Distribution network-multi-integrated energy system distributed optimization scheduling method considering interval uncertainty and multi-agent game

Abstract

A power distribution network-multi-integrated energy system distributed optimization scheduling method considering interval uncertainty and multi-agent game comprises the following steps: representing fluctuation characteristics of a distributed power supply and a load by adopting an interval number, and establishing a multi-agent game model with robustness; a dynamic electricity price transaction mechanism based on Nash bargaining is constructed, the income requirements of all subjects in the DN-MIES system are met, and system benefit balance is achieved; the MVA-ATC algorithm is proposed based on the interval information of the source load uncertainty to carry out distributed iterative solution, and the main body privacy is guaranteed while the solution efficiency is improved. For the problem of benefit distribution after the MIES alliance is accessed to the power distribution network, the invention provides a DN-MIES mixed game distributed optimization method considering multi-subject benefits, so that benefit distribution of the power distribution network accessed to multiple IESs is realized, and benefit balance during cooperative operation of the power distribution network and the multiple IESs is effectively guaranteed; meanwhile, an MVA-ATC distributed solving algorithm is provided by utilizing interval uncertainty and an ATC algorithm, so that the solving efficiency of the model is improved, and meanwhile, the fluctuation of the source load is stabilized.

Description

Technical Field

[0001] This invention relates to the field of integrated energy system optimization scheduling technology, specifically to a distributed optimization scheduling method for distribution networks and multiple integrated energy systems that considers interval uncertainty and multi-entity game theory. Background Technology

[0002] In existing technologies, integrated energy systems (IES) coupling multiple heterogeneous energy sources have become an important form of efficient energy utilization now and in the future. Interconnecting geographically proximate IESs to form multi-integrated energy systems (MIES) can improve the reliability, efficiency, low carbon emissions, and economy of MIE operation through energy mutual assistance and coordinated optimization control. The distribution network with MIEs (DN-MIES) thus becomes a complex network, and the superiority of MIEs depends on the coordinated optimization and control of each IES. Traditional dispatching modes are no longer applicable, posing new challenges to the dispatching of DN-MIES.

[0003] To address the challenges of source-load uncertainty, imbalance in the distribution of benefits among multiple stakeholders, and slow solution in the collaborative optimization of multi-energy systems (MIES) and distribution networks (DN), a distributed optimization scheduling strategy based on hybrid game theory and improved objective cascade analysis is proposed. First, interval numbers are used to characterize the fluctuation characteristics of distributed power sources and loads, establishing a robust multi-stakeholder game model. Second, a two-layer collaborative architecture of DN-MIES is constructed, and a dynamic electricity price trading mechanism is established by integrating a Nash bargaining model to solve the problems of multi-stakeholder benefit equilibrium and market incentive compatibility. Furthermore, an objective cascade algorithm based on maximum variation analysis (MVA-ATC) is designed to simultaneously handle uncertainty and the need for efficient solution during the distributed solution process. Simulation results show that this method has significant advantages in improving system economy, ensuring the balance of benefits among stakeholders, and reducing computational complexity, providing theoretical support and technical pathways for the collaborative optimization of multiple energy stakeholders in new power systems.

[0004] The uncertainties of the DN-MIES system mainly stem from errors in wind speed, solar intensity, and load forecasting. These factors make it difficult to determine the precise probability distribution of the uncertainty parameters. However, the boundary values ​​of these parameter fluctuations are relatively easy to obtain.

[0005] Game theory is often used to deal with the interest relationships among multiple entities in the DN-MIES joint system. However, single cooperative game is prone to over-pursuing overall interests and ignoring individual demands, as recorded in references [1] and [2]. Non-cooperative game is prone to imbalance of benefits among entities when maximizing individual benefits, as recorded in references [3] and [4]. For this reason, existing studies mostly use hybrid game to meet the balance of interests among multiple entities in the system. In references [5] and [6], an optimization strategy that considers the economic interests of producers and consumers and microgrids is proposed based on hybrid game to consider multi-energy coupling and shared energy storage. In order to further consider the impact of multi-entity market transactions in integrated energy, references [7] and [8] construct a two-layer energy management model based on hybrid game to meet the requirements of the balance of interests of the integrated energy system in the park and maximize the benefits of multiple entities. In order to effectively promote the local consumption of new energy and reduce the operating cost of energy storage, reference [9] proposes a multi-regional power-storage sharing operation mode based on hybrid game for the problem of sharing of power and energy storage resources in multiple regions. Reference

[10] considers the conflict of interests and information asymmetry among different subjects and proposes a two-layer energy trading strategy based on hybrid game theory.

[0006] Although the above studies have achieved multi-agent interaction through hybrid game theory, there is still a lack of in-depth exploration of the impact of market transactions on the economics among multiple agents, especially the electricity price-interest coupling mechanism.

[0007] Literature [1]: ZHOU Yanting, MAZhongjing, SHI Xingyu, et al. Multi-agent optimal scheduling for integrated energy system considering the global carbonemission constraint [J]. Energy, 2024, 288: 129732.

[0008] Literature [2]: WU Yanjuan, WANG Caiwei, WANG Yunliang. Cooperative gameoptimization scheduling of multi-region integrated energy system based on ADMM algorithm [J]. Energy, 2024, 302: 131728.

[0009] Reference [3]: Yin Chenxu, Sun Yonghui, Xie Dongliang, et al. Multi-objective collaborative optimization of integrated energy system with electric-gas interconnection from the perspective of game theory [J]. Automation of Electric Power Systems, 2024, 48(11):173-183.

[0010] Literature [4]: ​​WANG Zibo, DONG Lei, SHI Mengjie, et al. Market power modeling and restraint of aggregated prosumers in peer-to-peer energy trading: Agame-theoretic approach [J]. Applied Energy, 2023, 348: 121550.

[0011] Reference [5]: Wang Zeqi, Jia Yanbing, Han Xiaoqing, et al. Two-layer hybrid game optimization of microgrid considering producer-consumer response and uncertainty [J]. Power System Technology, 2024, 48(07):2754-2764.

[0012] Reference [6]: Lin Mohan, Liu Jia, Tang Zao, et al. Multi-agent hybrid game coordination optimization of microgrid with multi-energy coupling and shared energy storage [J]. Automation of Electric Power Systems, 2024, 48(04): 132-141.

[0013] Literature [7]: LIANG Ziwen, MU Longhua.Multi-agent low-carbon optimaldispatch of regional integrated energy system based on mixed game theory[J]. Energy, 2024, 295: 130953.

[0014] Reference [8]: Wang Yi, Jin Zikang, Wang Yaoqiang, et al. Coordinated optimization operation of integrated energy system in park based on hybrid game theory and shared energy storage characteristics of electric vehicles [J]. High Voltage Engineering, 2025, 51(02):135-145.

[0015] Reference [9]: Zhang Jun, Zhong Kanghua, Zhang Yongjun, et al. Analysis of the economic benefits of multi-regional power-storage sharing operation mode based on hybrid game theory [J]. Automation of Electric Power Systems, 2024, 48(03):31-41.

