A bi-level game optimization method for integrated energy system considering prosumer response and uncertainty

Abstract

The application discloses a kind of comprehensive energy system double-layer game optimization method considering producer and consumer response and uncertainty.The strategy is first constructed to energy operator as leader, multiple producers and consumers as follower's master-slave game double-layer optimization model in view of the challenge that comprehensive energy system equilibrium scheduling needs to consider multiple subject interests and market price uncertainty.The lower layer producer and consumer react to upper layer price information, and construct comprehensive demand response model;At the same time, opportunity constraint and robust optimization method are used to deal with the uncertainty of new energy and price.Then, the double-layer model is converted into a single-layer model by Karush-Kuhn-Tucker condition, and the original double-linear non-convex problem is convexly relaxed and solved by using McCormick envelope method.Finally, based on energy contribution degree function, the reasonable distribution of additional benefits is realized.The application can effectively balance the benefits of energy operators and producers and consumers, reduce the fluctuation influence of uncertainty on the system, and is conducive to the overall development of comprehensive energy system.

Description

Technical Field

[0001] This invention relates to the field of energy sales, and more specifically, to a two-level game optimization method for a comprehensive energy system that considers producer-consumer responses and uncertainties. Background Technology

[0002] As the energy market shifts from a traditional vertically integrated structure to a competitive one, the distributed nature of Integrated Energy Systems (IES) is becoming increasingly apparent. Therefore, optimizing IES operations requires considering the interests of different stakeholders. In this context, traditional centralized optimization methods are insufficient to effectively describe the interactions between multiple stakeholders.

[0003] To address the complex economic behaviors among different stakeholders, the Stackelberg game has been widely used as an effective tool. Existing research often constructs a Stackelberg game model with energy operators (ESOs) as leaders and users or prosumers as followers. At the prosumer level, electricity exchange can also effectively reduce users' operating costs.

[0004] However, the operation of IES is affected by many uncertainties, especially the uncertainty of market electricity prices. To address the challenges posed by electricity price uncertainty, most existing studies generate sets of electricity price uncertainty scenarios using the probability density function of electricity prices. However, due to the complexity of the factors influencing the electricity market, it is difficult to obtain an accurate probability distribution of electricity prices.

[0005] Therefore, how to achieve balanced dispatch that takes into account the uncertainty of market electricity prices, while balancing the interests of energy operators, producers and consumers, and other stakeholders, is a challenge currently facing the field of integrated energy systems. Summary of the Invention

[0006] Technical problem to be solved: The present invention aims to solve the technical problems existing in the machine learning-based power load forecasting method, which are low prediction accuracy, poor generalization ability and insufficient robustness during special events (such as statutory holidays) due to the sparse sample of special events in historical data.

[0007] Technical Solution: To address the aforementioned technical problems, this invention proposes a two-level game optimization method for integrated energy systems that considers producer-consumer responses and uncertainties, comprising the following steps: A master-slave game model is constructed with an energy operator as the leader and multiple prosumers as followers. The leader sets energy prices to maximize its own benefits, and the followers respond to the price information and optimize their integrated demand response and energy purchase decisions to maximize their own benefits. Furthermore, when constructing the model, a robust optimization method is used to deal with the uncertainty of market electricity prices, and an opportunity-constrained programming method is used to deal with the uncertainty of renewable energy output. The two-layer game model is converted into a single-layer optimization model using the Karush-Kuhn-Tucker conditions; and The McCormick envelope method is used to perform convex relaxation on the bilinear nonconvex problem in the single-layer optimization model and then solve it. Calculate the incremental benefits generated by the interaction of electricity between producers and consumers; Based on the energy contribution function, the contribution of each producer and consumer in the interaction of electrical energy is calculated; and the incremental benefit is allocated according to the proportion of the contribution.

[0008] Furthermore, the objective function of the leader is to maximize its own benefit, which is equal to the energy transaction benefit with the prosumer minus the total cost of the energy operator. The total cost includes at least: fuel cost, renewable energy abandonment penalty cost, transaction cost with the distribution network, and electricity price fluctuation penalty cost.

[0009] Furthermore, robust optimization methods are employed to address electricity price uncertainty, including: Construct a minimum-maximum objective function; By employing strong duality theory and introducing auxiliary variables, the mini-maximum problem is transformed into a mini-minimum problem.

