PIES multi-agent game collaborative optimization method considering user differentiation

Abstract

The application discloses a PIES multi-agent game collaborative optimization method considering user differentiation, considers the differentiation including the distribution of flexible resources of producers and consumers and user types, establishes user models of three typical types in the PIES, and reveals the optimization behavior and strategy adjustment law of different users under a dynamic price mechanism through differentiated modeling. A PIA model containing multiple energy equipment is established to overall plan the collaborative operation of park equipment; carbon emission of the PIES is considered, a reward and punishment type ladder carbon trading mechanism is introduced, and an electric-thermal-carbon trading market of the park is established to constrain carbon emission of the park comprehensive energy system. Based on Stackelberg game theory, a multi-agent master-slave game decision model containing multi-energy complementation is constructed, and an adaptive differential evolution algorithm is combined with a Gurobi toolbox to solve the model to obtain an optimal scheduling scheme, which can coordinate the information interaction between the PIA and the user under the premise of guaranteeing user privacy.

Description

Technical Field

[0001] This invention relates to the field of integrated energy system optimization and operation technology, specifically to a PIES multi-agent game collaborative optimization method that considers user differences. Background Technology

[0002] With rising energy demand and increasingly severe environmental pollution, safe, efficient, low-carbon, and clean energy has become the mainstream direction of energy development. Against this backdrop, Park Integrated Energy Systems (PIES), which coordinate and schedule multiple energy sources, have become an important form of efficient energy utilization.

[0003] Currently, user modeling in power parks typically employs a homogeneous, uniform approach, rarely delving into the heterogeneity of users caused by differences in resource characteristics. However, research indicates that different types of users exhibit significantly heterogeneous behavioral strategies in response to aggregated energy types and energy delivery destinations. From the user's perspective, these differences are mainly reflected in reliability requirements, electricity consumption time distribution, electricity consumption variations, and peak load. Introducing product differentiation features into the power system can not only effectively guide users to optimize their energy consumption behavior but also more accurately meet their personalized energy service needs.

[0004] The "Administrative Measures for Carbon Emission Trading" clearly stipulates the relevant responsibilities and obligations of each market participant in carbon emission control. However, current research in PIES game theory interaction only focuses on the self-interest of each participant, without fully considering the impact of pollution emissions on the overall system, which may pose a serious threat to the environment. Therefore, it is essential to develop a multi-stakeholder game model that incorporates environmental factors such as carbon emissions to achieve synergistic optimization of the economic interests of different participants and the overall environmental benefits of the PIES, thereby promoting a win-win situation for both economic and environmental benefits. Summary of the Invention

[0005] The purpose of this invention is to provide a PIES multi-agent game collaborative optimization method that takes into account user differences, so as to solve the above-mentioned defects.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A collaborative optimization method for PIES multi-agent game considering user differentiation includes the following steps:

[0008] S1. Based on the differentiated characteristics of different users and the differences in user flexible resources and user types, several typical user models were established within PIES.

[0009] S2. Based on the PIES internal electrical and thermal equipment models, establish a PIA model containing multiple energy equipment to coordinate the collaborative operation of equipment in the park.

[0010] S3. Considering the carbon emissions of PIES, introduce a reward-and-penalty tiered carbon trading mechanism to join the carbon market and establish an electricity-heat-carbon trading market in the park;

[0011] S4. Based on Stackelberg game theory, establish an interaction mechanism with PIA as the leader and differentiated users as followers, construct a multi-agent master-slave game decision model with multi-energy complementarity, and use the adaptive differential evolution algorithm combined with the Gurobi toolbox to solve the proposed model to obtain the optimal scheduling scheme.

[0012] Preferably, in step S2, there are several typical types of user models, including: park service center model, intelligent automated enterprise model and traditional enterprise model.

[0013] Preferably, the construction of the park service center model is as follows:

[0014] The Park Service Center (PSC) includes fixed loads of electricity and heat, as well as flexible loads; a net load model for the PSC is established using equation (1):

[0015]

[0016] In the formula, k represents the load type, k∈{e,h}; This represents the net load value for the k-th type of load during time period t; This represents the fixed load of type k during time period t; This represents the load that can be reduced during time period t for the k-th type of load; This represents the transferable load of the k-th load type during time period t; This represents the alternative load for the k-th load during time period t; This represents the photovoltaic power generation during time period t. If k is h, then it is 0.

[0017] ③ Fixed load The electrical and thermal loads remain unchanged;

[0018] ② It can reduce the load. The load can be reduced to a certain extent as needed, as shown in equations (2)–(4) below:

[0019]

[0020] In the formula, θ cut (t) is a 0-1 variable; γ t This is the reduction factor; To reduce the magnitude of the front load power; θmin and θ max The minimum and maximum number of load reductions; N max This is the maximum number of times a continuous reduction can be implemented;

[0021] ③ Transferable load The time dimension can be transferred within the scheduling period, as shown in equations (5)–(8) below:

[0022]

[0023] In the formula, This represents the power available for load transfer before load regulation during time period t for the k-th type of load; These are binary variables, representing the transfer-in and transfer-out parameters of the transferable load of the k-th type of load during time period t, respectively; Let represent the transfer-in and transfer-out power of the k-th type of load during time period t, respectively; Equation (7) indicates that the total amount of each type of load remains unchanged within a scheduling cycle; These represent the upper and lower limits of the interaction amount of the k-th type of transferable load in each time period. This constraint is used to ensure the energy quality requirements of users.

[0024] ④ Alternative loads As shown in equations (9)–(11):

[0025]

[0026] In the formula, These represent the electrical and thermal substitution load values ​​after the interaction; These represent the power of the electrical and thermal substitute loads before the interaction; These are binary variables, representing the input and output parameters of the electricity and heat substitution loads during time period t, respectively. These represent the input and output power of the electric and heat substitution loads during time period t, respectively.

[0027] ⑤ Photovoltaics With the vigorous promotion of clean energy, a certain proportion of renewable photovoltaic power exists among most users;

[0028] In summary, the cost E of PSC PCS It can be represented as:

[0029]

[0030] In the formula, For PSC's electricity and heat purchase costs, E PCS,e Here is the power consumption efficiency function for PSC; a1, b1, and c1 are the parameters of the power consumption efficiency function. These are the electricity sales price, electricity purchase price, and heat sales price set by PIA after a master-slave game. These represent the net electrical and thermal loads of the PSC, respectively.

