Optimization method of multi-microgrid bidirectional time-of-use electricity price based on multi-level game

Abstract

This multi-microgrid bidirectional time-of-use electricity price optimization method, based on a multi-level game, first designs a bidirectional time-of-use electricity price incentive mechanism for both generators and users in a multi-microgrid system-based electricity energy transaction. Secondly, a multi-level differentiated game model is established, with generators, mobile grid communication centers (MGCCs), and microgrid users as the main actors, coupling non-cooperative and master-slave game strategies. Finally, a two-layer particle swarm optimization algorithm combined with a Cplex solver is used to solve the established multi-level game model, resulting in an optimal bidirectional time-of-use electricity price optimization strategy. This proposed time-of-use electricity price optimization method can optimize energy management, reduce system operating costs and user electricity costs, and improve the economic benefits of generators.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-microgrid optimized operation, and in particular to a multi-microgrid bidirectional time-of-use electricity price optimization method based on multi-level game. Background Art

[0002] With the continuous growth of energy demand and the increasing prominence of environmental issues, microgrids, as a key carrier of renewable energy technology, are playing an increasingly important role in energy systems. Multi-microgrids, as a further development of microgrids, possess greater complexity and flexibility. By rationally arranging energy exchange between microgrids and maximizing the utilization of renewable energy, dependence on traditional energy sources can be reduced and sustainable energy development can be promoted. However, the economic efficiency of multi-microgrid systems is closely related to user participation, which relies on effective price incentives to mobilize user enthusiasm. As a result, demand response (DR) has gained widespread application.

[0003] In the existing technology: Literature [1]: "Cooperative Game Model of Multi-Microgrid System and Its Optimal Dispatching Strategy" (Li Demin, Wu Zaijun, Zhao Bo. Cooperative Game Model of Multi-Microgrid System and Its Optimal Dispatching Strategy [J]. Proceedings of the CSEE, 2022, 42(14): 5140-5154.) sets all microgrids in the multi-microgrid system as energy management entities with equal status, grants each microgrid the right to price power transactions with other microgrids and the right to decide on the amount of transaction volume, and constructs a distributed energy management architecture without a central management unit, effectively realizing the distributed energy management of the multi-microgrid system. This literature study uses the game theory framework to achieve the optimal operation of multiple microgrids, but does not consider the impact of user participation in demand response on the system optimization and dispatch.

[0004] Reference [2]: "Reliability assessment of incentive-and price-based demand response programs in restructured power systems" (Nikzad, M., Mozafari, B. Reliability assessment of incentive-and price-based demand response programs in restructured power systems. International Journal of Electrical Power & Energy Systems, 2014, 56: 83-96.) Incentives and penalties were formulated for users who responded to the demand and those who did not respond to the load reduction, and an incentive-based demand response model was constructed based on this to verify the improvement of the reliability of the restructured power system by the demand response program. This study considers the impact of DR on grid operation and dispatch, and provides an important reference for the operator's dispatch decision. However, the design and implementation of current demand response strategies rely more on relatively simplified and idealized user behavior models. These models usually assume that users' responses to price signals or incentives are immediate and linear, while ignoring the economic and psychological factors in the user's decision-making process.

[0005] Reference [3]: "Study on multi-type flexible load control method of active distribution network based on dynamic time-sharing electricity price" (Cui, J., Ran, Z., Shen, W., Xin, Y. Study on multi-type flexible load control method of active distribution network based on dynamic time-sharing electricity price. Applied Energy, 2024, 357: 122479.) proposed a dynamic time-of-use electricity price game model that takes into account the wishes of multiple users to maximize user satisfaction and benefits. However, in this study, the power generator did not adopt the time-of-use electricity price mechanism, but maintained a unified electricity sales price. This approach ignores the subjective initiative of the power generation side operator and the potential advantages of formulating the power generation side time-of-use electricity price in improving energy utilization efficiency. Summary of the Invention