[0016] Reference

[10] : Yang Dongfeng, Wang Yilin, Yang Shihui et al. Energy trading strategy based on hybrid game theory for multi-microgrid-shared energy storage dual-layer [J]. High Voltage Engineering, 2024, 50(04): 1392-1402. Summary of the Invention

[0017] To address the problems of source-load uncertainty, imbalance in the distribution of benefits among multiple stakeholders, and low solution efficiency in DN-MIES collaborative optimization, this invention proposes a distributed optimization scheduling method for distribution network-multi-energy integrated systems that considers interval uncertainty and multi-stakeholder game theory. This method constructs a multi-stakeholder game framework for the distribution network-multi-energy integrated system: First, it introduces interval numbers to represent source-load uncertainty, constructing a robust two-layer optimization model; second, it constructs a dynamic electricity price trading mechanism based on Nash bargaining to meet the revenue requirements of each stakeholder in the DN-MIES system and achieve system benefit equilibrium; finally, based on the interval information of source-load uncertainty, it proposes the MVA-ATC (maximum variation analysis based analytical target cascading) algorithm for distributed iterative solution, improving solution efficiency while protecting stakeholder privacy.

[0018] The technical solution adopted in this invention is as follows:

[0019] A distributed optimization scheduling method for distribution networks and multi-integrated energy systems, considering interval uncertainties and multi-stakeholder game dynamics, includes the following steps:

[0020] Step 1: Use interval numbers to characterize the fluctuation characteristics of distributed power sources and loads, and establish a robust multi-agent game model;

[0021] Step 2: Construct a dynamic electricity price trading mechanism based on Nash negotiation to meet the revenue requirements of all stakeholders in the DN-MIES system (distribution network with mies, DN-MIES) and achieve a balance of system interests;

[0022] Step 3: Based on the interval information of source load uncertainty, the MVA-ATC (maximum variation analysis based analytical target cascading) algorithm is proposed for distributed iterative solution, which improves the solution efficiency while protecting the privacy of the subject.

[0023] In step 1, the range of fluctuation of the uncertainty parameter is described using the interval number method, as follows:

[0024] 1) Based on historical wind power data, as shown in Table 1, the wind power output range with time statistical characteristics is obtained from the output of wind turbines.

[0025] Table 1 Historical Wind Power Data

[0026] time 1 2 3 4 5 6 7 8 power 338.333 461.667 440 551.667 228.333 135 120 235 time 9 10 11 12 13 14 15 16 power 71.667 20 33.333 20 8.333 80 143.333 576.667 time 17 18 19 20 21 22 23 24 power 478.333 883.333 818.333 746.667 1000 995 671.667 633.333

[0027] Within the wind power output range, the upper and lower limits of wind power output fluctuations are respectively... P WT Then the power range of the wind turbine is P' WT Uncertainty θ WT,t They are represented as follows:

[0028]

[0029]

[0030] In the above formula: Let t be the predicted output of the wind turbine.

[0031] 2) Uncertainty θ of photovoltaic output PV,t Represented as:

[0032]

[0033] In the above formula: Predict photovoltaic output at time t; This indicates the upper limit of wind power output fluctuation; P PV This indicates the lower limit of wind power output fluctuation.

[0034] 3) Uncertainty θ of electrical load L,t Represented as:

[0035]

[0036] In the above formula: Forecast load demand at time t; P L Indicates the lower limit of load fluctuation; This indicates the upper limit of load fluctuation.

[0037] Therefore, the source and load uncertainty model is as follows:

[0038]

[0039] In the above formula: P WT,t P PV,t and P L,t These represent wind and solar power output and load demand at time t, respectively.

[0040] Figure 1 The DN-MIES energy flow topology shown represents the multi-entity collaborative operation mechanism of the system:

[0041] The market-based energy base minimizes the operating costs of the Multi-Integrated Energy System (MIES) by coordinating the optimal allocation of multi-energy flows among various Integrated Energy Systems (IES) and regulating the energy exchange between the distribution network (DN) and the MIE via tie lines. The market-based energy base primarily controls the energy distribution among multiple IES through a remote control system.

[0042] In this architecture, the distribution network, as the upper-level grid operator, maximizes overall revenue by dynamically optimizing the power purchase and sale strategy, as shown in equations (4) and (10). Each integrated energy system, as a distributed energy source, constructs a revenue-maximizing optimized operation mode of the DN-IES alliance by adjusting the multi-energy flow allocation ratio, including equations (20) to (22), based on its multi-energy coupling characteristics and load demand response characteristics.

[0043] This multi-entity collaborative mechanism essentially constitutes a non-cooperative game process under bidirectional energy flow constraints: the distribution network DN takes the maximization of operating revenue as the objective function, and the maximization of the distribution network DN revenue is shown in equation (4); the MIES alliance takes the maximization of the comprehensive energy revenue itself as the optimization orientation, and the two parties form a strongly coupled game equilibrium condition through the interaction of tie line power; the maximization of the MIES alliance revenue is shown in equation (10).

[0044] In the multi-agent game model established in step 1, the upper layer takes the maximization of the distribution network operator's revenue as the objective function, including equations (4) to (9); the lower layer takes the maximization of the self-interest of the multi-IES system as the objective, including equations (10) to (12).

[0045] Multi-Integrated Energy Systems (MIES) are both energy producers and consumers. Distribution network operators set time-of-use pricing based on net load peak and valley periods to guide MIES responses to their peak shaving and valley filling scheduling needs.

[0046] For IES operators, power transactions with the distribution network are conducted to maximize profits while meeting their own load demands. In a Multi-Integrated Energy System (MIES), each IES forms a cooperative alliance, achieving mutual benefit and win-win results through energy sharing, and conducting bilateral power transactions with the distribution network through the MIE. This helps improve the IES's demand response capability to the distribution network, reduces the energy supply pressure on the distribution network, and ensures the smooth operation of the system. The distribution network and IES are different stakeholders with their own operational goals, but there is a high degree of similarity among the various IES entities. Therefore, in joint scheduling, this invention uses game theory to describe the optimal scheduling relationship between the distribution network and the integrated energy system IES, employing a master-slave game approach. Based on cooperative game theory, an IES alliance scheduling model is constructed, including equations (10) to (12), thus forming a multi-entity game scheduling framework for the "distribution network-IES alliance." Figure 2 As shown.

[0047] Distribution network operators set electricity prices as the dominant force, while follower IES operators formulate their own operating strategies through time-of-use pricing distributed across the distribution network. At the same time, they cooperate and redistribute revenue within the Multi Integrated Energy System (MIES). The optimization results are then fed back to the dominant force, and through repeated game theory, a globally optimal strategy is achieved.