[0010] Furthermore, opportunity-constrained planning is used to address uncertainties in new energy sources, including: The power balance constraint is described in the form of a chance constraint. The chance constraint is transformed into a deterministic constraint form using the inverse function of the standard normal distribution.

[0011] Furthermore, the optimization model for the follower includes: The objective function is to maximize the benefits for prosumers, and the objective function includes energy efficiency, energy satisfaction loss cost, energy cost, and the penalty cost for prosumers to discard new energy sources. The constraints include a comprehensive demand response model that incorporates transferable electrical loads and reduceable heat loads, as well as energy interaction constraints between producers and consumers.

[0012] Furthermore, the price constraints set by the leader include: Control the electricity price between the grid purchase price and the retail price; and constrain the average energy price.

[0013] Furthermore, the energy contribution function is determined based on the total amount of electricity sold by the prosumer to all other prosumers and the total amount of electricity purchased from all other prosumers.

[0014] Beneficial effects Compared with existing technologies, First, this invention employs a master-slave game model to accurately depict the real market interaction between the leader (ESO) and followers (prosumers) in an Energy Saving System (IES): the ESO, as the leader, sets prices to maximize its own benefits, while the prosumers, as followers, respond to prices and optimize their own energy consumption strategies. This game structure ensures that the optimization result is an equilibrium solution reached through the interaction of both parties, rather than a compromise of one party's interests in traditional centralized optimization, thus achieving an effective balance of benefits for multiple stakeholders. Second, this invention innovatively and collaboratively utilizes two uncertainty handling methods in the model construction stage to improve the robustness and realism of the model. For the uncertainty of market electricity prices, where probability distributions are difficult to obtain, a robust optimization method is adopted, requiring only the confidence intervals of uncertain variables. By solving the worst-case mini-maximum problem, the risk resistance of ESO decisions under electricity price fluctuations is guaranteed. Simultaneously, for the uncertainty of renewable energy output, opportunity-constrained programming is used to transform power balance constraints into deterministic constraints that meet a certain confidence level, ensuring the reliability of system operation. Finally, this invention provides a clear and efficient solution path: Addressing the two-layer structure resulting from the master-slave game, the Karush-Kuhn-Tucker (KKT) conditions are used to transform the optimization problem of the lower-level producers into constraints on the upper-level leader, thus "reducing the dimensionality" of the two-layer model to a single-layer optimization model. For the bilinear non-convex problem arising from the product of price and demand after the KKT transformation, this invention further utilizes the McCormick envelope method to perform convex relaxation on this non-convex problem, ultimately transforming the original problem into an efficiently solvable mixed-integer linear programming model. In summary, this invention, through the organic coordination of master-slave game theory, handling of dual uncertainties, KKT transformation, and McCormick relaxation, achieves equilibrium of the interests of multiple stakeholders, effectively reduces the impact of uncertainty on system fluctuations, and ensures the solvability of complex models. Attached Figure Description

[0015] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This invention relates to the integrated energy system structure; Figure 2 This is a schematic diagram of the solution process of this invention; Figure 3 This is the initial electricity demand curve for producers and consumers according to the present invention; Figure 4 This is the initial heat load demand curve for producers and consumers in this invention; Figure 5This invention provides a forecasted power output curve for renewable energy sources for producers and consumers. Figure 6 This is the result of ESO power optimization in this invention; Figure 7 This is the result of ESO thermal energy optimization in this invention; Figure 8 This invention relates to the electricity pricing strategy of ESO; Figure 9 This invention relates to the thermal energy pricing strategy for ESO. Figure 10 This invention represents the result of electrical energy interaction between producers and consumers. Figure 11 This is the result of the demand response from consumer 2 in this invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0018] 1. Integrated Energy System Structure like Figure 1 As shown, this paper mainly studies integrated energy systems, which include energy production units, storage units and energy consumption units, and fully considers clean energy sources such as wind and solar power.

[0019] Energy operators' equipment includes gas turbines (GT), gas boilers (GB), electric energy storage (eEES), and thermal energy storage (TES), which can provide users with electricity and heat. Prosumers mainly include flexible loads for electricity and heat and renewable energy generation devices. Through electricity exchange, surplus electricity is transferred to other prosumers to improve the level of renewable energy consumption and maximize the overall benefits of prosumers.