[0006] In response to the above problems, the present invention discloses a multi-microgrid bidirectional time-of-use electricity price optimization method based on multi-level game. First, in the electric energy transaction based on the multi-microgrid system, the method designs a bidirectional time-of-use electricity price incentive mechanism for both power generators and users; secondly, a multi-level differentiated game model is established with power generators, MGCCs and microgrid users as the main bodies, coupling non-cooperative games and master-slave games. Finally, a two-layer particle swarm algorithm is combined with a Cplex solver to solve the established multi-level differentiated game model to obtain the optimal bidirectional time-of-use electricity price optimization strategy. The time-of-use electricity price optimization method proposed in the present invention can optimize energy management, reduce system operating costs and user electricity costs, and improve the economic benefits of power generators.

[0007] The technical solution adopted by the present invention is:

[0008] The multi-microgrid bidirectional time-of-use electricity price optimization method based on multi-level game includes the following steps:

[0009] Step 1: In the context of energy trading in a multi-microgrid system, a two-way time-of-use electricity price incentive mechanism is designed for both generators and users.

[0010] Step 2: A multi-level differentiated game model was established, which is based on the coupling of non-cooperative game and master-slave game, with power generators, microgrid control center (MGCC) and microgrid users as the main bodies.

[0011] Step 3: Use the two-layer particle swarm optimization algorithm combined with the Cplex solver to solve the multi-level differentiation game model established in step 2 and obtain the optimal two-way time-of-use electricity price optimization strategy.

[0012] In step 1, rationally adjusting electricity prices is one of the key means to achieve efficient energy utilization and cost optimization in a multi-microgrid system. This invention promotes active interaction between power generators, MGCCs, and users by establishing a two-way time-of-use electricity pricing incentive mechanism, optimizing power distribution and promoting renewable energy utilization. This two-way time-of-use electricity pricing incentive mechanism sets electricity prices for different time periods, encouraging users to use electricity when prices are low and reducing their use when prices are low. This balances supply and demand, reduces system operating costs, and improves energy efficiency.

[0013] The two-way time-of-use electricity price incentive mechanism includes two parts: the division of two-way time-of-use electricity price periods and the two-way time-of-use electricity price optimization decision model. The division of two-way time-of-use electricity price periods is as follows:

[0014] Time-of-use electricity prices for MGCCs require clustering based on the amount of electricity purchased by the MGCCs to determine peak, flat, and valley time periods on the generation side. Time-of-use electricity prices for microgrid users also require clustering based on the amount of electricity purchased by the users. Since the amount of electricity purchased is one-dimensional, the k-means clustering algorithm is used to determine the time periods. The objective function of the k-means clustering algorithm is the sum of the mean squared deviations between the data and the cluster centers to which it belongs.

[0015] The clustering labels of the purchased electricity are obtained based on the k-means clustering algorithm. The peak, flat and valley time periods are determined according to the clustering labels. The expression is as follows:

[0016] S a =[δ1,δ2,…,δ 24 ]

[0017]

[0018] T F ∪T P ∪T G ={0,1,2,…,23}

[0019]

[0020] Where S a is the clustering label vector of the purchased electricity; δ t is the clustering mark of the electricity purchase and power generation in period t; δ F , δ P , δ G are the clustering marks of peak, flat and valley time periods respectively; T F 、T P 、T G They are respectively the peak, flat and valley time periods of electricity purchase.

[0021] The core goal of time-of-use electricity pricing is to smooth the system load curve by reducing the peak-to-valley difference in load. Therefore, the construction of a two-way time-of-use electricity pricing optimization decision model should consider minimizing the peak load and the peak-to-valley difference, while considering the economic benefit constraints of both supply and demand sides to ensure a balance of interests between the two sides.

[0022] When deciding the electricity price for power generators, the objective function includes:

[0023] (1) Minimize the peak value F1 of the power generation curve of the generator;

[0024] (2) Maximizing the valley value F2 of the generator's power generation curve;

[0025] (3) Minimize the peak-to-valley difference F3 of the generator’s power generation curve,

[0026] The specific objective function is as follows:

[0027]

[0028] In the above formula, P e t The amount of electricity generated for power generators; Indicates the maximum power generation of a power generator in a single period of 24 hours; indicates a period of 24 hours; 0-23 represents the 24 hours of a day.