[0048] The objective function is as follows:

[0049] (1) Objective function of distribution network operator:

[0050] Distribution network operators aim to maximize operational efficiency. DI For the goal:

[0051]

[0052] In the above formula: F DSO Indicates the revenue of the distribution network; This indicates that the power distribution network operator is maximizing operational efficiency; For system network loss costs; For the carbon trading cost of the distribution network; C buy The cost of purchasing electricity from the upper-level power grid for the distribution network; C dg The penalty cost for curtailment of wind and solar power generation by renewable energy units; m represents the m-th IES in the MIES alliance system; M represents the number of IES in the MIES alliance system. t represents time; T represents the intraday period. λ b,t / λ s,t These represent the electricity purchase / sale price of IES at time t; P b,m,t / P s,m,t These represent the amount of electricity purchased / sold by IES at time t, respectively. These are the penalty cost coefficients for curtailing wind and solar power, respectively. These represent the wind and solar power consumed during time period t, respectively. These are the active power loss of the line and the cost per unit power loss, respectively.

[0053] D s,fre Carbon emission allowances for power distribution networks. Ω l Indicates a power distribution network tie line; Ω s Let represent the set of nodes in the distribution network; α is the unit price of carbon emissions in the distribution network; β is the carbon emission coefficient per unit power in the distribution network. This represents the output power of each node in the distribution network; Indicates internet access power; P WT,t P represents the power output of the wind turbine during time period t; PV,t This represents the photovoltaic power during time period t.

[0054] (2) IES operator objective function:

[0055] IES operators aim to maximize their own profits. IES For the goal:

[0056]

[0057] In the above formula: F IES This indicates the revenue of the IES operator. Indicates the IES carbon trading cost; Represents the transmission cost between the i-th IES and the j-th IES; a D b D c D These represent the energy production cost coefficients for different equipment D; P D,t C represents the power generation of device D during time period t; pass P represents the grid transfer fee when IES operators trade electricity with each other; α and β are the grid transfer fee conversion factors that IES operators need to pay when trading electricity with each other; ij,t The power consumption during the time period t when each IES operator trades with each other.

[0058] The constraints are as follows:

[0059] 1) Distribution network power flow constraints:

[0060]

[0061] In equation (13): P ij,t Q ij,t P represents the active and reactive power flowing from node i to node j at time t; jk,t Q jk,t These represent the active and reactive power flowing from node i to node k at time t, respectively. These are the active and reactive power of the load at node j at time t, respectively. These represent the active power consumed by the P2G, gas boiler, and battery at node j at time t, respectively. These represent the wind turbine and photovoltaic outputs at node j at time t, respectively. These are the active and reactive power generated by the m-th combined heat and power plant at node j at time t, respectively. These represent the active and reactive power generated by the m-th conventional unit at node j at time t, respectively; r ij x ij V represents the resistance and reactance of the line from node i to node j, respectively; j,t Vj and V0 are the voltage and standard voltage of node j at time t, respectively. These are the maximum and minimum values ​​of the voltage at node j at time t, respectively. These represent the wind turbine and photovoltaic outputs at node j at time t, respectively. Let t represent the active power consumed by the battery at node j at time t; k represents node k in the distribution network.

[0062] 2) Output constraints of IES internal coupling devices:

[0063]

[0064] In equation (14): This represents the output of the i-th conventional device at time t; This represents the output power of the i-th CHP at time t; This represents the output power of the i-th GB at time t; This represents the power consumed by the i-th p2g at time t; This represents the charging and discharging power of the i-th energy storage unit at time t; This represents the interaction power between the m-th IES and the distribution network at time t; This represents the upper and lower limits of the output of the i-th conventional device; This represents the upper and lower limits of the output of the i-th CHP; This represents the upper and lower limits of the output of the i-th GB; These are the upper and lower limits of P2G power consumption, respectively. These are the upper and lower limits of energy storage charging and discharging power, respectively. These are the upper and lower limits of the power trading for IES and the distribution network, respectively.

[0065] 3) Equipment ramping constraints within IES:

[0066]

[0067] In equation (15): These are the ramp rates for conventional generating units, CHP, GB, P2G, and energy storage, respectively. This represents the output of the i-th conventional device at time t-1; This represents the output power of the i-th CHP at time t-1; This represents the output power of the i-th GB at time t-1; This represents the power consumed by the i-th p2g at time t-1; It represents the energy storage charging and discharging power at time t-1.

[0068] 4) Price constraints in electricity trading:

[0069] To avoid IES (Internet Industry Association) purchasing electricity from higher-level grids, the electricity price sold by the distribution network should be lower than the price of the electricity from the higher-level grid, as shown in equation (16):

[0070]

[0071] In equation (16): λ represents the upper limit of the marginal electricity price at the distribution network. b,t Represented as the electricity purchase price of IES; λ s,t This is represented as the electricity price in the IES.

[0072] Meanwhile, considering that the distribution network dominates pricing power in the game, in order to protect the interests of users, the IES electricity sales price is constrained as shown in equation (17):

[0073]

[0074] In equation (17): For the average λ s,t The maximum value.

[0075] 5) Power interaction constraints:

[0076] To ensure the interests of all stakeholders and the operational stability of DN-MIES, P ij,t Should meet:

[0077]

[0078] In equation (18): P b,m,t P represents the amount of electricity purchased by IES; s,m,t P represents the electricity sold by IES; ies,max P represents b,m,t The maximum value of P; ij,max This represents the maximum power of interaction between IES.

[0079] Within the MIE, each IES complements its energy supply through a connecting bus, achieving multi-energy mutual assistance. To ensure the interests of each IES are protected, the following rules are established: When an IES with excess energy transfers energy to an IES with a shortage of energy, the amount transferred cannot exceed its own excess energy; conversely, when an IES with a shortage of energy receives energy, the amount received cannot exceed its own energy deficit. Specific constraints are as follows:

[0080]

[0081] In equation (19): P m,1,t Let P be the load deficit of the m-th IES. A value greater than 0 indicates that the IES needs to purchase electricity, while a value less than 0 indicates that it is available for sale. ij,t P represents the power transferred from the i-th IES to the j-th IES at time t; ji,t This represents the power transmitted from the j-th IES to the i-th IES at time t.

[0082] 6) Electrical, thermal, and gas power balance constraints:

[0083]

[0084] In the above formula: This represents the output of the i-th conventional device at time t; This represents the output power of the i-th CHP at time t; Indicates the power purchased by the distribution network; Ω represents the power consumed by the i-th P2G at time t; ies Represents a set of IES; These are the electrical and thermal loads of the IES at time t, respectively. These refer to the power of the electric and thermal energy storage devices, respectively. These are the upper and lower limits of the gas source output.

[0085] This indicates the thermal power provided by CHP; This indicates the thermal power provided by GB; Indicates the gas power of CHP; Indicates the gas power of GB; This indicates the gas power of the P2G.

[0086] In step 2, the dynamic electricity price trading mechanism based on Nash bargaining is shown in equation (33).

[0087]

[0088] In step 3, since the dynamic trading mechanism based on Nash bargaining is a non-convex nonlinear optimization problem, it cannot be solved directly;

[0089] Therefore, the above cooperative game problem is transformed into two sub-problems: maximizing social benefits and maximizing payment benefits, as shown in equations (23) and (24). The optimal strategy for maximizing social benefits is the same as the optimal strategy in the Nash bargaining problem. The social benefits of this invention are defined as the sum of the payoffs of MIES.