[0031] Preferably, the construction of the intelligent automated enterprise model is as follows:

[0032] Intelligent automated enterprises, or APEs, include electrical loads, which are characterized by high power and transferability, and have a high proportion of PV on the source side; an APE net load model is established using equation (14):

[0033]

[0034] In the formula: This represents the electrical load of APE during time period t; This represents the fixed load of APE during time period t; This represents the transferable load of APE during time period t; This represents the photovoltaic power generation of APE during time period t;

[0035] The cost of APE E APE It can be represented as:

[0036]

[0037] In the formula, For APE's electricity purchase cost, This is the power consumption function of the APE;

[0038] Preferably, the construction of the traditional enterprise model is as follows:

[0039] Traditional enterprises, or TE, include fixed loads of electricity and heat, as well as flexible loads. Flexible loads only include replaceable loads and also include electric boilers, which obtain heat energy through electric heating when electricity prices are low or electricity is plentiful.

[0040] Establish the TE net load model using equation (17):

[0041]

[0042] In the formula: This represents the net load value of TE for the k-th type of load during time period t; This represents the fixed load of type k in time period t for TE; This represents the alternative load for the k-th type of load in time period t; K represents the power of the electric boiler during time period t. If k is e, it represents the power consumption; if k is h, it represents the power generation.

[0043] An electric boiler heats water or an organic carrier inside the boiler to a certain temperature and pressure through resistance or electromagnetic induction, and then outputs heat energy. Its mathematical model is as follows:

[0044]

[0045] In the formula, η represents the electrical input power and thermal output power of the electric boiler during time period t; EB This indicates the electrothermal conversion coefficient of the electric boiler;

[0046] In summary, the cost of TE is E TE It can be represented as:

[0047]

[0048] In the formula, For TE's electricity and heat purchase costs, E TE,e Let TE be the power efficiency function. These represent TE net electrical and thermal loads, respectively.

[0049] Preferably, step S2 includes the following steps:

[0050] S21 and PIA utilize the heat and electricity generated by the CHP unit for user consumption. The relationship between the electrical power output through GT and the gas consumption can be expressed as:

[0051]

[0052] In the formula, For the power generation of GT, η e For the power generation efficiency of GT, H L It is a low-calorific-value natural gas. Natural gas consumed by GT This is the upper limit for power generation of the CHP unit;

[0053] In a CHP unit, natural gas is burned via GT (Gas Torque) to generate electricity, and the waste heat discharged is recovered by WHB (Waste Heat Pump) for heating. Its heating model can be expressed as:

[0054]

[0055] In the formula, Let η be the exhaust waste heat of GT at time t. loss η is the heat loss rate. h For waste heat recovery efficiency, C represents the heating capacity of WHB. OP,h The flue gas recovery rate of WHB.

[0056] S22. To optimize the operation of PIA equipment and provide flexible heating, GB, which has higher heating efficiency, is introduced. Its heating model is as follows:

[0057]

[0058] In the formula, For GB heating power, η GB,h The heating efficiency is GB. The natural gas consumed by GB These are the upper and lower limits of heating power specified in GB standards.

[0059] The addition of ESS to S23 and PIA enables efficient energy sharing among users; considering the energy loss during charging and discharging, the relationship between state of charge and charging / discharging power can be defined as:

[0060]

[0061] In the formula, Let BT be the state of charge at time t. Let BT be the state of charge at time t-1. Let η be the charging and discharging power of BT at time t. ESS,chg η ESS,dis Let be the charging and discharging efficiency of BT at time t;

[0062] Within any given time period, the state of charge and charging / discharging power of the ESS should be within a certain range, which can be defined as:

[0063]

[0064] In the formula, Indicates the upper and lower limits of the ESS state of charge. This refers to the upper limit of the charging and discharging power of the ESS.

[0065] S24. In the electricity-heat market, the PIA's strategy set consists of the price of heat and electricity sold to users, and the purchase of excess photovoltaic power generated by users. The optimal selling price strategy set is determined using a master-slave game. The constraints on the electricity and heat prices set by the PIA are:

[0066]

[0067] In the formula, These refer to the electricity purchase price and the electricity sales price of the power grid, respectively. These are the upper and lower limits of the heating price, respectively, derived from historical data on user heating purchases.

[0068] Preferably, step S3 includes the following steps:

[0069] S31. Domestically, quotas are mainly allocated free of charge. The main carbon emission sources in PIES are: upstream coal-fired power units, GT, and GB. The initial quota model is shown in the formula:

[0070]

[0071] In the formula, E a χ is the initial carbon allowance for the system. e , χ g Carbon quota coefficient for unit power and heat output. Let t be the power of electricity purchased from outside the park. Let GB be the heating power at time t; Let t represent the heating and power output of the CHP unit at time t;

[0072] S32. Use equation (34) to establish a real carbon emission model:

[0073]

[0074] In the formula, E P E represents the system's actual carbon emissions. e,buy E represents the actual carbon emissions from electricity purchased by the higher-level authority. total This represents the actual carbon emissions of the CHP unit and the total emissions from GB. Let t represent the equivalent output power of the CHP and GB units, a2, b2, and c2 be the carbon emission calculation parameters for coal-fired power units, and a3, b3, and c3 be the carbon emission calculation parameters for natural gas-fired power units. This represents the amount of electricity that PIA purchases from the power grid;

[0075] S33. Construct a reward-and-punishment tiered carbon trading model using formula (35):

[0076]

[0077] E PIES =E P -E a (36),

[0078] In the formula, E CET Let E be the carbon trading cost of the system at time t, where a positive value represents the purchase quota and a negative value represents obtaining subsidies using the remaining quota; PIES E represents the actual carbon emissions of the park. P With the initial carbon quota E a The difference, k is the carbon trading base price on the day, α is the compensation coefficient, β is the price increase rate, and d is the length of the carbon emission range corresponding to each tier;

[0079] S34. In the electricity-heat-carbon joint trading market, the profit function E of PIA PIA It is divided into the following parts: revenue from electricity and heat trading with users, costs from electricity trading with the grid, gas costs, equivalent lifetime loss costs of ESS, and costs generated by the CET mechanism;

[0080]

[0081] In the formula, The cost of electricity purchased from the grid by PIA; For PIA, the cost of purchasing gas from the gas network; μ g For gas purchase price; E SSD For the operating cost of PIA source-side equipment, λ ESS , λ CHP , λ GB For PIA's ESS, CHP units, and GB operating cost coefficients.

