operation cost is included therein, and energy balance, demand response, equipment operation, carbon emission and other factors are used as constraint condition;S3, the output of each device in system at t time is calculated by particle swarm algorithm, and the preliminary control scheme is obtained;S4, according to the demand adjustment parameter until the control scheme that output meets own demand target is provided.The application can provide decision reference for the operation control of comprehensive energy system, and can optimize the carbon emission of system while ensuring the economy of comprehensive energy system operation.
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Description

Technical Field

[0001] This invention relates to integrated energy systems in power systems, and more particularly to an optimized operation and control method for integrated energy systems that takes into account carbon emission costs. Background Technology

[0002] The energy sector is a major source of carbon emissions and possesses enormous potential for carbon reduction, making it a key force in promoting energy conservation and emission reduction. Integrating various energy sources within a region into a comprehensive energy system that combines the production, conversion, storage, and consumption of multiple energy sources can effectively achieve multi-energy synergy and complementarity through energy coupling, thereby improving energy efficiency and representing a crucial pathway for energy transformation.

[0003] The optimized operation of integrated energy systems is crucial for achieving complementary advantages and coordinated operation of various heterogeneous energy sources, and thus holds significant research importance. Economic efficiency is the foundation for the system's sustainable operation and a primary factor that must be considered during optimization. Simultaneously, the system's carbon emissions also affect its vitality. Therefore, incorporating carbon emissions and other factors into the consideration of economic operation is a developing trend in the optimized operation and control of integrated energy systems. Existing methods for optimizing the operation and control of integrated energy systems primarily focus on economic efficiency, aiming for minimum cost or maximum profit. They introduce carbon trading mechanisms based on conventional operating costs, converting carbon emissions into economic value to guide carbon reduction in integrated energy systems. However, they fail to consider that carbon emission control has gradually become a task indicator broken down into various sectors and regions, exhibiting a semi-mandatory nature. Furthermore, they do not simultaneously consider the impact of demand on integrated energy systems. Different regions, during the energy transition period, prioritize different energy supply methods (centralized or distributed energy supply, degree of energy interaction with external systems, etc.) to incentivize and penalize carbon emission reductions, and consider other factors such as the absorption of renewable energy sources like wind and solar power. These methods lack in terms of enforceability, flexibility, locality, and cleanliness. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a comprehensive energy system optimization that takes into account carbon emission costs while ensuring the economical operation of the system and achieving low-carbon operation of the system.

[0005] Technical solution: The integrated energy system optimization operation control method of the present invention includes the following steps:

[0006] S1 collects parameters of the integrated energy system to be optimized, conventional operating cost parameters, carbon emission cost parameters, and other adjustable parameters;

[0007] S2 aims to minimize the operating cost of an integrated energy system. It incorporates the impacts of operation and maintenance, energy interaction, wind and solar curtailment, carbon emissions, and demand response on the system's operating cost to construct a system calculation model. The system calculation model includes an objective function and constraints, among which the constraints include energy balance, demand response, equipment operation, and carbon emissions.

[0008] S3. Substitute the data collected in step S1 into the system calculation model constructed in step S2, and use the particle swarm optimization algorithm to calculate the output of each device in the integrated energy system at time t to obtain a preliminary operation control scheme.

[0009] S4. The preliminary operation control scheme obtained in step S3 is evaluated. Based on the equipment output, the system carbon emissions, wind and solar curtailment rate, and demand response are calculated to determine whether the control scheme meets the expected effect.

[0010] If the expected results are achieved, the operation control scheme is saved and the optimization results are output.

[0011] If the expected effect period is not met, adjust the adjustable parameters and return to step S1 until the optimization expectation is met.

[0012] Furthermore, in step S1, the parameters of the integrated energy system to be optimized include equipment configuration, load forecast, and maximum wind and solar power output forecast; the conventional operating cost parameters include the operation and maintenance costs of various equipment, energy purchase price, and load reduction compensation; the carbon emission cost parameters include carbon tax, carbon emissions of various energy supply methods, and carbon quotas; and the other adjustable parameters include wind and solar curtailment penalties, various cost weighting coefficients, and energy interaction incentive coefficients.