[0020] 2. Two-level game optimization model for integrated energy system 2.1 Energy Operator Model 2.1.1 Objective Function As the leader of the entire IES, ESO sets electricity and heat purchase prices based on the electricity and heat purchase responses from producers and consumers to maximize its own benefits. The objective function is shown in equation (1).

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028] Where: Where: The total cost of ESO; for Fuel costs of gas turbines and gas boilers at all times; for The cost of discarding renewable energy sources at all times; for The transaction costs between ESO and the distribution network at any given time; for The cost of electricity price fluctuations for ESO at any given time; for The benefits of energy trading between ESO and producers / consumers at any given time; , The price at which ESO sells electricity and heat to producers and consumers; For natural gas prices; , The purchase and sale price of electricity traded with the power grid; Penalty coefficient for discarding new energy sources; This refers to the amount of renewable energy discarded. , For the community Purchase of electricity and heat; This is a parameter representing the uncertainty of electricity price deviation; For parameters related to periods of electricity price uncertainty, This indicates that the uncertainty of electricity prices was not taken into account. This indicates that the uncertainty of electricity prices at any given moment is taken into account. , These represent the power purchased and sold by the ESO and the upstream power grid, respectively.

[0029] The electricity market has a significant impact on IES's decision-making, and considering the uncertainty of market electricity prices is more in line with the actual operation of IES.

[17] Considering the uncertainty of electricity prices, a min-max objective function is used. The inner terms of the objective function give the worst-case electricity price, while the outer terms of the objective function are minimized.

[18] In equation (5), we can... Defined as a penalty term related to the real-time electricity market to mitigate its bias, maximizing this condition leads to finding the worst-case scenario in real-time prices. However, due to the complexity of the electricity market, the probability distribution of electricity prices is difficult to obtain.

[19] Robust optimization only requires knowledge of the confidence intervals of the uncertain variables, not the probability distribution function; therefore, the uncertainty of electricity prices can be described using robust optimization methods. An auxiliary variable is introduced to relax the price penalty term for easier solution, in the following form:

[0030]

[0031]

[0032]

[0033] In the formula: , These are the dual variables of equations (8) and (9), respectively. Using strong duality theory, this is transformed into a Min problem:

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] In the formula: An auxiliary variable is introduced to linearize the Min problem.

[0041] Then the objective function of the Min-Max problem in equation (1) after being transformed into a Min-Min problem is:

[0042] 2.1.2 Constraints (1) Price constraints.

[0043] To ensure that producers and consumers do not bypass the ESO and interact directly with the grid, electricity prices must be consistently controlled between the grid purchase price and the grid selling price. To prevent the ESO from maximizing its own profits and setting the highest possible prices for users, an average energy price constraint is needed, namely:

[0044]

[0045]

[0046]

[0047]

[0048] In the formula: , These represent the upper and lower limits of the price of thermal energy, respectively. , These are the average prices of electricity and heat sold by energy operators, respectively.

[0049] (2) Constraints on cogeneration.

[0050] Gas turbines generate both electricity and heat by burning natural gas. The electrothermal output and constraints of gas turbines are as follows:

[0051]

[0052]

[0053]

[0054] In the formula: , For the power generation and heating capacity of gas turbines; , These are the power generation and heating efficiency of the gas turbine, respectively. It has the low calorific value of natural gas; This refers to the gas consumption of the gas turbine. , , , These are the upper and lower limits of the power generation and heating capacity of the gas turbine, respectively. A gas-fired boiler burns natural gas for heating, and its heating power and constraints are as follows:

[0055]

[0056] In the formula: This refers to the heating power of the gas-fired boiler. These are the heating efficiencies of the gas-fired boilers; This refers to the gas consumption of a gas-fired boiler. , These are the upper and lower limits of the heating power of the gas-fired boiler.

[0057] (3) Energy storage constraints.

[0058] Energy storage constraints are as follows:

[0059]

[0060]

[0061]

[0062]

[0063]

[0064] In the formula: For energy storage devices The amount of electricity stored at any given time; , These represent the upper and lower limits of the state of charge of the energy storage device, respectively. , The charging and discharging efficiency of electrical energy storage; , They represent energy storage devices. The charging and discharging power at any given moment; , These are energy storage devices The charging and discharging flags at specific times; the constraints of thermal energy storage are similar to those of electrical energy storage, and will not be elaborated here.

[0065] (4) Power grid interaction constraints.