[0082] Preferably, step S4 specifically includes the following steps:

[0083] S41. Construct a multi-agent master-slave game decision-making model with multi-energy complementarity:

[0084] The market is constructed as a Stackelberg game process, in which PIA acts as the leader, incentivizing users to actively participate in demand response by adjusting dynamic pricing strategies and scheduling strategies for ESS, CHP units, and GB units; users act as followers, adjusting their energy consumption behavior to maximize benefits after receiving PIA's strategies.

[0085] During the game, PIA first initializes the dispatch strategies for ESS, CHP units, and GB, while simultaneously setting electricity sales prices, electricity purchase prices, and heat sales prices, and publishes this information to users. Subsequently, each user, based on the received strategy set and their own operational constraints and optimization objectives, optimizes their energy consumption plan through GUROBI to maximize their benefits, and submits the feedback results to PIA. Based on the users' strategies, PIA adjusts its strategies accordingly. and The strategy, including the one mentioned above, aims to maximize its benefits; PIA and users interact iteratively, constantly adjusting the strategy until it converges to the Stackelberg game equilibrium.

[0086] S42. Distributed iterative method based on Adaptive Differential Evolution (ADE) algorithm:

[0087] PIA guides users to optimize their energy consumption plans by dynamically adjusting the action strategies and price signals of ESS, CHP units, and GB units. Users maximize their own benefits through local solution tools based on the strategy set provided by PIA. The above interaction process is continuously iterated until the game system converges to the Stackelberg equilibrium point, and the proposed model is solved to obtain the optimal scheduling scheme.

[0088] The Stackelberg game consists of the following components: the leader, PIA, and the followers, users; each participant's payoff is a objective function of the aforementioned entities; the interaction strategies include PIA's power supply output and energy price set. and users' net electricity and heat load

[0089] When a set of strategies When a Stackelberg game equilibrium is reached, if no player can increase their own benefit by unilaterally changing their own strategy set, then that strategy set is the optimal scheduling scheme and must satisfy the following condition:

[0090]

[0091] The beneficial effects of this invention are as follows:

[0092] (1) This invention considers the PIES multi-agent game collaborative optimization method with user differentiation, explores the user heterogeneity problem caused by differences in resource characteristics, constructs a variety of typical user types to participate in park energy market transactions, and reveals the optimization behavior and strategy adjustment rules of different users under dynamic price mechanism through differentiated modeling.

[0093] (2) The method of the present invention fully considers the impact of pollution emissions on the overall system, and further constrains the carbon emissions of the park’s integrated energy system by introducing a reward and punishment tiered carbon trading mechanism, thereby further reducing carbon emissions.

[0094] (3) The method of this invention constructs a multi-agent master-slave game decision model with multi-energy complementarity. The optimal scheduling scheme is obtained by solving the proposed model using an adaptive differential evolution algorithm combined with the Gurobi toolbox. This can coordinate the information interaction between PIA and users while ensuring user privacy. Attached Figure Description

[0095] Figure 1 This is a schematic diagram of the PIES electricity-heat-carbon joint market framework;

[0096] Figure 2 This is a diagram illustrating the PIA dynamic electricity price;

[0097] Figure 3 This is a diagram illustrating the PIA dynamic heat price.

[0098] Figure 4 This is a schematic diagram of PIES user power dispatch;

[0099] Figure 5 This is a schematic diagram of thermal energy dispatching for PIES users;

[0100] Figure 6This is a schematic diagram of the interaction strategy of thermal power units in PIA;

[0101] Figure 7 This is a diagram illustrating the interaction strategy of ESS in PIA;

[0102] Figure 8 This is a diagram showing the comparison of carbon emissions;

[0103] Figure 9 This is a flowchart of the PIES multi-agent game;

[0104] Figure 10 It is a flowchart of the function implementation. Detailed Implementation

[0105] Example 1:

[0106] Figure 1 This is a schematic diagram of the PIES electricity-heat-carbon joint market framework. Figure 10 It is a flowchart of the functional implementation. For example... Figure 1 , Figure 9 As shown, the PIES multi-agent game collaborative optimization method considering user differentiation includes the following steps:

[0107] S1. To address the differentiated characteristics of different users, and based on variations in user flexible resource distribution and user types, several typical user models were established within PIES. These typical user models include: a park service center model, an intelligent automated enterprise model, and a traditional enterprise model.

[0108] S11. The construction of the park service center model is as follows:

[0109] The park service center (PSC) includes fixed loads of electricity and heat, as well as flexible loads; a net load model of the PSC is established using equation (1):

[0110]

[0111] In the formula, k represents the load type, k∈{e,h}; This represents the net load value for the k-th type of load during time period t; This represents the fixed load of type k during time period t; This represents the load that can be reduced during time period t for the k-th type of load; This represents the transferable load of the k-th load type during time period t; This represents the alternative load for the k-th load during time period t; This represents the photovoltaic power generation during time period t. If k is h, then it is 0.

[0112] ④ Fixed load The electrical and thermal loads remain unchanged;

[0113] ② It can reduce the load. The load can be reduced to a certain extent as needed, as shown in equations (2)–(4) below:

[0114]

[0115] In the formula, θ cut (t) is a 0-1 variable; γ t This is the reduction factor; To reduce the magnitude of the front load power; θ min and θ max The minimum and maximum number of load reductions; N max This is the maximum number of times a continuous reduction can be implemented;

[0116] ③ Transferable load The time dimension can be transferred within the scheduling period, as shown in equations (5)–(8) below:

[0117]

[0118] In the formula, This represents the power available for load transfer before load regulation during time period t for the k-th type of load; These are binary variables, representing the transfer-in and transfer-out parameters of the transferable load of the k-th type of load during time period t, respectively; Let represent the transfer-in and transfer-out power of the k-th type of load during time period t, respectively; Equation (7) indicates that the total amount of each type of load remains unchanged within a scheduling cycle; These represent the upper and lower limits of the interaction amount of the k-th type of transferable load in each time period. This constraint is used to ensure the energy quality requirements of users.

[0119] ④ Alternative loads As shown in equations (9)–(11):

[0120]

[0121] In the formula, These represent the electrical and thermal substitution load values ​​after the interaction; These represent the power of the electrical and thermal substitute loads before the interaction; These are binary variables, representing the input and output parameters of the electricity and heat substitution loads during time period t, respectively. These represent the input and output power of the electric and heat substitution loads during time period t, respectively.