[0013] Furthermore, in step S2, the objective function expression is constructed as follows:

[0014]

[0015] In the formula:

[0016] ∑(U J,on ∑ i∈J P i,t ) represents the operation and maintenance costs of energy equipment; U J,on The maintenance cost per unit power output for Class J equipment, P i,t Let i be the output power of device i at time t;

[0017] c e P EG,t +c g (V GT,t +V GB,t +V GL,t The energy interaction cost of supplying energy to an integrated energy system; e c gFor electricity and gas purchase prices, P EG,t Let V be the power exchanged between the power grids at time t. GT,t V GB,t V GL,t Let t represent the gas consumption of the gas turbine, the gas consumption of the gas boiler, and the gas load.

[0018] For wind and solar power curtailment penalties; F WT F PV The penalty coefficient for wind and solar power curtailment. Let P be the maximum power output of wind power and photovoltaic power generation at time t. WT,t P PV,t Let t be the actual output power of wind power generation and photovoltaic power generation at time t;

[0019] c tax [∑U j,run,c (∑ i∈J P i,t )+αU EG,C P EG +βU GG,C (V GT +V GB +V GL [ ] represents the carbon emission cost (carbon tax) of the system; c tax For carbon tax, U J,run,C For Class J equipment, the carbon emissions per unit power output, U EG,C U GG,C Carbon emissions from purchased electricity and gas; α and β are the energy interaction excitation coefficients for electricity and gas; P EG For grid interaction power, V GT V GB V GL This includes gas turbine gas consumption, gas boiler gas consumption, and gas load.

[0020] c com P DR,t The cost of compensating for incentive-based demand response; c com To reduce the compensation cost per unit of electricity load, P DR,t Let t be the reduction value of the flexible load due to the incentive-driven demand response;

[0021] a i Let a1 be the weighting coefficient for each type of cost, where i = 1, 2, 3, 4, 5, and a1 + a2 + a3 + a4 + a5 = 1.

[0022] Furthermore, in step S2, the constructed constraints include energy balance constraints, demand response constraints, equipment operation constraints, and carbon emission constraints, where energy includes electrical energy, thermal energy, and cold energy; the constraints are as follows:

[0023] Power balance constraints:

[0024]

[0025] in, P DR,t P EG,t P WT,t P PV,t P GT,t P HP,t P EB,t P EC,t These represent the electrical load at time t, the load reduction due to incentive-driven demand response, the grid interaction power, the wind power output, the photovoltaic power output, the gas turbine power output, the heat pump power output, the electric power consumed by the electric boiler, and the electric power consumed by the electric chiller; P ES,t The energy storage capacity is μ, where + represents storage and - represents release. HP The heat pump's electro-thermal efficiency;

[0026] Thermal energy balance constraints:

[0027]

[0028] in, P EB,t P GB,t P HB,t P HP,t Let P be the heat load at time t, the output power of the electric boiler, the output power of the gas boiler, the output power of the waste heat boiler, and the output heat power of the heat pump. HS,t Let be the thermal energy storage power at time t, where + represents storage and - represents release;

[0029] Cold energy balance constraint:

[0030]

[0031] in, P AC,t P EC,t , where is the cooling load at time t, the output power of the electric chiller, and the output power of the absorption chiller; P CS,t Let be the cold energy storage power at time t, where + represents storage and - represents release;

[0032] Demand response constraints:

[0033] 0≤P DR,t ≤R DR,con

[0034] Among them, P DR,t For demand response at time t, reduce load, P DR,con Flexible loads for signing demand response contracts;

[0035] Equipment operation constraints mainly include the coupling constraints of combined cooling, heating and power units, the output constraints of each piece of equipment, and the state constraints of energy storage equipment;

[0036] Coupling constraints of combined cooling, heating and power units:

[0037] Q HB,t +Q AC,t ≤Q GT,t

[0038] Among them, Q HB,t Q AC,t Q GT,t These represent the heat power consumed by the waste heat boiler, the power consumed by the absorption chiller, and the waste heat output power of the gas turbine at time t, respectively.