[0066] For an ESO to interact with the power grid, the following constraints must be met:

[0067]

[0068]

[0069] In the formula: , These are the upper limits for power purchase and sale for the IES and the upstream power grid, respectively; , These are the power purchase and sale status bits for the IES and the upstream power grid, respectively; This represents the equivalent interactive power between the IES and the upstream power grid.

[0070] (5) Consider the power balance constraint of new energy uncertainty.

[0071] The IES contains a large amount of renewable energy, and the uncertainty of its output poses a potential risk to dispatching.

[0072]

[0073] In the formula: Contribute to new energy; The predicted output value of new energy sources.

[0074] The actual output of wind and solar power is considered as the sum of the predicted value and random error, and it is assumed that in the day-ahead scheduling problem, the short-term error of wind and solar power is significant. It usually follows a normal distribution with a variance of . .

[0075]

[0076] Describe the power balance constraints under wind and solar uncertainties using opportunity constraints:

[0077] In the formula: Producers and consumers respectively i The demand for electricity; Given the confidence level, according to probability theory, the above chance constraint can be transformed into a definite form for computation.

[0078]

[0079] In the formula: It is the inverse function of the standard normal distribution.

[0080] (6) Thermal power balance constraint.

[0081]

[0082] In the formula: Producers and consumers respectively i The demand for heating.

[0083] 2.2 Prosumer Model 2.2.1 Objective Function In an Energy Component Regulator (IES), producers and consumers, under the management of energy operators, implement integrated demand response (ICR) for electricity and heat, optimizing available electrical loads and available heat loads at various times, and negotiating with energy operators to maximize benefits. This can be represented as:

[0084] In the formula: For producers and consumers Energy efficiency; For producers and consumers Costs related to energy satisfaction loss; For producers and consumers Energy costs; For producers and consumers The cost of penalties for discarding new energy sources.

[0085] For industrial or commercial users, increased energy consumption is often directly proportional to increased production output and profits.

[20] Therefore, the energy efficiency of a community can be expressed as...

[0086]

[0087] In the formula: , and , These represent the electricity efficiency coefficient and the heat efficiency coefficient, respectively. , These are demand response electrical load and demand response thermal load, respectively. Consumers' energy consumption is most comfortable before comprehensive demand response. After receiving energy instructions and adjusting energy consumption at different times, a loss of energy satisfaction is inevitable, which can be expressed as...

[0088] In the formula: , The energy satisfaction loss coefficient for the community; , Predict power for electrical and thermal loads; The energy purchase costs for producers and consumers and the penalty costs for discarding renewable energy can be expressed as:

[0089]

[0090] 2.2.2 Constraints (1) Constraints of the integrated demand response model of producers and consumers.

[0091] The flexible electrical and thermal loads within the IES include transferable electrical loads and reduceable thermal loads.

[21] The specific relevant constraints are as follows:

[0092]

[0093]

[0094]

[0095]

[0096] In the formula: , These are respectively the transferable electrical load power and the reduceable thermal load power; , These are the transferable electrical load rate and the reduceable heat load rate, respectively.

[0097] (2) Electrical energy interaction constraints.

[0098] The exchange of electricity between producers and consumers needs to ensure that the amount of exchange is within a certain limit, and that the transaction volume of producers and consumers is equal, that is:

[0099]

[0100] In the formula: This is a limit on the maximum amount of electrical energy exchanged between producers and consumers.

[0101] (3) Power balance constraint.

[0102]

[0103]

[0104] In the formula: For producers and consumers The new energy source is contributing power.

[0105] 3. Energy Operator-Producer-Consumer Master-Slave Game Model 3.1 Master-Slave Game Model In the IES framework proposed in this paper, both ESOs and prosumers are stakeholders with independent decision-making power, and their respective decisions affect each other's benefits or costs. ESOs maximize their benefits by optimizing unit output and energy pricing, while prosumers maximize their benefits by optimizing their energy purchase demand and demand response strategies. Since both parties' strategies are based on adjustments to each other's strategies, and ESOs, as energy sellers, have the ability to offer preferential pricing, this paper establishes a two-level game model between ESOs and prosumers based on master-slave game theory.

[0106] The basic elements of a game include participants, strategies, and payoffs. This master-slave game is defined as... The elements are explained as follows: (1) Participants.

[0107] Participant set Including energy operators (ESOs) and prosumers .

[0108] (2) Strategy.