[0122] ⑤ Photovoltaics With the vigorous promotion of clean energy, a certain proportion of renewable photovoltaic power exists among most users;

[0123] In summary, the cost E of PSC PCS It can be represented as:

[0124]

[0125] In the formula, For PSC's electricity and heat purchase costs, E PCS,e Here is the power consumption efficiency function for PSC; a1, b1, and c1 are the parameters of the power consumption efficiency function. These are the electricity sales price, electricity purchase price, and heat sales price set by PIA after a master-slave game. These represent the net electrical and thermal loads of the PSC, respectively.

[0126] S12. The construction of the intelligent automation enterprise model is as follows:

[0127] Intelligent automated production enterprises (APEs) include electrical loads, which are characterized by high power and transferability, and have a high proportion of PV on the source side; an APE net load model is established using equation (14):

[0128]

[0129] In the formula: This represents the electrical load of APE during time period t; This represents the fixed load of APE during time period t; This represents the transferable load of APE during time period t; This represents the photovoltaic power generation of APE during time period t;

[0130] The cost of APE E APE It can be represented as:

[0131]

[0132] In the formula, For APE's electricity purchase cost, This is the power consumption function of the APE;

[0133] S13. The construction of the traditional enterprise model is as follows:

[0134] Traditional enterprises (TE) include fixed loads of electricity and heat, as well as flexible loads. Flexible loads only include alternative loads and also include electric boilers, which obtain heat energy through electric heating when electricity prices are low or electricity is plentiful.

[0135] Establish the TE net load model using equation (17):

[0136]

[0137] In the formula: This represents the net load value of TE for the k-th type of load during time period t; This represents the fixed load of type k in time period t for TE; This represents the alternative load for the k-th type of load in time period t; K represents the power of the electric boiler during time period t. If k is e, it represents the power consumption; if k is h, it represents the power generation.

[0138] An electric boiler heats water or an organic carrier inside the boiler to a certain temperature and pressure through resistance or electromagnetic induction, and then outputs heat energy. Its mathematical model is as follows:

[0139]

[0140] In the formula, η represents the electrical input power and thermal output power of the electric boiler during time period t; EB This indicates the electrothermal conversion coefficient of the electric boiler;

[0141] In summary, the cost of TE is E TE It can be represented as:

[0142]

[0143]

[0144] In the formula, For TE's electricity and heat purchase costs, E TE,e Let TE be the power efficiency function. These represent TE net electrical and thermal loads, respectively.

[0145] S2. Based on the PIES internal electrical and thermal equipment models, establish a PIA model containing multiple energy devices to coordinate the collaborative operation of equipment in the park. The specific steps are as follows:

[0146] S21 and PIA utilize the heat and electricity generated by the CHP unit for user consumption. The relationship between the electrical power output through GT and the gas consumption can be expressed as:

[0147]

[0148] In the formula, For the power generation of GT, η e For the power generation efficiency of GT, H L It is a low-calorific-value natural gas. Natural gas consumed by GT This is the upper limit for power generation of the CHP unit;

[0149] In a CHP unit, natural gas is burned via GT (Gas Torque) to generate electricity, and the waste heat discharged is recovered by WHB (Waste Heat Pump) for heating. Its heating model can be expressed as:

[0150]

[0151] In the formula, Let η be the exhaust waste heat of GT at time t. loss η is the heat loss rate. h For waste heat recovery efficiency, C represents the heating capacity of WHB. OP,h The flue gas recovery rate of WHB;

[0152] S22. To optimize the operation of PIA equipment and provide flexible heating, GB, which has higher heating efficiency, is introduced. Its heating model is as follows:

[0153]

[0154] In the formula, For GB heating power, η GB,h The heating efficiency is GB. The natural gas consumed by GB These are the upper and lower limits of heating power specified in GB standards.

[0155] The addition of ESS to S23 and PIA enables efficient energy sharing among users; considering the energy loss during charging and discharging, the relationship between state of charge and charging / discharging power can be defined as:

[0156]

[0157] In the formula, Let BT be the state of charge at time t. Let BT be the state of charge at time t-1. Let η be the charging and discharging power of BT at time t. ESS,chg η ESS,dis Let be the charging and discharging efficiency of BT at time t.

[0158] Within any given time period, the state of charge and charging / discharging power of the ESS should be within a certain range, which can be defined as:

[0159]

[0160] In the formula, Indicates the upper and lower limits of the ESS state of charge. This refers to the upper limit of the charging and discharging power of the ESS.

[0161] S24. In the electricity-heat market, the PIA's strategy set consists of the price of heat and electricity sold to users, and the purchase of excess photovoltaic power generated by users. The optimal selling price strategy set is determined using a master-slave game. The constraints on the electricity and heat prices set by the PIA are:

[0162]

[0163] In the formula, These refer to the electricity purchase price and the electricity sales price of the power grid, respectively. These are the upper and lower limits of the heating price, respectively, derived from historical data on user heating purchases.

[0164] S3. Considering the carbon emissions of PIES, introduce a reward-and-penalty tiered carbon trading mechanism to join the carbon market and establish an electricity-heat-carbon trading market in the park. The specific steps are as follows:

[0165] S31. Domestically, quotas are mainly allocated free of charge. The main carbon emission sources in PIES are: upstream coal-fired power units, GT, and GB. The initial quota model is shown in the formula:

[0166]

[0167] In the formula, E a χ is the initial carbon allowance for the system. e , χ g Carbon quota coefficient for unit power and heat output. Let t be the power of electricity purchased from outside the park. Let GB be the heating power at time t; Let t represent the heating and power output of the CHP unit at time t.

[0168] S32. Use equation (34) to establish a real carbon emission model:

[0169]

[0170] In the formula, E P E represents the system's actual carbon emissions. e,buy E represents the actual carbon emissions from electricity purchased by the higher-level authority. total This represents the actual carbon emissions of the CHP unit and the total emissions from GB. Let t represent the equivalent output power of the CHP and GB units, a2, b2, and c2 be the carbon emission calculation parameters for coal-fired power units, and a3, b3, and c3 be the carbon emission calculation parameters for natural gas-fired power units. This represents the amount of electricity that PIA purchases from the power grid.

[0171] S33. Construct a reward-and-punishment tiered carbon trading model using formula (35):

[0172]

[0173] E PIES =E P -E a (36),

[0174] In the formula, E CET Let E be the carbon trading cost of the system at time t, where a positive value represents the purchase quota and a negative value represents obtaining subsidies using the remaining quota; PIES E represents the actual carbon emissions of the park. P With the initial carbon quota E a The difference is given by k, where k is the base price of carbon trading on that day, α is the compensation coefficient, β is the price increase rate, and d is the length of the carbon emission range corresponding to each tier.