[0090]

[0091]

[0092] In the above formula: F IES,m Z represents the revenue and cost of the m-th IES; m Let m be the bargaining benefit offset of the m-th IES;

[0093] In equation (24), the variable marked with "*" is the optimal value obtained from equation (23); the variable marked with "0" is the value when the IES negotiations break down.

[0094] This invention uses the ATC multi-level system architecture to analyze the transformed model, which includes equations (23) to (24); the relevant ATC multi-level system architecture is as follows: Figure 10 As shown.

[0095] The first step is to separate the distribution network from the MIE (Multi-Instrument System): In this process, the distribution network treats the power of the tie lines as virtual loads. IES, on the other hand, treats the power of the same tie line as the output of a virtual power plant.

[0096] The second step, at the upper level of the system, is that after optimizing its operation plan, the distribution network transmits the tie-line power to the IES; the third step, at the lower level of the system, is that the IES, based on the tie-line power provided by the distribution network... Optimization is performed, and the results are fed back to the distribution network. It is important to note that because the system involves parameters with interval uncertainties, the coupling variables are no longer fixed values ​​but possess a degree of uncertainty.

[0097] A two-layer system optimization framework is proposed based on the MVA-ATC algorithm, where the upper-layer distribution network optimization framework is shown in Equation (25).

[0098]

[0099] In equation (25): f dn This indicates the deviation in operating costs of the upper-level distribution network. This indicates the operating cost of the upper-level power distribution network; Inequality constraint functions; Represents the equality constraint function; X dn Indicates the cost type of the upper-level distribution network; Indicates the baseline control variable; u dn Error range; P dn,m Indicates the output power of the tie line; Represents the tie-line power provided by the distribution network; ||·|| represents the vector norm, the degree of quantization bias; π m ω m ζ is the positive weight coefficient of the deviation term; ζ is a coordination factor to balance the convergence error and coupling differences between the master and subsystems, adjusting the weight of the constraint function so that the constraint function better meets the requirements to obtain a robust solution.

[0100] Similarly, the optimization framework of the lower-level IES is shown in Equation (26).

[0101]

[0102] In equation (26): f ies,m Indicates the operating cost of the lower-level IES; X m Indicates the IES cost type; Indicates the deviation penalty term; P m,dn Indicates the power of interaction with the distribution network; This represents the reference interactive power of the upper-level distribution network; This represents the bias penalty term for the lower-level IES; ω m t This represents the deviation weighting coefficient; Indicates the baseline control variable; △g m Indicates uncertainty deviation; △h m Indicates the deviation of the equality constraint; △f m Indicates the deviation in IES operating costs; p m Indicates the crosslink switching power; u m Indicates the range of deviation; g m (X m U m () indicates an inequality constraint; h represents the baseline value for inequality constraints. m (X m U m () represents an equality constraint; The reference value representing the equality constraint;

[0103] C dn (X m U m () indicates operating costs; A benchmark value representing operating costs;

[0104] According to the above method, the following convergence conditions must be met during the iterative process to obtain the optimal solution of the system.

[0105]

[0106] ||ε1||+||ε2||≤ε (29); Where ε1 and ε2 are the system coupling variable deviation and the system benefit variation, respectively; ε is the convergence error constant; This indicates the interaction power between the distribution network and the IES; This indicates the power received by the IES from the distribution network. This represents the operating cost of the distribution network at the k-th iteration; This represents the (k-1)th power distribution network operating cost; This represents the cost of the k-th IES run; Ω represents the cost of the (k-1)th IES run; m This represents a collection of IES alliance systems.

[0107] When they satisfy equation (29), the system reaches the optimal state; otherwise, the weight coefficients are updated according to equation (30).

[0108] k is the step size, and generally k∈[2,3].

[0109]

[0110] In equation (30): This represents the cumulative deviation of IES at the k-th iteration; This represents the cumulative deviation of IES at the (k-1)th iteration; This represents the weighting coefficient of the k-th IES; This represents the weighting coefficient of the (k-1)th IES;

[0111] Based on the convergence criterion obtained from the MVA-ATC algorithm, it is known that two conditions need to be considered: convergence of coupled variables and convergence of system benefit changes. However, in addition to energy output regulation optimization, electricity price is also one of the game-related aspects considered in this invention. Therefore, in addition to satisfying the convergence condition shown in equation (29), it is also necessary to control and optimize the electricity price, which needs to satisfy the following convergence condition:

[0112] ||λ b,k -λ b,k-1 ||+||λ s,k -λ s,k-1 ||≤ε3 (31);

[0113] In equation (31): λ b,k λ represents the electricity purchase price of the distribution network in the k-th iteration; b,k-1 λ represents the electricity purchase price of the distribution network in the (k-1)th iteration; s,k λ represents the electricity price sold by the distribution network in the k-th iteration; s,k-1 ε represents the electricity price sold in the distribution network during the (k-1)th iteration; ε3 is the allowable error for price changes.

[0114] If the convergence condition is not met, the transaction price shall be updated according to formula (32):

[0115]

[0116] In equation (32): λ is the electricity price adjustment factor. b,t,k λ represents the electricity purchase price of the distribution network in the k-th iteration; s,t,k λ represents the electricity price of the distribution network in the k-th iteration; b,t,k-1 λ represents the electricity purchase price of the distribution network in the (k-1)th iteration; s,t,k-1 This represents the electricity sales price of the distribution network in the (k-1)th iteration; This indicates the interaction power between the distribution network and the IES; This indicates the power received by the IES from the distribution network.

[0117] As can be seen from the convergence form of the above equation, the convergence trend of the traded electricity volume and the electricity price is the same.

[0118] The solution process for the fmincon function in MVA-ATC nested in MATLAB is as follows: Figure 3 As shown, the process includes the following steps: Step 1: Initialize parameters, including coupling variables between the distribution network and MIES, and electricity price;

[0119] Step 2: Each IES independently participates in the distribution network optimization scheduling, specifically including equations (10) to (12), and the optimization results are used as the negotiation breakdown point for subsequent game optimization scheduling.

[0120] Step 3: Perform DN-MIES master-slave game optimization. After the distribution network master problem is optimized nonlinearly, the electricity price and coupled power parameters are passed to the lower-level MIES, specifically including equations (23) to (25).

[0121] Step 4: Solve the MIES subproblems in the lower-level MIES to optimize scheduling, specifically including equation (26).

[0122] Step 5: Each IES entity allocates an effective cooperation allocation based on Nash bargaining according to the benefits of alliance cooperation and the negotiation breakdown parameters obtained in Step 2. Specifically, this includes equations (27) to (28). If a cooperation equilibrium is reached, proceed to the next step; otherwise, return to Step 4.

[0123] Step 6: Determine whether the data obtained from the upper and lower layers meet the convergence condition, i.e., equation (29). If it does, output the optimal result; otherwise, update the electricity price and weight coefficient according to equation (32) and return to Step 3 until the condition is met.