[0109] , A strategy set for energy, including the selling price of electricity / heat energy containing ESO. / Power generation / heat generation of gas turbines / Heating power of gas boiler Power purchased from and sold to the power grid / Charging / discharging power of electrical energy storage The charging / discharging power of electrical energy storage / ; , For the strategy set of prosumers, their strategies Includes the electricity / heat purchase capacity submitted to the ESO by each producer and consumer during each scheduling period. / Instantaneous electrical / thermal load power of each producer and consumer Power transfer of electrical load between producers and consumers and heat load reduction power .

[0110] (3) Benefits.

[0111] ESO benefits Equations (1)-(6) represent the benefits for producers and consumers. It is represented by (39)-(43).

[0112] In the master-slave game model proposed in this paper, energy operators first make energy price decisions and release them to lower-level producers and consumers. The latter optimize their load demand and energy purchase decisions to achieve the best benefits, while simultaneously feeding their energy purchase demands back to the upper level. The energy operators then adjust their own strategies based on the decisions of the lower level and release them to the lower level again. This cycle continues until neither party can obtain greater benefits by adjusting their strategies, that is, the game equilibrium is reached. At this point, the strategies of each participant are the game equilibrium solutions.

[0113] 3.2 Solution Method The solution process is as follows Figure 2 As shown, the master-slave game model is a two-level nonlinear optimization model, which is mostly solved through iterative processes, resulting in a long solution time. When the upper-level price is given, the lower-level producer-consumer optimization model is linear. Therefore, according to linear optimization theory, the lower-level optimization model is transformed into KKT conditions as constraints for the upper level, thus converting the two-level optimization model into a single-level optimization model for solution.

[22] This transforms the two-level game model into a single-level optimization problem. Furthermore, the Big-M method is used to introduce Boolean variables, converting nonlinear constraints into linear constraints. Additionally, the literature...

[23] The McCormick envelope method in the upper-level objective function is used for bilinear terms. Convex relaxation is performed to obtain the mixed-integer linear programming model. The mixed-integer linear programming problem is solved using the commercial solver GUROBI 10.0 and the YALMIP toolbox in MATLAB 2021b.

[0114] 4. Benefits redistribution strategy Benefit redistribution mainly addresses the problem of maximizing the total benefit of producers and consumers after it has been solved.

[24] The incremental benefits after energy exchange are redistributed compared to before the exchange. The formula for the incremental benefits for producers and consumers before and after energy exchange is:

[0115]

[0116] In the formula: , Prosumers before and after interaction The benefits.

[0117] First, calculate the total energy provided and received by each producer and consumer during the optimization period. Second, the benefit redistribution is based on the contribution of each producer and consumer, taking into account time-of-use pricing. The energy contribution function is as follows:

[0118]

[0119]

[0120]

[0121] In the formula: For producers and consumers The degree of contribution; Representative of producers and consumers The total amount of electricity sold to all other producers and consumers; Producers and consumers The total amount of electricity purchased and distributed to all other producers and consumers.

[0122] Finally, the increased benefits resulting from the interaction of electricity between producers and consumers are distributed proportionally according to the proportion of each producer's contribution to the total contribution of all producers and consumers.

[0123] In the formula: For producers and consumers The ultimate benefit.

[0124] 5. Simulation Analysis 5.1 Case Setup The actual case study described in this article involves three producers and consumers, each equipped with renewable energy power generation equipment. Simulation parameters are set as follows: the initial load demand curves for each producer and consumer and the predicted renewable energy output are shown in [link to simulation parameters]. Figure 3 , Figure 4 as well as Figure 5 As shown, producer-consumer 1's renewable energy source is wind power. Producers-consumers 2 and 3, due to their high building density, are not well-suited for installing wind power resources, so their renewable energy source is mainly rooftop photovoltaic. The allowable trading volume between energy operators and producers-consumers is 2000kW above and below the allowable limit for each time period. The grid time-of-use electricity price is shown in Table 1; the initial uncertainty deviation coefficient for electricity prices is set at 0.1, and the initial number of uncertain time periods is set at 10.

[0125] To verify the effectiveness of the proposed method, the following different schemes were set up for comparative analysis.