[0175] S34. In the electricity-heat-carbon joint trading market, the profit function E of PIA PIA It is divided into the following parts: revenue from electricity and heat trading with users, costs from electricity trading with the grid, gas costs, equivalent lifetime loss costs of ESS, and costs generated by the CET mechanism;

[0176]

[0177] In the formula, The cost of electricity purchased from the grid by PIA; For PIA, the cost of purchasing gas from the gas network; μ g For gas purchase price; E SSD For the operating cost of PIA source-side equipment, λ ESS , λ CHP , λ GB For PIA's ESS, CHP units, and GB operating cost coefficients.

[0178] S4. Based on Stackelberg game theory, an interaction mechanism is established with PIA as the leader and differentiated users as followers. A multi-agent master-follower game decision-making model with multi-energy complementarity is constructed. The optimal scheduling scheme is obtained by solving the proposed model using an adaptive differential evolution algorithm combined with the Gurobi toolbox. The specific steps are as follows:

[0179] S41. Construct a multi-agent master-slave game decision-making model with multi-energy complementarity:

[0180] The PIA and users are distinct entities. The dispatch strategies of ESS, CHP units, and GB, along with the PIA's dynamic interactive pricing, significantly impact users' flexible load actions. Conversely, users' flexible load arrangements influence the PIA's optimization strategies. Therefore, the electricity-heat-carbon trading market between the PIA and users exhibits a clear characteristic of strategic mutual influence. To characterize this two-way interaction, the market is constructed as a Stackelberg game process, where the PIA, as the leader, incentivizes users to actively participate in demand response by adjusting its dynamic pricing strategy and the dispatch strategies of ESS, CHP units, and GB. Users, as followers, adjust their energy consumption behavior to maximize their benefits after receiving the PIA's strategies.

[0181] During the game, the PIA first initializes the dispatch strategies for the ESS, CHP units, and GB, and simultaneously sets the electricity sales price, electricity purchase price, and heat sales price, and publishes this information to users. Subsequently, each user, based on the received strategy set and their own operational constraints and optimization objectives, optimizes their energy consumption plan to maximize their benefits and submits the feedback results to the PIA. Based on the users' strategies, the PIA adjusts its strategies accordingly. and The strategy, including the one mentioned above, aims to maximize its benefits; PIA and users interact iteratively, constantly adjusting the strategy until it converges to the Stackelberg game equilibrium.

[0182] S42. Distributed iterative method based on Adaptive Differential Evolution (ADE) algorithm:

[0183] PIA guides users to optimize their energy consumption plans by dynamically adjusting the action strategies and price signals of ESS, CHP units, and GB units. Users maximize their own benefits by using local solution tools (such as GUROBI) based on the strategy set provided by PIA. The above interaction process iterates continuously until the game system converges to the Stackelberg equilibrium point. Figure 9 The flowchart for multi-agent game theory using the adaptive differential evolution algorithm in PIES is as follows: Figure 9 As shown, PIA first initializes population a, which is PIA's policy set, and publishes it to users. Different users optimize their own load based on price information and feed it back to PIA. PIA obtains the optimization results based on the feedback information, performs mutation and crossover operations on the initial population a to obtain a new population b, publishes it to users, and repeats the above operations until convergence is achieved.

[0184] The Stackelberg game consists of the following components: the leader, PIA, and the followers, users; each participant's payoff is a objective function of the aforementioned entities; the interaction strategies include PIA's power supply output and energy price set. and users' net electricity and heat load

[0185] When a set of strategies When a Stackelberg game equilibrium is reached, if no player can increase their own benefit by unilaterally changing their own strategy set, then that strategy set is the optimal scheduling scheme and must satisfy the following condition:

[0186]

[0187] In the PIES multi-agent game collaborative optimization method of the present invention that considers user differentiation, a PIES case study was conducted on the PIA-based electricity-heat-carbon joint market through a PIES case study containing three types of users with different attributes.

[0188] All load data are derived from actual statistics from a certain industrial park in Anhui Province. The case study includes ESS, CHP units, and GB units, managed and operated by PIA. The ESS capacity is set to 1200kW, with a maximum charge / discharge capacity of 600kW. The initial state of the ESS is set to 0.2, and the minimum and maximum energy storage states are set to 0.2 and 0.9, respectively. The CHP unit has a maximum output capacity of 800kWh, an electrical efficiency of 0.45, and a thermal efficiency of 0.35. The GB unit has a maximum output capacity of 600kWh and an efficiency of 0.95. Time-of-use electricity and gas prices are shown in Table 1. Set to 0.35 yuan / kWh.

[0189] Table 1. Detailed Price List for Electricity and Gas

[0190]

[0191] Figure 2 This is a diagram illustrating the PIA dynamic electricity pricing. Figure 3 This is a diagram illustrating the PIA dynamic heat price. (Example) Figure 2 , Figure 3 As shown, the dynamic price trends of the PIA in the electricity and heat markets are illustrated. To enhance users' willingness to purchase electricity from the PIA, the PIA sets its electricity sales price lower than the price they pay when purchasing electricity from the grid. This strategy effectively reduces users' energy costs while ensuring the PIA's revenue objectives. Furthermore, the PIA sets its electricity purchase price slightly higher than the price they pay when purchasing electricity from the grid. This strategy, by increasing users' revenue from selling electricity, reduces their incentive to directly feed excess electricity back to the grid, thus further promoting the safe and stable operation of the power grid while sacrificing some of the PIA's economic benefits.

[0192] The dynamic adjustment of heat energy prices is based on historical sales price ranges. When heat energy demand is high, prices are appropriately increased; when demand is low, prices are correspondingly decreased. This dynamic pricing strategy not only conforms to market supply and demand laws but also ensures the economic benefits of the PIA in the heat energy market. The final results show that the pricing strategies for both electricity and heat energy have achieved a win-win effect for both the PIA and users. This demonstrates that the dynamic pricing mechanism has a significant positive effect on optimizing energy interaction within the PIES.