[0124] This invention provides a distributed optimization scheduling method for a distribution network-multi-integrated energy system that considers interval uncertainty and multi-agent game theory. The technical effects are as follows:

[0125] (1) The introduction of the MIES alliance into the distribution network and the formulation of purchase and sale electricity prices through the Nash negotiation mechanism have promoted the economic benefits between IES and between the distribution network and IES in the system.

[0126] (2) Regarding the issue of benefit distribution after the MIES alliance is connected to the distribution network, this invention proposes a distributed optimization method of DN-MIES hybrid game that considers the interests of multiple stakeholders, which realizes the benefit distribution of the distribution network connected to multiple IES and effectively ensures the balance of interests when the distribution network and multiple IES operate in coordination.

[0127] (3) By utilizing interval uncertainty and ATC algorithm, an MVA-ATC distributed solution algorithm is proposed to improve the solution efficiency of the model and smooth out the source load fluctuation. Attached Figure Description

[0128] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0129] Figure 1This is a schematic diagram of the distribution network-multi-IES structure and energy flow.

[0130] Figure 2 Distribution network - a multi-stakeholder game framework with multiple IES.

[0131] Figure 3 A flowchart for solving multi-player game problems.

[0132] Figure 4 This is a diagram of the electrical and thermal loads of MIE.

[0133] Figure 5 The daily curves of wind, light, and load for IES1 under uncertainty.

[0134] Figure 6 This is a diagram showing the electricity purchase and sale prices for the power distribution network.

[0135] Figure 7 This is the power balance diagram for IES3.

[0136] Figure 8 This is the thermal power balance diagram for IES3.

[0137] Figure 9 To optimize electricity pricing results.

[0138] Figure 10 This is a diagram of the ATC system architecture. Detailed Implementation

[0139] Verification Example:

[0140] The structure selected in this invention is as follows Figure 1 The DN-MIES coalition system shown is analyzed, and the distribution network of the IEEE 33 nodes is improved using three typical IES accesses in industrial, commercial and residential areas. The DG output cost coefficient is shown in Table 2.

[0141] Table 2 Renewable Energy Related Parameters

[0142] type Unit capacity (kW) Operation and maintenance costs (RMB / kWh) Photovoltaics 50 0.15 Fan 50 0.2

[0143] Basic data for each IES load, such as Figure 4 As shown, the range of fluctuations in the uncertainty parameters of wind, solar, and load forecasts is described by the interval number. Figure 5As shown, wind power output is higher and fluctuates drastically during the nighttime period from 0:00 to 6:00, while output decreases during the daytime period from 12:00 to 18:00, but fluctuations are still significant. Photovoltaic output is affected by solar radiation intensity, with output only occurring from 6:00 to 20:00, and the peak output occurring between 12:00 and 14:00 at noon. The load of IES1 exhibits a typical daily pattern, with the morning peak between 8:00 and 10:00, the midday trough between 12:00 and 14:00, and the evening peak between 18:00 and 22:00.

[0144] Time-of-use electricity pricing, such as Figure 6 As shown, during the off-peak period from 00:00 to 6:00, the electricity purchase price of the distribution network is relatively high (0.8-1.0 yuan / kWh), while the electricity sales price is relatively low (0.4-0.6 yuan / kWh). During this period, IES (Environmentally Independent Systems) may purchase electricity during the low-price period through energy storage or flexible equipment to reduce operating costs. During the peak period from 18:00 to 21:00, the electricity sales price of the distribution network increases significantly to 1.2 yuan / kWh. The distribution network incentivizes IES to sell electricity during the peak period through high prices to alleviate load pressure, while purchasing electricity at low prices reduces costs.

[0145] Parameters for carbon trading and equipment are shown in Table 3.

[0146] Table 3 Some parameters of IES operation

[0147]

[0148] Based on the multi-agent game strategy of the DN-MIES system proposed in this invention, this section analyzes the actual operation of IES3 as an example. Figure 7 , Figure 8 The figures shown are the system electrical and thermal power balance diagrams for IES3.

[0149] Figure 7 During the 0:00-8:00 electricity period, wind power is abundant while distribution network electricity prices are low. IES3 meets its load demand by supporting renewable energy output and purchasing electricity from the distribution network. Simultaneously, it provides surplus electricity within the system to P2G equipment for electricity-to-gas conversion, supplying more natural gas energy to CHP, GB, and other equipment, and also sells it to other IES systems. Furthermore, IES3 has a relatively large electrical load. To pursue system operational economy, the output of unit CHP_A is always at maximum. This is because unit CHP_A is more efficient than CHP_B and operates on a "heat-driven power generation" model, thus unit CHP_A is always at full capacity. Secondly, due to the ramp-up constraints and higher production costs of conventional units, IES3 tries to purchase electricity from the distribution network and other IES systems during periods of low trading prices to meet user electricity demand and reduce the output of the three conventional units. Figure 7It can be seen that IES3 interacts with other IES during 0:00-5:00 and 11:00-19:00. This is because when meeting the load of IES3, priority is given to the consumption of internal new energy sources. At the same time, in order to maximize the benefits of its own system, more efficient power generation equipment is used first, and then the load is met through interaction with other IES.

[0150] Figure 8 In terms of heating capacity, CHP units are less flexible and have weaker adjustment capabilities compared to GB units. Therefore, the heat output of CHP units fluctuates less. In order to meet the heat power balance, GB units mainly undertake the adjustment task and adjust the heat output according to the heat load. Figure 8 The CHP_A unit has a higher thermal output than the CHP_B unit during different time periods because the CHP_A unit has a higher thermal conversion efficiency. Therefore, the output of the CHP_A unit is prioritized to improve energy efficiency while meeting the system's heat load requirements. Meanwhile, since IES3 is equipped with thermal energy storage, the heat load is relatively low between 11:00 and 20:00. During this period, the energy storage device stores thermal energy and releases it during peak heat load periods of 2:00-4:00 and 20:00-23:00, reducing heat load pressure and achieving peak shaving and valley filling of the system's heat load, thus improving the system's economic efficiency.

[0151] (1) Analysis of the optimization results of cooperative game theory in DN-MIES:

[0152] To verify the superiority of the DN-MIES multi-agent game optimization model proposed in this invention.

[0153] Strategy 1: Each IES participates independently in the distribution network scheduling process;

[0154] Strategy 2: All IES participate in the collaboration, but Nash bargaining is not used to distribute benefits during the collaboration;

[0155] Strategy 3: In the strategy proposed in this invention, MIES participates in the form of cooperative game and distributes the benefits generated by cooperation through the Nash negotiation mechanism.