[0029] When deciding the MGCC electricity price, the objective function is:

[0030] (1) Minimize the peak value F4 of the microgrid user load curve;

[0031] (2) Maximize the valley value F5 of the microgrid user load curve;

[0032] (3) Minimize the peak-to-valley difference F6 of the microgrid user load,

[0033] The specific objective function is as follows:

[0034]

[0035] In the above formula, The amount of electricity purchased by the mth microgrid user from MGCC; It is expressed as the maximum amount of electricity purchased by the user from MGCC in a single period of 24 hours; It is expressed as the minimum value of electricity purchased from MGCC in a single period of 24 hours.

[0036] The constraints of the game equilibrium cover the revenue of power producers, the benefits of MGCCs, and the overall satisfaction of users. After the time-of-use electricity price adjustment, the interests or satisfaction of all relevant parties should at least remain at the level before the adjustment to ensure that no one suffers losses under the new pricing mechanism. The specific constraints are as follows:

[0037] C F,after ≥C F,before

[0038] C Fy,after ≤C Fy,before

[0039] C M,after ≥C M,before

[0040] F U,after ≥F U,before

[0041]

[0042] In the above formula, C F,after represents the revenue of the power generator after the electricity price adjustment, CF,before represents the revenue of the power generator before the electricity price adjustment; C Fy,after is the operation and maintenance cost of the power generator after the electricity price adjustment; C Fy,before is the operation and maintenance cost of the power generator before the electricity price adjustment; C M,after is the profit of MGCC after electricity price adjustment, C M,before is the profit of MGCC before electricity price adjustment; F U,after is the comprehensive satisfaction of users with electricity after electricity price adjustment, F U,before It is the comprehensive satisfaction of users with electricity consumption before the electricity price adjustment; The amount of electricity purchased by microgrid users from MGCC after the electricity price adjustment. The amount of electricity purchased by microgrid users from MGCC before the electricity price adjustment;

[0043] Formula C F,after ≥C F,before 、Formula C M,after ≥C M,before Japanese style F U,after ≥F U,before It means that the objective function of each subject should be optimized after adjustment;

[0044] Formula C Fy,after ≤C Fy,before It indicates that power generators’ operation and maintenance costs need to be reduced after the electricity price adjustment;

[0045] Mode It means that the user’s unit electricity purchase cost cannot increase after the electricity price adjustment.

[0046] In step 2, the multi-level game mechanism is as follows:

[0047] In the multi-level game mechanism, there is a non-cooperative game between the power generator and the MGCC, and a master-slave game relationship between the MGCC and the microgrid users; the power generator formulates the power sales price based on the power demand of each microgrid, taking into account the fixed cost of power generation and the operation and maintenance cost; the MGCC conducts day-ahead planning and dispatching, giving priority to absorbing the renewable energy output and energy storage within the microgrid. If there is still demand, it will purchase electricity from other microgrids and finally from the power generator. The MGCC formulates the load-side time-of-use electricity price considering its own benefits; users adjust their electricity consumption behavior in different time periods according to the load-side time-of-use electricity price and psychological expectations. The three stakeholders, the power generator, MGCC and the user, influence each other through decision-making on the on-grid time-of-use electricity price, the load-side time-of-use electricity price and time-of-use electricity consumption behavior, and obtain the optimal equilibrium solution through the game;

[0048] The game specifically includes the following steps:

[0049] Step 2.1: The power generator sets the initial grid-connected time-of-use electricity price on the power generation side.

[0050] Step 2.2: MGCC formulates power purchase strategy and load-side TOU electricity price based on TOU electricity price and power demand.

[0051] Step 2.3: Microgrid users independently shift or reduce loads based on the load-side time-of-use electricity price.

[0052] Step 2.4: MGCC updates the dispatch strategy and power purchase plan based on the user's time-of-use load demand.