[0193] Figure 4 This is a schematic diagram of PIES user power dispatch. Figure 5 This is a schematic diagram of PIES user thermal energy scheduling. (For example...) Figure 4 , Figure 5 As shown, the impact of user demand response on energy market transactions can be summarized in three aspects. First, most users choose to shift flexible loads to lower-priced periods while reducing energy use during higher-priced periods to minimize costs. For example, PSC shifts transferable loads to the 1:00-7:00 period and reduces loads during the 19:00-21:00 period, while TE shifts alternative loads to the 1:00-7:00 and 15:00-18:00 periods. Second, when photovoltaic energy is abundant, users increase their power utilization by increasing energy consumption. For example, PSC shifts transferable loads to the 12:00-14:00 period, while APE shifts alternative loads to the 10:00-14:00 period. Third, in response to dynamic pricing and to promote energy interaction, users analyze fluctuations in electricity and heat prices and flexibly adjust the allocation between electricity and heat loads. This allows them to weigh the benefits of using different energy forms. Specifically, PSC and TE adjust heat load to electricity load to varying degrees during periods 3-7, while PSC adjusts electricity load to heat load during periods of 9:00-10:00, 21:00, and 23:00-24:00. By optimizing costs and resource utilization through load adjustment and energy selection, users not only effectively balance the supply and demand relationship in the energy market but also improve the absorption capacity of distributed energy resources, providing strong support for the sustainable operation of the energy system.

[0194] As three different user groups within the PIES (Power, Intake, and Electricity) ecosystem, PSC, APE, and TE require specific analysis of their energy consumption patterns. PSC, as a prosumer in the PIES, consumes energy and utilizes distributed photovoltaic (PV) power generation, its energy usage shifting according to dynamic prices (changing from buyer to seller during 11 time periods). Furthermore, analysis of heat load changes shows that both loads change based on dynamic prices, enhancing energy flexibility. APE, as a smart enterprise, experiences smaller fluctuations in its electricity load due to its 24 / 7 production characteristics, but its high electricity demand leads to higher electricity purchase costs. To alleviate this pressure, APE has deployed a high-power PV system, significantly reducing net load during midday and even causing energy overflow. Guided by the dynamic pricing mechanism, APE shifts some load to periods of high PV output, significantly improving its self-consumption of PV power and reducing its dependence on external power purchases. TE, as a traditional enterprise, has relatively weak load regulation capabilities, deploying only a small amount of alternative load and electric boilers to meet its heat demand. Similar to PSC, TE also adjusts the allocation of electricity and heat loads based on dynamic prices. However, unlike PSC, TE actually increased its power purchases during the 7:00-8:00 PM period when electricity prices were higher. This was because heat prices were too high at the time, and TE chose to operate its electric boilers at full capacity to significantly reduce the net heat load purchased from PIA, thereby achieving an overall reduction in energy purchase costs.

[0195] Figure 6 This is a schematic diagram of the interaction strategy for thermal power units in PIA. For example... Figure 6 As shown, the CHP unit can simultaneously produce electricity and heat, improving economic efficiency through optimized PIA energy purchase strategies. Specifically, when electricity prices are low, the PIA prioritizes purchasing electricity from the grid, with the shortfall supplemented by the GB (Power Grid) (e.g., during the 1:00-7:00 period). During the higher-priced period of 19:00-21:00, the PIA prioritizes utilizing the output of the CHP unit; in this time, the heat demand can be met even without GB output, thereby reducing operating losses and carbon emissions from the industrial park. The introduction of the CHP unit strengthens the coupling of electricity and heat in the PIES, providing greater flexibility for the operational optimization of PIES equipment and further improving the dispatch efficiency of the combined electricity-heat market.

[0196] Figure 7 This is a diagram illustrating the interaction strategy of ESS in PIA. For example... Figure 7As shown, the interaction strategy of the ESS in PIA (Producer-Edge Utilization) primarily sources its charging energy from three sources: 1) electricity purchased from the grid during periods of low electricity load; 2) electricity generated by the CHP (Consumer-Generated Power) unit during periods of higher thermal load than electrical load; and 3) electricity purchased from users with surplus photovoltaic (PV) power generation. PIA's ESS discharge energy provides electricity to prosumers. Between 1:00 and 7:00, when the grid's electricity price is relatively low, PIA purchases electricity from the grid to charge its ESS. Between 8:00 and 11:00, when the grid's electricity price is high, PIA reduces its purchases of electricity from the grid to charge the ESS. Between 11:00 and 15:00, when PV power is abundant, PIA purchases electricity from users with surplus PV power generation at a lower dynamic price, and also uses excess electricity generated by the CHP unit for heating to charge the ESS, then sells it to prosumers at a higher electricity-carbon coupling price in subsequent periods. In traditional energy sharing models, if the photovoltaic and PIA (Power Generation Association) CHP (Consumer Power Generation) units in the cluster generate excess power after direct transactions between buyers and sellers, the excess power is fed back to the grid, which is clearly detrimental to the economic benefits of the PIA. This phenomenon is mainly due to the joint optimization of ESS (Energy Saving System) and CHP unit strategies and dynamic electricity pricing.

[0197] Table 2 shows the comparison results of PIES with and without carbon trading optimization, as shown below.

[0198] Table 2 shows the comparison results of PIES with and without carbon trading optimization.

[0199]

[0200] As shown in Table 2, in the combined electricity-heat market, PIES's electricity-heat market revenue was RMB 1606.9233, with an energy efficiency of 0.6783. Compared to the combined electricity-heat-carbon market, the electricity-heat market revenue increased by approximately 36%, and the energy efficiency increased by approximately 9%. This is because the former increased the utilization rate of the more efficient GB (Gross Gas) and reduced the purchase of natural gas. Furthermore, during periods of low electricity prices, it purchased large amounts of electricity from the grid and stored it in ESS (Energy Saving System) to sell to users when electricity prices were high, thus generating profits. However, these actions undoubtedly significantly increased PIES's carbon emissions. Although GB is more efficient, as a thermal power unit and supplied by the grid, it emits large amounts of greenhouse gases such as carbon dioxide. Figure 8 It's clear that carbon emissions differ by more than double between 3:00 and 5:00-6:00, far exceeding the scenario considering the combined electricity-heat-carbon market. Furthermore, considering the carbon market, PIES limits the output of thermal power units, resulting in a more balanced electricity purchase from the grid, reducing grid pressure. Since PIES carbon emission allowances exceed actual carbon emissions, profitability is achieved in the carbon market. Ultimately, the total profit is greater than in the scenario considering only the combined electricity-heat market.