[0156] Table 4. Operating Costs of Each IES under the Three Strategies

[0157] Operating cost / yuan <![CDATA[IES1]]> <![CDATA[IES2]]> <![CDATA[IES3]]> MIES Strategy 1 342810 10965 304321 658096 Strategy 2 339395 21284 295209 655988 Strategy 3 340654 10386 300367 651407

[0158] This invention sets up three different strategies, and their corresponding operating costs are shown in Table 4. In Strategy 1, the three typical IES entities—industrial, commercial, and residential—operate independently, each responsible only for its own users. Therefore, the operating costs of each IES vary greatly depending on the user's energy consumption scenario and demand. In Strategy 2, the IES engage in cooperative game theory, with decisions among the IES influencing each other. Ultimately, through cooperation and negotiation, the total cost of the MIE is reduced by 2108 yuan compared to Strategy 1. However, the operating cost of IES 2 is significantly increased by 10319 yuan, which may lead to the breakdown of the cooperative alliance and its independent operation. In Strategy 3 proposed in this invention, the influence of the distribution network is added to the alliance of IES, and the transaction pricing and Nash negotiation mechanism of the distribution network are introduced to further influence the interaction of interests among different entities in the alliance system. As a result, the total cost of the MIE alliance is lower than that of Strategy 1 and Strategy 2, and the operating costs of each IES member under this invention's strategy are lower than the operating costs of the independent entities in the previous two strategies. Therefore, the hybrid game strategy based on Nash bargaining proposed in this invention can more effectively improve the economic benefits of multi-agent systems compared with non-cooperative game strategies and traditional cooperative game strategies.

[0159] (2) Uncertainty Optimization Analysis

[0160] To verify the optimized control of system uncertainty and low carbon emissions under the game-theoretic coupling relationship of this invention, and thus the impact on the economic efficiency of system scheduling, the following four scenarios are set up for comparative analysis.

[0161] Scenario 1: Fixed electricity price, without considering uncertainties, carbon trading, etc., each IES operates independently.

[0162] Scenario 2: Fixed electricity price, considering the impact of uncertainties, carbon trading, etc., each IES operates independently.

[0163] Scenario 3: Fixed electricity price, considering uncertainties, carbon trading, and other factors, with various IES operating collaboratively.

[0164] Scenario 4: Under the strategy of this invention, which takes into account the impact of uncertainty, carbon trading, etc., each IES operates in cooperation.

[0165] Table 5. Optimization results under different scenarios

[0166] Total operating cost / yuan Carbon trading cost / yuan Carbon emissions / kg Wind curtailment and solar curtailment rates (%) Scene 1 1847713 -- 105961 16.6 Scene 2 2272711 6347 105810 10 Scene 3 1916165 6085 101364 7.3 Scene 4 839911 5810 99113 5.6

[0167] Table 5 shows the optimization results under four different scenarios. It can be seen that compared to the system optimization in Scenario 1, which does not consider uncertainty or carbon trading, Scenario 2, by supplementing unit output to mitigate source-load output fluctuations, resulted in a total operating cost increase of 424,998 yuan, while the renewable energy utilization rate significantly increased by 6.6%. Although increased unit output leads to increased carbon emissions, Scenario 2 considers the impact of the carbon trading mechanism, minimizing system carbon emissions as much as possible, thus reducing carbon emissions by 151 kg compared to Scenario 1. In Scenario 3, the cooperative operation of each IES promotes multi-energy coupling and complementary utilization of the system. Compared to Scenario 2, the operating cost decreased by 424,998 yuan, the carbon trading cost decreased by 262 yuan, carbon emissions decreased by 4,446 kg, and the wind and solar curtailment rates decreased by 2.7%. In Scenario 4, considering the game-theoretic scheduling between the distribution network and IES, and among the various IES, the interaction and rational allocation of benefits among the subsystems in the coupled system are promoted, thereby further improving the system's wind and solar absorption rate and its economic efficiency and low-carbon characteristics.

[0168] Based on the game-theoretic optimization strategy described in this invention, the equilibrium result of optimizing the time-of-use pricing of the distribution network is as follows: Figure 9 As shown, the distribution network ensures profitability by optimizing electricity pricing and setting purchase and sale prices for the integrated energy system. Meanwhile, to obtain better prices within the alliance system, the IES consistently sets its distribution network prices lower than those of the upper-level grid. Specifically, from 0:00 to 8:00, as predicted earlier regarding renewable energy output, wind power generation in the distribution network is high, leading to oversupply and thus low electricity prices. Furthermore, the IES's purchase and sale prices to the distribution network are almost identical. From 12:00 to 16:00 and from 20:00 to 23:00, user demand is high, and energy supply is tight, meaning wind and solar power output is insufficient to offset load demand; therefore, purchase and sale prices are at peak times. Outside of these periods, from 9:00 to 12:00 and from 16:00 to 20:00, electricity supply and demand are generally balanced, and the set prices fall between the peak and off-peak prices of the upper-level grid. In general, the game-like scheduling between the distribution network and the IES causes electricity prices to fluctuate at every moment, but the trend of electricity sales prices is consistent with the trend of time-of-use electricity prices on the grid, while the trend of electricity purchase prices is consistent with load demand, so as to ensure the economic benefits of all parties.

[0169] This invention studies the coordinated operation problem of distribution network and MIES, and introduces game theory to construct a DN-MIES multi-agent alliance hybrid game scheduling optimization model, realizing multi-agent collaborative optimization scheduling between distribution network and IES, and between IES and IES.

Claims

1. A distributed optimization scheduling method for distribution network-multi-integrated energy system considering interval uncertainty and multi-agent game, characterized in that... Includes the following steps: Step 1: Use interval numbers to characterize the fluctuation characteristics of distributed power sources and loads, and establish a robust multi-agent game model; Step 2: Construct a dynamic electricity price trading mechanism based on Nash negotiation to meet the revenue requirements of all stakeholders in the DN-MIES system and achieve a balance of system interests; Step 3: Based on the interval information of source load uncertainty, the MVA-ATC algorithm is proposed for distributed iterative solution, which improves the solution efficiency while protecting the privacy of the subject.

2. The distributed optimization scheduling method for distribution network-multi-integrated energy system considering interval uncertainty and multi-agent game as described in claim 1, characterized in that: In step 1, the range of fluctuation of the uncertainty parameter is described using the interval number method, as follows: Based on historical wind power data, a wind power output range with time-based statistical characteristics is obtained for the wind turbine's output. Within this range, the upper and lower limits of wind power output fluctuations are respectively... P WT Then the power range of the wind turbine is P' WT Uncertainty θ WT,t They are represented as follows: In the above formula: The predicted output of the wind turbine at time t; 2) Uncertainty θ of photovoltaic output PV,t Represented as: In the above formula: Predict photovoltaic output at time t; This indicates the upper limit of wind power output fluctuation; P PV This indicates the lower limit of wind power output fluctuation; 3) Uncertainty θ of electrical load L,t Represented as: In the above formula: Forecast load demand at time t; P L Indicates the lower limit of load fluctuation; Indicates the upper limit of load fluctuation; Therefore, the source and load uncertainty model is as follows: In the above formula: P WT,t P PV,t and P L,t These represent wind and solar power output and load demand at time t, respectively.