[0053] Step 2.5: The power generator adjusts its power generation plan and updates the grid-connected time-of-use electricity price based on the MGCC's power purchase plan.

[0054] Step 2.6: Repeat steps 2.2 to 2.5 until the generator's on-grid time-of-use electricity price, the MGCC's power purchase strategy, the load-side time-of-use electricity price, and the user's electricity consumption plan remain stable and the game equilibrium is reached.

[0055] Step 2.7: Energy trading is performed with the game equilibrium solution as the final result.

[0056] In step 2, the multi-level differentiated game model includes:

[0057] (1): Non-cooperative game model:

[0058] The multi-level game proposed in this paper involves a non-cooperative game between power generators and MGCCs, and a master-slave game between MGCCs and users. The two parties involved in the non-cooperative game use grid-connected time-of-use electricity prices and power purchase plans as game items, establishing a non-cooperative game economic optimization model based on multiple microgrids.

[0059] 1) Participant collection:

[0060] Y={F,MGCC1,MGCC2,iii,MGCC m ,MGCC M}

[0061] Where, F represents the generator; MGCC m Indicates the mth microgrid control center; MGCC1 indicates the first microgrid control center; MGCC2 indicates the second microgrid control center; MGCC M represents the Mth microgrid control center.

[0062] 2) Strategy set:

[0063] The strategy set of the generator is expressed as:

[0064]

[0065] Where, represents the power generation of the generator during period t; Ω Frepresents the strategy set of the generator; Respectively represent the upper and lower limits of power generation; represents the time-of-use electricity price sold by the power generator during period t; They respectively represent the upper and lower limits of the electricity sales price of power generators.

[0066] The strategy set of the mth MGCC is expressed as:

[0067]

[0068] Where, Ω represents the amount of electricity purchased by the mth MGCC from the generator during period t; M,m represents the strategy set of the mth MGCC; Respectively represent the upper and lower limits of electricity purchase amount.

[0069] 3) Utility function:

[0070] Power generators pursue their own benefits in the game process C F The maximum is expressed as follows:

[0071] C F =C Mbuy -C Fy -C Fe

[0072] Where C F is the revenue of the power generator; C Mbuy is the electricity purchase cost of MGCC and the electricity sales income of the generator; C Fy is the operation and maintenance cost of the generator; C Fe It is the environmental protection cost of power generators.

[0073] MGCC pursues benefits in the game process M The maximum is expressed as follows:

[0074] C M,m =C Ubuy,m -(C PV,m +C WT,m +C GT,m +C ESS,m +C Mbuy,m +C Ms,m +C Me,m )

[0075] Where C M,m is the total revenue of MGCC in the mth microgrid system; C Ubuy,m is the electricity cost of microgrid user m, which is equivalent to the electricity sales revenue of the mth MGCC; C PV,m is the operation and maintenance cost of photovoltaic equipment; C WT,m is the operation and maintenance cost of wind power equipment; CGT,m is the power generation and operation and maintenance cost of gas turbine; C ESS,m The charging and discharging operation and maintenance cost of energy storage equipment; C Mbuy,m is the electricity purchase cost of MGCC; C Ms,m is the interaction cost between microgrids; C Me,m is the environmental protection cost of MGCC.

[0076] 4) Nash equilibrium:

[0077] When the game reaches equilibrium, the generator and MGCC need to meet the following conditions:

[0078]

[0079] Where, It represents the revenue of the generator after the generator's power generation, the electricity sales price set by the generator and the amount of electricity purchased by the mth MGCC from the generator reach a game equilibrium. represents the power generation of the generator when the game reaches equilibrium; It represents the electricity price set by the generator when the game reaches equilibrium; It represents the amount of electricity purchased by the mth MGCC from the generator when the game reaches equilibrium.

[0080] It represents the revenue of the generator only when the electricity price set by the generator and the amount of electricity purchased by the mth MGCC from the generator reach the game equilibrium; It represents the power generation of the generator when the game equilibrium is not reached.