[0201] In summary, compared with existing technologies, this invention's PIES multi-agent game-theoretic collaborative optimization method, which considers user differentiation, fully takes into account differences such as the distribution of flexible user resources and user types, flexibly coordinating supply and demand, and promoting multi-energy complementarity to further improve energy efficiency. It delves into the user heterogeneity problem caused by differences in resource characteristics, constructs various typical user types to participate in park energy market transactions, and reveals the optimization behavior and strategy adjustment patterns of different users under dynamic pricing mechanisms through differentiated modeling. It fully considers the impact of pollution emissions on the overall system, introducing a reward-and-punishment tiered carbon trading mechanism to further constrain carbon emissions from the park's integrated energy system, thereby further reducing carbon emissions. In the optimized scheduling, it fully considers the typical differentiated characteristics of park users and constructs a multi-agent master-slave game decision-making model with multi-energy complementarity based on the roles and interests of each entity. Based on this model, it uses an adaptive differential evolution algorithm combined with the Gurobi toolbox to solve the proposed model to obtain the optimal scheduling scheme, achieving low-carbon and economical operation of PIES and promoting the development of the park's integrated energy system towards a green and low-carbon direction.

[0202] The above is an exemplary description of the invention. Obviously, the specific implementation of the invention is not limited to the above-described manner. Any non-substantial improvement made using the inventive concept and technical solution of the invention, or the direct application of the inventive concept and technical solution to other situations without modification, is within the protection scope of the invention.

Claims

1. A PIES multi-agent game collaborative optimization method considering user differentiation, characterized in that, Includes the following steps: S1. Based on the differentiated characteristics of different users and the differences in user flexible resources and user types, several typical user models were established within PIES. S2. Based on the PIES internal electrical and thermal equipment models, establish a PIA model containing multiple energy equipment to coordinate the collaborative operation of equipment in the park. S3. Considering the carbon emissions of PIES, introduce a reward-and-penalty tiered carbon trading mechanism to join the carbon market and establish an electricity-heat-carbon trading market in the park; S4. Based on Stackelberg game theory, establish an interaction mechanism with PIA as the leader and differentiated users as followers, construct a multi-agent master-slave game decision model with multi-energy complementarity, and use the adaptive differential evolution algorithm combined with the Gurobi toolbox to solve the proposed model to obtain the optimal scheduling scheme. In step S2, various typical types of user models are included, such as: park service center model, intelligent automated enterprise model and traditional enterprise model; The specific steps of step S4 are as follows: S41. Construct a multi-agent master-slave game decision-making model with multi-energy complementarity: The market is constructed as a Stackelberg game process, in which PIA acts as the leader, incentivizing users to actively participate in demand response by adjusting dynamic pricing strategies and scheduling strategies for ESS, CHP units, and GB units; users act as followers, adjusting their energy consumption behavior to maximize benefits after receiving PIA's strategies. During the game, PIA first initializes the dispatch strategies for ESS, CHP units, and GB, while simultaneously setting electricity sales prices, electricity purchase prices, and heat sales prices, and publishes this information to users. Subsequently, each user, based on the received strategy set and their own operational constraints and optimization objectives, optimizes their energy consumption plan through GUROBI to maximize their benefits, and submits the feedback results to PIA. Based on the users' strategies, PIA adjusts its strategies accordingly. and The strategy, including the one mentioned above, aims to maximize its benefits; PIA and users interact iteratively, constantly adjusting the strategy until it converges to the Stackelberg game equilibrium. S42. Distributed iterative method based on Adaptive Differential Evolution Algorithm (ADE): PIA guides users to optimize their energy consumption plans by dynamically adjusting the action strategies and price signals of ESS, CHP units, and GB units; users maximize their own benefits through local solution tools based on the strategy set provided by PIA; the above interaction process is continuously iterated until the game system converges to the Stackelberg equilibrium point. The Stackelberg game consists of the following components: the leader, PIA, and the followers; each participant's payoff is their objective function; and the interaction strategies include PIA's power supply output and energy price set. and users' net electricity and heat load When a set of strategies When a Stackelberg game equilibrium is reached, if no player can increase their own benefit by unilaterally changing their own strategy set, then that strategy set is the optimal scheduling scheme and must satisfy the following condition:

2. The PIES multi-agent game collaborative optimization method considering user differences as described in claim 1, characterized in that, The construction of the park service center model is as follows: The Park Service Center (PSC) includes fixed loads of electricity and heat, as well as flexible loads; a net load model for the PSC is established using equation (1): In the formula, k represents the load type, k∈{e,h}; This represents the net load value for the k-th type of load during time period t; This represents the fixed load of type k during time period t; This represents the load that can be reduced during time period t for the k-th type of load; This represents the transferable load of the k-th load type during time period t; This represents the alternative load for the k-th load during time period t; This represents the photovoltaic power generation during time period t. If k is h, then it is 0. ② Fixed load The electrical and thermal loads remain unchanged; ② It can reduce the load. The load can be reduced to a certain extent as needed, as shown in equations (2)–(4) below: In the formula, θ cut (t) is a 0-1 variable; γ t This is the reduction factor; To reduce the magnitude of the front load power; θ min and θ max The minimum and maximum number of load reductions; N max This is the maximum number of times a continuous reduction can be implemented; ③ Transferable load The time dimension can be transferred within the scheduling period, as shown in equations (5)–(8) below: In the formula, This represents the power available for load transfer before load regulation during time period t for the k-th type of load; These are binary variables, representing the transfer-in and transfer-out parameters of the transferable load of the k-th type of load during time period t, respectively; Let represent the transfer-in and transfer-out power of the k-th type of load during time period t, respectively; Equation (7) indicates that the total amount of each type of load remains unchanged within a scheduling cycle; These represent the upper and lower limits of the interaction amount of the k-th type of transferable load in each time period. This constraint is used to ensure the energy quality requirements of users. ④ Alternative loads As shown in equations (9)–(11): In the formula, These represent the electrical and thermal substitution load values ​​after the interaction; These represent the power of the electrical and thermal substitute loads before the interaction; These are binary variables, representing the input and output parameters of the electricity and heat substitution loads during time period t, respectively. These represent the input and output power of the electric and heat substitution loads during time period t, respectively. ⑤ Photovoltaics With the vigorous promotion of clean energy, a certain proportion of renewable photovoltaic power exists among most users; In summary, the cost E of PSC PCS It can be represented as: In the formula, For PSC's electricity and heat purchase costs, E PCS,e Here is the power consumption efficiency function for PSC; a1, b1, and c1 are the parameters of the power consumption efficiency function. These are the electricity sales price, electricity purchase price, and heat sales price set by PIA after a master-slave game. These represent the net electrical and thermal loads of the PSC, respectively.