3. The distributed optimization scheduling method for distribution network-multi-integrated energy system considering interval uncertainty and multi-agent game as described in claim 2, characterized in that: The multi-agent game model established in step 1 includes the following objective function: (1) Objective function of distribution network operator: Distribution network operators aim to maximize operational efficiency. DI For the goal: In the above formula: F DSO Indicates the revenue of the distribution network; This indicates that the power distribution network operator is maximizing operational efficiency; For system network loss costs; For the carbon trading cost of the distribution network; C buy The cost of purchasing electricity from the upper-level power grid for the distribution network; C dg The penalty cost for curtailment of wind and solar power generation by renewable energy units; m represents the m-th IES in the MIES alliance system; M represents the number of IES in the MIES alliance system; t represents the time; T represents the intraday period; λ b,t / λ s,t These represent the electricity purchase / sale price of IES at time t; P b,m,t / P s,m,t These represent the amount of electricity purchased / sold by IES at time t, respectively. These are the penalty cost coefficients for curtailing wind and solar power, respectively. These represent the wind and solar power consumed during time period t, respectively. These are the active power loss of the line and the cost per unit power loss, respectively. D s,fre For distribution network carbon emission quotas; Ω l Indicates a power distribution network tie line; Ω s Let represent the set of nodes in the distribution network; α is the unit price of carbon emissions in the distribution network; β is the carbon emission coefficient per unit power in the distribution network. This represents the output power of each node in the distribution network; Indicates internet access power; P WT,t P represents the power output of the wind turbine during time period t; PV,t This represents the photovoltaic power during time period t; (2) IES operator objective function: IES operators maximize their own profits F IES For the goal: In the above formula: F IES This indicates the revenue of the IES operator. Indicates the IES carbon trading cost; Represents the transmission cost between the i-th IES and the j-th IES; a D b D c D These represent the energy production cost coefficients for different equipment D; P D,t C represents the power generation of device D during time period t; pass P represents the grid transfer fee when IES operators trade electricity with each other; α and β are the grid transfer fee conversion factors that IES operators need to pay when trading electricity with each other; ij,t The power consumption during the time period t when each IES operator trades with each other.

4. The distributed optimization scheduling method for distribution network-multi-integrated energy system considering interval uncertainty and multi-agent game as described in claim 3, characterized in that: The objective function constraints are as follows: 1) Distribution network power flow constraints: In equation (13): P ij,t Q ij,t P represents the active and reactive power flowing from node i to node j at time t; jk,t Q jk,t These represent the active and reactive power flowing from node i to node k at time t, respectively. These are the active and reactive power of the load at node j at time t, respectively. These represent the active power consumed by the P2G, gas boiler, and battery at node j at time t, respectively. These represent the wind turbine and photovoltaic outputs at node j at time t, respectively. These are the active and reactive power generated by the m-th combined heat and power plant at node j at time t, respectively. These represent the active and reactive power generated by the m-th conventional unit at node j at time t, respectively; r ij x ij V represents the resistance and reactance of the line from node i to node j, respectively; j,t Vj and V0 are the voltage and standard voltage of node j at time t, respectively. These are the maximum and minimum values ​​of the voltage at node j at time t, respectively. These represent the wind turbine and photovoltaic outputs at node j at time t, respectively. Let be the active power consumed by the battery at node j at time t; k represents node k in the distribution network. 2) Output constraints of IES internal coupling devices: In equation (14): This represents the output of the i-th conventional device at time t; This represents the output power of the i-th CHP at time t; This represents the output power of the i-th GB at time t; This represents the power consumed by the i-th p2g at time t; This represents the charging and discharging power of the i-th energy storage unit at time t; This represents the interaction power between the m-th IES and the distribution network at time t; This represents the upper and lower limits of the output of the i-th conventional device; This represents the upper and lower limits of the output of the i-th CHP; This represents the upper and lower limits of the output of the i-th GB; These are the upper and lower limits of P2G power consumption, respectively. These are the upper and lower limits of energy storage charging and discharging power, respectively. These are the upper and lower limits of the power trading capacity for IES and the distribution network, respectively. 3) Equipment ramping constraints within IES: In equation (15): These are the ramp rates for conventional generating units, CHP, GB, P2G, and energy storage, respectively. This represents the output of the i-th conventional device at time t-1; This represents the output power of the i-th CHP at time t-1; This represents the output power of the i-th GB at time t-1; This represents the power consumed by the i-th p2g at time t-1; This represents the charging and discharging power of the i-th energy storage unit at time t-1; 4) Price constraints in electricity trading: To avoid IES (Internet Industry Association) purchasing electricity from higher-level grids, the electricity price sold by the distribution network should be lower than the price of the electricity from the higher-level grid, as shown in equation (16): In equation (16): λ represents the upper limit of the marginal electricity price at the distribution network. b,t Represented as the electricity purchase price of IES; λ s,t The electricity price is represented as the IES price. Meanwhile, considering that the distribution network dominates pricing power in the game, in order to protect the interests of users, the IES electricity sales price is constrained as shown in equation (17): In equation (17): For the average λ s,t The maximum value; 5) Power interaction constraints: To ensure the interests of all stakeholders and the operational stability of DN-MIES, P ij,t Should meet: In equation (18): P b,m,t P represents the amount of electricity purchased by IES; s,m,t P represents the electricity sold by IES; ies,max P represents b,m,t The maximum value of P; ij,max This represents the maximum power of interaction between IES.

5. The distributed optimization scheduling method for distribution network-multi-integrated energy system considering interval uncertainty and multi-agent game as described in claim 4, characterized in that: Within the MIE, each IES complements its energy through a connecting bus, achieving multi-energy mutual assistance. To ensure the interests of each IES are protected, the following rules are established: When an IES with excess energy transfers energy to an IES with a shortage of energy, the amount transferred cannot exceed its own excess energy; simultaneously, when an IES with a shortage of energy receives energy, the amount received cannot exceed its own energy deficit. The specific constraints are as follows: In equation (19): P m,1,t Let P be the load deficit of the m-th IES. A value greater than 0 indicates that the IES needs to purchase electricity, while a value less than 0 indicates that it is available for sale. ij,t P represents the power transferred from the i-th IES to the j-th IES at time t; ji,t This represents the power transmitted from the j-th IES to the i-th IES at time t; 6) Electrical, thermal, and gas power balance constraints: In the above formula: This represents the output of the i-th conventional device at time t; P represents the output power of the i-th CHP at time t; t m Indicates the power purchased by the distribution network; Ω represents the power consumed by the i-th P2G at time t; ies Represents a set of IES; These are the electrical and thermal loads of the IES at time t, respectively. These refer to the power of the electric and thermal energy storage devices, respectively. These are the upper and lower limits of the gas source output; This indicates the thermal power provided by CHP; Indicates the thermal power provided by GB; Indicates the gas power of CHP; Indicates the gas power of GB; This indicates the gas power of the P2G.