[0126] Option 1: There is electrical energy interaction between producers and consumers, and the response of producers and consumers is considered, which is the method proposed in this paper; Option 2: There is no energy exchange between producers and consumers; consider producer-consumer responses. Option 3: There is electrical energy exchange between producers and consumers; producer-consumer responses are not considered. Option 4: There is no energy exchange between producers and consumers, and producer-consumer responses are not considered; Table 1 Time-of-use Electricity Prices for Power Purchase and Sale

[0127] 5.2 Analysis of Integrated Energy System Operation Results under Different Schemes The results of IES operation for different schemes are shown in Table 2: Table 2 Scheduling results under different scenarios

[0128] Comparing Schemes 1 and 2 in Table 1, we can see that Scheme 1's total producer-consumer benefit is 1474.61 yuan higher than Scheme 2. This is because Scheme 1 considers the electricity interaction among producer-consumers, fully utilizing the capacity structure characteristics of each producer-consumer to achieve multi-energy complementarity, reducing the producer-consumer's dependence on ESO, and consequently reducing the ESO benefit by 1020.2 yuan. Comparing Schemes 1 and 3, we can see that Scheme 1's comprehensive demand response, which considers the producer-consumer's overall demand response, results in a 33533.33 yuan increase in total producer-consumer benefit compared to Scheme 3, while reducing the ESO benefit by 1823.93 yuan. This is because without demand response, producer-consumers are more dependent on ESO, purchasing large amounts of energy when energy prices are high, leading to lower self-efficacy and increased ESO benefits. The introduction of demand response can shift load during periods of higher electricity prices, effectively improving the producer-consumer's efficiency. Comparing Schemes 1 and 4 reveals that Scheme 4, which does not consider the energy interaction and demand response between prosumers and consumers, results in the lowest benefit for prosumers and the strongest dependence on ESO. Therefore, the total benefit of ESO is increased by 2000.99 yuan. The comparison of the above schemes demonstrates that the model proposed in this paper effectively improves the benefits for prosumers and consumers. Furthermore, comparing the total benefit of IES in each scheme shows that Scheme 1 has the highest total benefit for IES, confirming the effectiveness of the method and contributing to the overall development of integrated energy systems.

[0129] 5.3 Energy Operator Decision Analysis Based on Scheme 1, the main decisions of the ESO include optimizing the output of each device within the IES, the power interaction with the upstream grid, and the energy prices published to producers and consumers. The optimization results for electrical and thermal energy in the ESO are as follows: Figure 6 , Figure 7 As shown. Regarding the optimization of electricity, during the period from 0:00 to 7:00, the electricity demand from prosumers is at a low level, and the demand is met by the gas turbines. During the period from 9:00 to 16:00, the electricity demand from prosumers is not high. In order to absorb more renewable energy, the gas turbines reduce their power generation accordingly, and the surplus electricity is sold to the upstream grid to maximize their own benefits. During the period from 19:00 to 22:00, when electricity prices are high, ESOs reduce their purchases from the grid and increase the power generation of gas turbines. The energy storage equipment is mainly charged during periods of low electricity prices or when renewable energy is being generated, and discharged during periods of high electricity prices. Regarding the optimization of thermal energy, ESOs mainly use gas turbines and gas boilers for heating. During the period from 9:00 to 16:00, the heat generation of gas turbines decreases. In order to meet the energy demand of downstream prosumers, the missing heat is provided by gas boilers. Excess heat is stored in thermal storage tanks and released when needed.

[0130] The energy trading prices for ESOs and producer-consumers are as follows: Figure 8 , Figure 9 As shown. By Figure 8As is known, ESO's electricity sales prices are all within the grid's purchase and sale price range at all times. Therefore, all producers and consumers can buy electricity at a price lower than the grid's sales price, while ESO sells electricity to producers and consumers at a price higher than the grid's purchase price. During the period from 18:00 to 22:00, ESO's electricity price is higher because, at this time, ESO purchases some electricity from the grid to meet the high demand from producers and consumers, leading to an increase in ESO's electricity sales price. Figure 9 It is evident that the ESO's heat energy price is typically set at its maximum value. Since producers and consumers lack heat production equipment, they can only accept the price set by the ESO. Compared to external prices, this is acceptable for both the ESO and the producers and consumers. In conclusion, compared to trading directly with the grid, producers and consumers can improve their efficiency by purchasing electricity and heat from the ESO and engaging in electricity exchange.