[0039] Output constraints for each device:

[0040]

[0041] Among them, P i,t This represents the output power of device i at time t. Indicates the upper and lower limits of the output power of device i;

[0042] State constraints of energy storage devices:

[0043]

[0044]

[0045]

[0046]

[0047] in, P represents the initial values ​​of electrical, thermal, and cold energy storage at time t; ES,t P HS,t P CS,t Let t represent the electrical, thermal, and cold energy storage power at time t, where + indicates storage and - indicates release; Energy storage capacity for electricity, heat, and cold;

[0048] Carbon emission constraints:

[0049] Δt[∑U J,run,C (∑ i∈J P i,t )+αU EG,C P EG +βU GG,C (V GT +V GB +V GL )]≤θq C,Δt

[0050] Where, q C,△t Let θ represent the carbon allowance allocated to the region where the energy system is located during the time period Δt, and let θ represent the proportion of carbon emissions from the energy sector.

[0051] Furthermore, the equipment power corresponding items included in the energy balance constraint are added or removed according to the equipment contained in the actual integrated energy system.

[0052] Furthermore, in step S4, the adjustable parameters include various cost weighting coefficients a. i Wind curtailment penalty coefficient F WT Discard penalty coefficient F PV , where i = 1, 2, 3, 4, 5.

[0053] Compared with the prior art, the significant advantages of this invention are as follows:

[0054] 1. This invention incorporates carbon emissions into the system operating cost in the form of cost in the objective function, guiding the system to operate in a way that is both economical and low-carbon; it also introduces wind and solar curtailment penalties into the objective function, further considering the issue of renewable energy consumption while ensuring the orderly operation of the system.

[0055] 2. The compensation cost of incentive-driven demand response is included in the objective function, and the impact of the demand side on the system is further considered in addition to the energy supply side; while the objective function guides the system to reduce carbon emissions, carbon emission constraints are used in the constraints to ensure that the system meets the carbon emission requirements proposed by the region during operation. Attached Figure Description

[0056] Figure 1 This is a flowchart of the method of the present invention;

[0057] Figure 2 This is a system topology diagram of the present invention. Detailed Implementation

[0058] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0059] like Figure 1 The diagram shown is a flowchart of the integrated energy system optimized operation control method of the present invention. Figure 2 The diagram shows the topology of the integrated energy system.

[0060] The integrated energy system optimization operation control method of the present invention includes the following steps:

[0061] Step 1: Collect and optimize basic system data

[0062] The basic data to be collected includes parameters of the integrated energy system to be optimized, conventional operating cost parameters, carbon emission cost parameters, and other adjustable parameters. The parameters of the integrated energy system to be optimized include equipment configuration, load forecasting, and maximum wind and solar power output forecasting; conventional operating cost parameters include maintenance costs of various equipment, energy purchase prices, and load reduction compensation; carbon emission cost parameters include carbon tax, carbon emissions from various energy supply methods, and carbon quotas; other adjustable parameters include penalties for wind and solar curtailment, various cost weighting coefficients, and energy interaction incentive coefficients.

[0063] Step 2: With the goal of minimizing the operating cost of the integrated energy system, construct a system calculation model, which includes the objective function and constraints.

[0064] The constructed objective function is

[0065]

[0066] In the formula:

[0067] ∑(U J,on ∑ i∈J P i,t ) represents the operation and maintenance costs of energy equipment; U J,on The maintenance cost per unit power output for Class J equipment, P i,t Let i be the output power of device i at time t;

[0068] c e P EG,t +c g (V GT,t +V GB,t +V GL,t The energy interaction cost of supplying energy to an integrated energy system; e c g For electricity and gas purchase prices, P EG,t Let V be the power exchanged between the power grids at time t. GT,t V GB,t V GL,t Let t represent the gas consumption of the gas turbine, the gas consumption of the gas boiler, and the gas load.