3. The PIES multi-agent game collaborative optimization method considering user differences according to claim 2, characterized in that, The construction of the intelligent automation enterprise model is as follows: Intelligent automated enterprises, or APEs, include electrical loads, which are characterized by high power and transferability, and have a high proportion of PV on the source side; an APE net load model is established using equation (14): In the formula: This represents the electrical load of APE during time period t; This represents the fixed load of APE during time period t; This represents the transferable load of APE during time period t; This represents the photovoltaic power generation of APE during time period t; The cost of APE E APE It can be represented as: In the formula, For APE's electricity purchase cost, This is the power efficiency function for APE.

4. The PIES multi-agent game collaborative optimization method considering user differences according to claim 3, characterized in that, The construction of the traditional enterprise model is as follows: Traditional enterprises, or TE, include fixed loads of electricity and heat, as well as flexible loads. Flexible loads only include replaceable loads and also include electric boilers, which obtain heat energy through electric heating when electricity prices are low or electricity is plentiful. Establish the TE net load model using equation (17): In the formula: This represents the net load value of TE for the k-th type of load during time period t; This represents the fixed load of type k in time period t for TE; This represents the alternative load for the k-th type of load in time period t; K represents the power of the electric boiler during time period t. If k is e, it represents the power consumption; if k is h, it represents the power generation. An electric boiler heats water or an organic carrier inside the boiler to a certain temperature and pressure through resistance or electromagnetic induction, and then outputs heat energy. Its mathematical model is as follows: In the formula, This represents the electrical input power and thermal output power of the electric boiler during time period t. η EB This indicates the electrothermal conversion coefficient of the electric boiler; In summary, the cost of TE is E TE It can be represented as: In the formula, For TE's electricity and heat purchase costs, E TE,e Let TE be the power efficiency function. These represent TE net electrical and thermal loads, respectively.

5. The PIES multi-agent game collaborative optimization method considering user differences according to claim 4, characterized in that, The specific steps of step S2 are as follows: S21 and PIA utilize the heat and electricity generated by the CHP unit for user consumption. The relationship between the electrical power output through GT and the gas consumption can be expressed as: In the formula, For the power generation of GT, η e For the power generation efficiency of GT, H L It is a low-calorific-value natural gas. Natural gas consumed by GT This is the upper limit for power generation of the CHP unit; In a CHP unit, natural gas is burned via GT (Gas Torque) to generate electricity, and the waste heat discharged is recovered by WHB (Waste Heat Pump) for heating. Its heating model can be expressed as: In the formula, Let η be the exhaust waste heat of GT at time t. loss η is the heat loss rate. h For waste heat recovery efficiency, C represents the heating capacity of WHB. OP,h The flue gas recovery rate of WHB; S22. To optimize the operation of PIA equipment and provide flexible heating, GB, which has higher heating efficiency, is introduced. Its heating model is as follows: In the formula, For GB heating power, η GB,h The heating efficiency is GB. The natural gas consumed by GB These are the upper and lower limits of heating power specified in GB standards. The addition of ESS to S23 and PIA enables efficient energy sharing among users; considering the energy loss during charging and discharging, the relationship between state of charge and charging / discharging power can be defined as: In the formula, Let BT be the state of charge at time t. Let BT be the state of charge at time t-1. Let η be the charging and discharging power of BT at time t. ESS,chg η ESS,dis Let be the charging and discharging efficiency of BT at time t; Within any given time period, the state of charge and charging / discharging power of the ESS should be within a certain range, which can be defined as: In the formula, Indicates the upper and lower limits of the ESS state of charge. The upper limit of the charging and discharging power of the ESS; S24. In the electricity-heat market, the PIA's strategy set consists of the price of heat and electricity sold to users, and the purchase of excess photovoltaic power generated by users. The optimal selling price strategy set is determined using a master-slave game. The constraints on the electricity and heat prices set by the PIA are: In the formula, These refer to the electricity purchase price and the electricity sales price of the power grid, respectively. These are the upper and lower limits of the heating price, respectively, derived from historical data on user heating purchases.

6. The PIES multi-agent game collaborative optimization method considering user differences according to claim 5, characterized in that, The specific steps of step S3 are as follows: S31. Domestic quotas are allocated free of charge. The carbon emission sources in PIES include: upstream coal-fired power units, GT, and GB. The initial quota model is shown in the formula: In the formula, E a χ is the initial carbon allowance for the system. e , χ g Carbon quota coefficient for unit power and heat output. Let t be the power of electricity purchased from outside the park. Let GB be the heating power at time t; Let t represent the heating and power output of the CHP unit at time t; S32. Use equation (34) to establish a real carbon emission model: In the formula, E P E represents the system's actual carbon emissions. e,buy E represents the actual carbon emissions from electricity purchased by the higher-level authority. total This represents the actual carbon emissions of the CHP unit and the total emissions from GB. Let be the equivalent output power of the gas turbine unit during time period t; a2, b2, and c2 are the carbon emission calculation parameters for coal-fired power units; and a3, b3, and c3 are the carbon emission calculation parameters for natural gas-fired power units. This represents the amount of electricity that PIA purchases from the power grid; S33. Construct a reward-and-punishment tiered carbon trading model using formula (35): AND PIES =And P -AND a (36), In the formula, E CET Let E be the carbon trading cost of the system at time t, where a positive value represents the purchase quota and a negative value represents obtaining subsidies using the remaining quota; PIES E represents the actual carbon emissions of the park. P With the initial carbon quota E a The difference, k is the carbon trading base price on the day, α is the compensation coefficient, β is the price increase rate, and d is the length of the carbon emission range corresponding to each tier; S34. In the electricity-heat-carbon joint trading market, the profit function E of PIA PIA It is divided into the following parts: revenue from electricity and heat trading with users, costs of electricity trading with the grid, gas costs, equivalent lifetime loss costs of ESS, and costs generated by the CET mechanism: In the formula, The cost of electricity purchased from the grid by PIA; For PIA, the cost of purchasing gas from the gas network; μ g For gas purchase price; E SSD For the operating cost of PIA source-side equipment, λ ESS , λ CHP , λ GB For PIA's ESS, CHP units, and GB operating cost coefficients.

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