[0131] 5.4 Prosumer Decision Analysis Based on Scheme 1, the results of energy interaction between producers and consumers are as follows: Figure 10 As shown in the diagram. Prosumer 1 exhibits low electricity load and surplus wind power generation during the periods of 00:00-07:00 and 17:00-24:00, thus exhibiting a high-electricity-consumption pattern; during the period of 08:00-16:00, it exhibits a low-electricity-consumption pattern. Prosumer 2 exhibits insufficient photovoltaic power generation during the periods of 00:00-07:00 and 19:00-24:00, thus exhibiting a low-electricity-consumption pattern; during the period of 08:00-17:00, it exhibits a high-electricity-consumption pattern. Prosumer 3 exhibits a high-electricity-consumption pattern during the periods of 10:00, 15:00-17:00, and 21:00, and a low-electricity-consumption pattern during the remaining periods.

[0132] Due to space limitations, this analysis will focus on the demand response strategies of producer-consumer 2 as an example. The demand outcome for producer-consumer 1 is as follows: Figure 11 As shown, regarding the load transfer, Prosumer 1's total load demand during the periods of 0:00-8:00 and 19:00-24:00 is greater than the original load demand. However, the load during the period of 9:00-18:00 is significantly lower than the original load demand. This is mainly because wind power output is sufficient at night. Prosumer 1 transfers the load from the power shortage period (daytime 9:00-18:00) to the nighttime to meet the demand through wind power output, and shares the surplus electricity with other prosumers. During the power shortage period, electricity prices are at their peak. Prosumer 1 can reduce electricity costs and maximize benefits by trading electricity with other (photovoltaic) prosumers. Analyzing the heat load reduction, Prosumer 1 experiences a significant heat load reduction during the period of 7:00-20:00. This is consistent with Prosumer 1's original heat load curve and... Figure 4 According to the ESO heat price, most of the heat energy during this period is provided by gas boilers, which leads to an increase in heat price. As a result, consumer 1 reduces its heat load during the 7:00-20:00 period, thus reducing its heat purchase cost.

[0133] 5.5 Analysis of the Results of Benefit Redistribution Based on Scheme 1, the energy interaction quantities obtained from the above-mentioned problem of maximizing the benefits of prosumers are substituted into the contribution function of time-sharing energy mapping to obtain their respective contributions. Then, the additional benefits obtained after prosumer interaction can be further redistributed according to these contributions to maximize the benefits. The results are shown in Table 3. As shown in Table 3, the total benefits of prosumers increased by 1474.96 yuan through energy interaction. Among them, the benefits of prosumer 1 increased from 44943.47 yuan to 44419.86 yuan; the benefits of prosumer 2 increased from 30071.59 yuan to 30737.08 yuan; and the benefits of prosumer 3 increased from 21555.40 yuan to 22888.47 yuan.

[0134] Table 3. Results of the Reasonable Allocation of Producer-Consumer Energy Interaction Benefits

[0135] Although the benefits of interaction improved for all producers and consumers, the combination of... Figure 7 It can be seen that there is an unreasonable distribution of benefits among the prosumers. Therefore, further redistribution of benefits is needed. First, by inputting the energy interaction information after sharing the results into the energy contribution function, the contribution ratio of each prosumer can be calculated. Then, the benefits are distributed to each prosumer according to their respective contribution ratios, achieving a reasonable redistribution of benefits. Ultimately, the benefits of prosumer 1 increased from 44943.47 yuan to 45781.67 yuan, an increase of 838.19%; the benefits of prosumer 2 increased from 30071.59 yuan to 30439.70 yuan, an increase of 368.10%; and the benefits of prosumer 3 increased from 21555.40 yuan to 21824.05 yuan, an increase of 268.65%. This demonstrates that a reasonable distribution of benefits is achieved among the prosumers, confirming that the benefits redistribution advantage of this model is more prominent.

[0136] 5.6 The impact of uncertainty on the system Tables 4 and 5 show the impact of the electricity price deviation coefficient and the number of periods of electricity price deviation on the benefits of energy operators and producers / consumers under Scheme 1. It can be seen that as the electricity price deviation coefficient gradually increases from 0.10 to 0.19, the benefits of energy operators and producers / consumers gradually decrease, indicating that the increased penalty for electricity price fluctuations leads to a significant increase in the risk corresponding to the integrated energy system, resulting in reduced benefits for the main stakeholders. As the number of periods of electricity price uncertainty increases from 5 to 20, electricity prices will fluctuate at more times, thus reducing the benefits for energy operators and producers / consumers. Table 6 shows that as the confidence level of new energy uncertainty increases from 0.85 to 0.98, the returns of ESOs and individual producers / consumers continuously increase. This indicates that under the constraint of new energy output opportunity, the system's ability to cope with the uncertainty risk of new energy output is improved at the cost of sacrificing returns.