[0069] For wind and solar power curtailment penalties; F WT F PV The penalty coefficient for wind and solar curtailment (generally higher than other unit costs to promote the consumption of new energy sources; the coefficient can be adjusted according to the region's requirements for the degree of new energy consumption and the trend of encouraging new energy types, and the penalty coefficient for different new energy sources can be distinguished, prioritizing the consumption of new energy sources and specifying the type). Let P be the maximum power output of wind power and photovoltaic power generation at time t. WT,t P PV,tLet t be the actual output power of wind power generation and photovoltaic power generation at time t;

[0070] c tax [∑U J,run,c (∑ i∈j P i,t )+αU EG,C P EG +βU GG,C (V GT +V GB +V GL [ ] represents the carbon emission cost (carbon tax) of the system; c tax For carbon tax, U J,run,C For Class J equipment, the carbon emissions per unit power output, U EG,C U GG,C Carbon emissions from purchased electricity and gas; α and β are the energy interaction excitation coefficients for electricity and gas; P EG For grid interaction power, V GT V GB V GL This includes gas turbine gas consumption, gas boiler gas consumption, and gas load.

[0071] c com P DR,t The cost of compensating for incentive-based demand response; c com To reduce the compensation cost per unit of electricity load (as determined by the established load reduction contract), P DR,t Let t be the reduction value of the flexible load due to the incentive-driven demand response;

[0072] a i (i = 1, 2, 3, 4, 5) are the weighting coefficients for each type of cost, and a1 + a2 + a3 + a4 + a5 = 1.

[0073] The constraints established include energy balance constraints (electricity, heat, and cold), demand response constraints, equipment operation constraints, and carbon emission constraints.

[0074] Power balance constraints:

[0075]

[0076] in, P DR,t P EG,t P WT,t P PV,t P GT,t P HP,t P EB,t P EC,t P ES,tThese represent the electrical load at time t, the load reduction due to incentive-driven demand response, the grid interaction power, the output power of wind power, the output power of photovoltaic power, the output electrical power of gas turbines, the output thermal power of heat pumps, the electrical power consumed by electric boilers, the electrical power consumed by electric chillers, and the power of electric energy storage (+ for storage, - for release), μ. HP This refers to the heat pump's electro-thermal conversion efficiency.

[0077] Thermal energy balance constraints:

[0078]

[0079] in, P EB,t P GB,t P HB,t P HP,t P HS,t Let t represent the heat load, electric boiler output power, gas boiler output power, waste heat boiler output power, heat pump output heat power, and thermal energy storage power (+ for storage, - for release).

[0080] Cold energy balance constraint:

[0081]

[0082] in, P AC,t P EC,t P CS,t Let t represent the cooling load, output power of the electric chiller, output power of the absorption chiller, and cold energy storage power (+ represents storage, - represents release).

[0083] The corresponding equipment power items included in the above energy balance constraints (electrical energy, thermal energy, and cold energy) can be added or removed according to the equipment contained in the actual integrated energy system.

[0084] Demand response constraints:

[0085] 0≤P DR,t ≤R DR,con (5)

[0086] Among them, P DR,t For demand response at time t, reduce load, P DR,con Flexible loads for signing demand response contracts.

[0087] The equipment operation constraints mainly include the coupling constraints of the combined cooling, heating and power (CCHP) unit, the output constraints of each piece of equipment, and the state constraints of the energy storage equipment. The expressions for each constraint are as follows:

[0088] Coupling constraints of combined cooling, heating and power units:

[0089] Q HE,t +Q AC,t ≤QGT,t (6)

[0090] Among them, Q HB,t Q AC,t Q GT,t These represent the heat power consumed by the waste heat boiler, the power consumed by the absorption chiller, and the waste heat output power of the gas turbine at time t, respectively.