6. The distributed optimization scheduling method for distribution network-multi-integrated energy system considering interval uncertainty and multi-agent game as described in claim 5, characterized in that: In step 2, the dynamic electricity price trading mechanism based on Nash bargaining is shown in equation (33); 7. The distributed optimization scheduling method for distribution network-multi-integrated energy system considering interval uncertainty and multi-agent game as described in claim 6, characterized in that: In step 3, since the dynamic trading mechanism based on Nash bargaining is a non-convex nonlinear optimization problem, it cannot be solved directly; Therefore, the cooperative game problem is transformed into two sub-problems: maximizing social benefits and maximizing payment benefits, as shown in equations (23) and (24); where the optimal strategy for maximizing social benefits is the optimal strategy for the Nash bargaining problem, and social benefits are defined as the sum of the payoffs of MIES; In the above formula: F IES,m Z represents the revenue and cost of the m-th IES; m Let m be the bargaining benefit offset of the m-th IES; In equation (24), the variable marked with "*" is the optimal value obtained from equation (23); the variable marked with "0" is the value when the IES negotiations break down.

8. The distributed optimization scheduling method for distribution network-multi-integrated energy system considering interval uncertainty and multi-agent game as described in claim 7, characterized in that: The transformed model, which includes equations (23) to (24), was analyzed using the ATC multi-level system structure. The first step is to separate the distribution network from the MIE (Multi-Instrument System): In this process, the distribution network treats the power of the tie lines as virtual loads. IES, on the other hand, treats the power of the same tie line as the output of a virtual power plant. The second step is that, at the upper level of the system, after optimizing its own operation plan, the distribution network transmits the tie-line power to the IES; Third, at the lower level of the system, IES determines the tie-line power provided by the distribution network. The optimization is performed, and the results are sent back to the distribution network.

9. The distributed optimization scheduling method for distribution network-multi-integrated energy system considering interval uncertainty and multi-agent game as described in claim 8, characterized in that: A two-layer system optimization framework is proposed based on the MVA-ATC algorithm, where the upper-layer distribution network optimization framework is shown in Equation (25). In equation (25): f dn This indicates the deviation in operating costs of the upper-level distribution network. This indicates the operating cost of the upper-level power distribution network; Inequality constraint functions; Represents the equality constraint function; X dn Indicates the cost type of the upper-level distribution network; Indicates the baseline control variable; u dn Error range; P dn,m Indicates the output power of the tie line; Represents the tie-line power provided by the distribution network; ||·|| represents the vector norm, the degree of quantization bias; π m ω m ζ is the positive weight coefficient of the deviation term; ζ is a coordination factor to balance the convergence error and coupling differences between the master and subsystems, and to adjust the weight of the constraint function so that the constraint function better meets the requirements to obtain a robust solution. Similarly, the optimization framework of the lower-level IES is shown in Equation (26); In equation (26): f ies,m Indicates the operating cost of the lower-level IES; X m Indicates the IES cost type; Indicates the deviation penalty term; P m,dn Indicates the power of interaction with the distribution network; This represents the reference interactive power of the upper-level distribution network; This represents the bias penalty term for the lower-level IES; ω m,t This represents the deviation weighting coefficient; Indicates the baseline control variable; △g m Indicates uncertainty deviation; △h m Indicates the deviation of the equality constraint; △f m Indicates the deviation in IES operating costs; p m Indicates the crosslink switching power; u m Indicates the range of deviation; g m (X m U m ) represents an inequality constraint; Indicates the baseline value of the inequality constraint; h m (X m U m () represents an equality constraint; The reference value representing the equality constraint; C dn (X m U m () indicates operating costs; A benchmark value representing operating costs; According to the above method, the following convergence conditions must be met during the iterative process in order to obtain the optimal solution of the system; Where ε1 and ε2 are the system coupling variable deviation and the system benefit variation, respectively; ε is the convergence error constant; This indicates the interaction power between the distribution network and the IES; This indicates the power received by the IES from the distribution network. This represents the operating cost of the distribution network at the k-th iteration; This represents the (k-1)th power distribution network operating cost; This represents the cost of the k-th IES run; Ω represents the cost of the (k-1)th IES run; m Represents a set of IES alliance systems; When they satisfy equation (29), the system reaches the optimal state; otherwise, the weight coefficients are updated according to equation (30). k is the step size; In equation (30): This represents the cumulative deviation of IES at the k-th iteration; This represents the cumulative deviation of IES at the (k-1)th iteration; This represents the weighting coefficient of the k-th IES; This represents the weighting coefficient of the (k-1)th IES; Based on the convergence criterion obtained from the MVA-ATC algorithm, it is known that two conditions need to be considered: convergence of coupled variables and convergence of system benefit changes. However, in addition to energy output regulation optimization, electricity price is also one of the game-related factors. Therefore, in addition to satisfying the convergence condition shown in equation (29), it is also necessary to control and optimize the electricity price, which needs to satisfy the following convergence condition: ||l b,k -l b,k-1 ||+||l s,k -l s,k-1 ||≤ε3 (31); In equation (31): λ b,k λ represents the electricity purchase price of the distribution network in the k-th iteration; b,k-1 λ represents the electricity purchase price of the distribution network in the (k-1)th iteration; s,k λ represents the electricity price sold by the distribution network in the k-th iteration; s,k-1 ε represents the electricity price sold in the distribution network during the (k-1)th iteration; ε3 is the allowable error for price changes; If the convergence condition is not met, the transaction price shall be updated according to formula (32): In equation (32): λ is the electricity price adjustment factor. b,t,k λ represents the electricity purchase price of the distribution network in the k-th iteration; s,t,k λ represents the electricity price of the distribution network in the k-th iteration; b,t,k-1 λ represents the electricity purchase price of the distribution network in the (k-1)th iteration; s,t,k-1 This represents the electricity sales price of the distribution network in the (k-1)th iteration; This indicates the interaction power between the distribution network and the IES; This indicates the power received by the IES from the distribution network. As can be seen from the convergence form of the above equation, the convergence trend of the traded electricity volume and the electricity price is the same.

10. The distributed optimization scheduling method for distribution network-multi-integrated energy system considering interval uncertainty and multi-agent game as described in claim 9, characterized in that: The solution process for the fmincon function in MVA-ATC nested within MATLAB includes the following steps: Step 1: Initialize parameters, including coupling variables between the distribution network and MIES, and electricity price; Step 2: Each IES independently participates in the distribution network optimization scheduling, specifically including equations (10) to (12), and the optimization results are used as the negotiation breakdown point for subsequent game optimization scheduling; Step 3: Perform DN-MIES master-slave game optimization. After the distribution network master problem is optimized nonlinearly, the electricity price and coupled power parameters are passed to the lower-level MIES, specifically including equations (23) to (25). Step 4: Solve the MIES subproblems in the lower-level MIES to optimize scheduling, specifically including equation (26); Step 5: Each IES entity allocates an effective cooperation allocation based on Nash bargaining according to the benefits of alliance cooperation and the negotiation breakdown parameters obtained in Step 2, specifically including equations (27) to (28); if a cooperation equilibrium is reached, proceed to the next step; otherwise, return to Step 4. Step 6: Determine whether the data obtained from the upper and lower layers meet the convergence condition, i.e., equation (29). If it does, output the optimal result; otherwise, update the electricity price and weight coefficient according to equation (32) and return to Step 3 until the condition is met.

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