[0137] Table 4. Analysis of the impact of the uncertainty coefficient of electricity price in Scheme 1 Table 5. Analysis of the Impact of the Number of Periods of Electricity Price Uncertainty in Scheme 1 Table 6. Analysis of the impact of uncertainty confidence level on new energy under Scheme 1 6 Conclusions To address the multi-stakeholder nature of integrated energy systems and the system volatility caused by market electricity price uncertainty, this paper proposes a two-layer game-theoretic optimization strategy for integrated energy systems that considers producer-consumer responses and uncertainty. The constructed energy operator-producer-consumer master-slave game model effectively balances the impact of decisions made by energy operators and various producers-consumers, aligning with the efficiency requirements of multiple stakeholders. Energy operators implement differentiated energy management for different producers-consumers through electricity price decisions, effectively improving the overall efficiency of the integrated energy system. Opportunity constraints and robust optimization methods effectively reduce the impact of uncertainties in renewable energy and electricity prices on system volatility, better reflecting the actual operational scenarios of future integrated energy systems. Producers-consumers, based on electricity price decisions, conduct integrated demand response and achieve local consumption of renewable energy. Furthermore, producers-consumers' integrated demand response and electricity interaction have advantages in improving efficiency and help reduce their energy dependence on energy operators.

[0138] In summary, the embodiments of the present invention provide a solution with fundamental advantages over existing technologies in predicting power load for special events by introducing a series of non-obvious combinations of multi-source knowledge bases, deep metric learning, and dynamic weighted prior construction.

Claims

1. A two-level game optimization method for a comprehensive energy system considering producer-consumer responses and uncertainties, characterized in that, Includes the following steps: A master-slave game model is constructed with an energy operator as the leader and multiple prosumers as followers. The leader sets energy prices to maximize its own benefits, and the followers respond to the price information and optimize their integrated demand response and energy purchase decisions to maximize their own benefits. Furthermore, when constructing the model, a robust optimization method is used to deal with the uncertainty of market electricity prices, and an opportunity-constrained programming method is used to deal with the uncertainty of renewable energy output. The two-layer game model is converted into a single-layer optimization model using the Karush-Kuhn-Tucker conditions; and The McCormick envelope method is used to perform convex relaxation on the bilinear nonconvex problem in the single-layer optimization model and then solve it. Calculate the incremental benefits generated by the interaction of electricity between producers and consumers; Based on the energy contribution function, the contribution of each producer and consumer in the interaction of electrical energy is calculated; And the incremental benefit is allocated according to the proportion of the contribution.

2. The method according to claim 1, characterized in that, The objective function of the leader is to maximize its own benefits, which are equal to the benefits of energy transactions with producers and consumers minus the total costs of the energy operator. The total costs include at least: fuel costs, renewable energy abandonment penalty costs, transaction costs with the distribution network, and electricity price fluctuation penalty costs.

3. The method according to claim 1 or 2, characterized in that, Robust optimization methods for addressing electricity price uncertainty include: Construct a minimum-maximum objective function; By employing strong duality theory and introducing auxiliary variables, the mini-maximum problem is transformed into a mini-minimum problem.

4. The method according to claim 1, characterized in that, Opportunity-constrained planning is used to address uncertainties in new energy sources, including: The power balance constraint is described in the form of a chance constraint. The chance constraint is transformed into a deterministic constraint form using the inverse function of the standard normal distribution.

5. The method according to claim 1, characterized in that, The optimization model for the follower includes: The objective function is to maximize the benefits for prosumers, and the objective function includes energy efficiency, energy satisfaction loss cost, energy cost, and the penalty cost for prosumers to discard new energy sources. The constraints include a comprehensive demand response model that incorporates transferable electrical loads and reduceable heat loads, as well as energy interaction constraints between producers and consumers.

6. The method according to claim 1, characterized in that, The price constraints set by the leader include: Control the electricity price between the grid purchase price and the retail price; and constrain the average energy price.

7. The method according to claim 1, characterized in that, The energy contribution function is determined based on the total amount of electricity sold by a producer to all other producers and the total amount of electricity purchased from all other producers.

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