[0091] Output constraints for each device:

[0092] P i min ≤P i,t ≤P i max (7)

[0093] Among them, P i,t This represents the output power of device i at time t. This indicates the upper and lower limits of the output power of device i.

[0094] State constraints of energy storage devices:

[0095]

[0096]

[0097]

[0098]

[0099] in, Let P be the initial values ​​of electrical, thermal, and cold energy storage at time t. ES,t P HS,t P CS,t Let t represent the electrical, thermal, and cold energy storage power (+ indicates storage, - indicates release). Energy storage capacity for electricity, heat, and cold.

[0100] Carbon emission constraints:

[0101] Δt[∑U J,run,c (∑ i∈J P i,t )+αU EG,C P EG +βU GG,C (V GT +V GB +V GL )]≤θ qc,Δt (12)

[0102] Where, q C,△t Let θ represent the carbon allowance allocated to the region where the energy system is located during the time period Δt, and let θ represent the proportion of carbon emissions from the energy sector.

[0103] Step 3: Solve the system model to obtain a preliminary solution.

[0104] Substitute the data collected in step 1 into the system calculation model constructed in step 2, and use the particle swarm optimization algorithm to calculate the output of each device in the system at time t to obtain a preliminary control scheme.

[0105] Step 4: Determine the calculation results and adjust parameters as needed.

[0106] The operation control scheme obtained in step 3 is evaluated. Based on the equipment output, the system carbon emissions, wind and solar curtailment rates, and demand response status, it is determined whether the control scheme meets the expected results (i.e., compared with not using the above operation control scheme, whether the improvement in new energy consumption, reduction in carbon emissions, and improvement in load peak-valley difference have been achieved, and whether the optimization degree of the most important regional indicators has been achieved). If the optimization expectations are not met, the process returns to step 1, and after adjusting the adjustable parameters, the optimization process is recalculated until the expectations are met, at which point the loop is exited and the optimization results (adjustable parameter values ​​and equipment output control scheme) are output. Among them, the adjustable parameters include various cost weight coefficients a. i (i = 1, 2, 3, 4, 5), wind curtailment penalty coefficient F WT Discard penalty coefficient F PV The final output adjustable parameter values ​​can be directly used or used as a reference in subsequent optimization calculations of this integrated energy system.

Claims

1. A comprehensive energy system optimization operation control method taking into account carbon emission costs, characterized in that, The steps include the following: S1 collects parameters of the integrated energy system to be optimized, conventional operating cost parameters, carbon emission cost parameters, and other adjustable parameters; S2 aims to minimize the operating cost of an integrated energy system. It incorporates the impacts of operation and maintenance, energy interaction, wind and solar curtailment, carbon emissions, and demand response on the system's operating cost to construct a system calculation model. The system calculation model includes an objective function and constraints, among which the constraints include energy balance, demand response, equipment operation, and carbon emissions. S3. Substitute the data collected in step S1 into the system calculation model constructed in step S2, and use the particle swarm optimization algorithm to calculate the output of each device in the integrated energy system at time t to obtain a preliminary operation control scheme. S4. The preliminary operation control scheme obtained in step S3 is evaluated. Based on the equipment output, the system carbon emissions, wind and solar curtailment rate, and demand response are calculated to determine whether the control scheme meets the expected effect. If the expected results are achieved, the operation control scheme is saved and the optimization results are output. If the expected results are not met, adjust the adjustable parameters and return to step S1 until the optimization expectation is met; In step S2, the objective function expression is constructed as follows: , In the formula: For the operation and maintenance costs of energy equipment; The maintenance cost per unit power output for Class J equipment. Let i be the output power of device i at time t; The energy interaction cost of supplying energy to an integrated energy system; , For electricity and gas purchase prices, Let be the power exchange between the power grids at time t. , , Let t represent the gas consumption of the gas turbine, the gas consumption of the gas boiler, and the gas load. Penalties for curtailment of wind and solar power generation; , The penalty coefficient for wind and solar power curtailment. , Let t be the maximum power output of wind power and photovoltaic power generation. , Let t be the actual output power of wind power generation and photovoltaic power generation at time t; The carbon emission cost of the system; Carbon emissions per unit power output for Class J equipment. , Carbon emissions from purchased electricity and gas; , The interaction excitation coefficient between electric and gas energy; For grid interaction power, , , This includes gas turbine gas consumption, gas boiler gas consumption, and gas load. Compensation costs for incentive-based demand responses; To reduce the compensation cost per unit of electricity load, Let t be the reduction value of the flexible load due to the incentive-driven demand response; Let i be the weighting coefficients for various costs, where i = 1, 2, 3, 4, 5. .

2. The integrated energy system optimization operation control method considering carbon emission costs according to claim 1, characterized in that, In step S1, the parameters of the integrated energy system to be optimized include equipment configuration, load forecast, and maximum wind and solar power output forecast; the conventional operating cost parameters include the operation and maintenance costs of various equipment, energy purchase price, and load reduction compensation; the carbon emission cost parameters include carbon tax, carbon emissions of various energy supply methods, and carbon quotas; and the other adjustable parameters include wind and solar curtailment penalties, various cost weighting coefficients, and energy interaction incentive coefficients.

3. The integrated energy system optimization operation control method considering carbon emission costs according to claim 1, characterized in that, In step S2, the constraints constructed include energy balance constraints, demand response constraints, equipment operation constraints, and carbon emission constraints, where energy includes electrical energy, thermal energy, and cold energy; the constraints are as follows: Power balance constraints: , in, , , , , , , , , These are, respectively, the electrical load at time t, the load reduction due to incentive-driven demand response, the grid interaction power, the output power of wind power, the output power of photovoltaic power, the output electrical power of gas turbine, the output thermal power of heat pump, the electrical power consumed by electric boiler, and the electrical power consumed by electric chiller; This represents the electrical energy storage capacity, where + indicates storage and - indicates release. The heat pump's electro-thermal efficiency; Thermal energy balance constraints: , in, , , , , Let t represent the heat load, electric boiler output power, gas boiler output power, waste heat boiler output power, and heat pump output heat power. Let be the thermal energy storage power at time t, where + represents storage and - represents release; Cold energy balance constraint: , in, , , , where t is the cooling load, the output power of the electric chiller, and the output power of the absorption chiller; Let be the cold energy storage power at time t, where + represents storage and - represents release; Demand response constraints: , in, To reduce the load in response to demand at time t, Flexible loads for signing demand response contracts; Equipment operation constraints mainly include the coupling constraints of combined cooling, heating and power units, the output constraints of each piece of equipment, and the state constraints of energy storage equipment; Coupling constraints of combined cooling, heating and power units: , in, , , These represent the heat power consumed by the waste heat boiler, the power consumed by the absorption chiller, and the waste heat output power of the gas turbine at time t, respectively. Output constraints for each device: , in, This represents the output power of device i at time t. , Indicates the upper and lower limits of the output power of device i; State constraints of energy storage devices: , , , , in, , , The initial values ​​of electrical, thermal, and cold energy storage at time t; , , Let t represent the electrical, thermal, and cold energy storage power at time t, where + indicates storage and - indicates release; , , Energy storage capacity for electricity, heat, and cold; Carbon emission constraints: , in, The energy system is distributed equally to the region where it is located. Carbon allowances for a given period of time This represents the percentage of carbon emissions from the energy sector.

4. The integrated energy system optimization operation control method considering carbon emission costs according to claim 3, characterized in that, The equipment power corresponding items included in the energy balance constraint are added or removed according to the equipment contained in the actual integrated energy system.

5. The integrated energy system optimization operation control method considering carbon emission costs according to claim 1, characterized in that, In step S4, the adjustable parameters include various cost weighting coefficients. Wind curtailment penalty coefficient Discard penalty coefficient , where i = 1, 2, 3, 4, 5.

Citation Information

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