[0081] It represents the revenue of the generator only when the power generation of the generator and the power purchase amount of the mth MGCC from the generator reach the game equilibrium; It represents the electricity sales price set by the power generator when the game equilibrium is not reached.

[0082] It represents the revenue of the generator only when the power generation of the generator and the electricity price set by the generator reach the equilibrium of the game; It represents the amount of electricity purchased by the mth MGCC from the generator when the game equilibrium is not reached. From the above formula, it can be seen that when the non-cooperative game between the generator and the MGCC reaches the Nash equilibrium, no participant can unilaterally change the strategy to obtain a better benefit function without affecting other participants.

[0083] (2): Master-slave game model:

[0084] The master-slave game model proposed in this invention is a decision-making process in which MGCC and microgrid users participate in the game as leaders and followers, pursuing the optimal goal of each. The master-slave game model can be expressed as:

[0085] 1) Participant collection:

[0086] Y={MGCC m ,U m}

[0087] Where, MGCC m represents the mth MGCC; U m represents the mth microgrid user.

[0088] 2) Strategy set:

[0089] The strategy of the leader MGCC is Ω M,m represents the strategy set of the mth MGCC;

[0090] The strategy of the follower microgrid user is Ω U,m represents the strategy set of the m-th microgrid user;

[0091] in, Respectively represent the upper and lower limits of MGCC’s electricity sales price; They are the upper and lower limits of the amount of electricity that microgrid users can purchase.

[0092] 3) Utility function:

[0093] As the leader, MGCC seeks to maximize its own benefits during the game, as shown in the following expression:

[0094] C M,m =C Ubuy,m -(C PV,m +C WT,m +C GT,m +C ESS,m +C Mbuy,m +C Ms,m +C Me,m )

[0095] Microgrid users pursue the highest comprehensive satisfaction with electricity consumption during the game, which can be expressed as follows:

[0096]

[0097]

[0098] Where, α t Indicates the user's satisfaction with electricity consumption behavior; β t Indicates user satisfaction with electricity costs;t The comprehensive satisfaction of users is measured; ω1 and ω2 represent the weight coefficients of user satisfaction with electricity consumption behavior and user satisfaction with electricity costs, respectively, and ω1+ω2=1; is the original load before demand response; ρ1 and ρ2 are the user electricity efficiency coefficients, with values ​​of ρ1 = 0.0009 and ρ2 = 1.5; is the original electricity price before demand response.

[0099] 4) Stcakelberg equilibrium:

[0100] When the follower microgrid users make the best response according to the leader MGCC's strategy and MGCC also accepts this response, the game reaches the Stcakelberg equilibrium; if When it is the equilibrium solution of the master-slave game, it must satisfy:

[0101]

[0102] Where, It represents the revenue of MGCC when the time-of-use electricity price set by MGCC and the amount of electricity purchased by microgrid users from MGCC reach the game equilibrium; It represents the time-of-use electricity price set by MGCC when the game equilibrium is reached;

[0103] It represents the revenue of MGCC only when the time-of-use electricity price set by MGCC reaches the game equilibrium.

[0104] Ω M,m represents the strategy set of the mth MGCC; Ω U,m represents the policy set of the m-th microgrid user.

[0105] After the master-slave game between MGCC and microgrid users reaches an equilibrium solution, neither party can obtain greater benefits by unilaterally changing its strategy.

[0106] In step 3, a two-layer particle swarm optimization algorithm combined with a Cplex solver is used to solve the established multi-level differentiated game model. The upper-level game is a non-cooperative game between the generator and the MGCC. The game objectives include maximizing the revenue of the generator and the MGCC, and determining the generator's electricity sales price and power generation plan. The lower-level game is a master-slave game between the MGCC and users. The game objectives include maximizing the MGCC's benefits and overall user satisfaction, determining the MGCC's electricity purchase plan and sales price, and determining the user's electricity consumption plan.

[0107] The solution of the multi-level differentiated game model includes the following steps:

[0108] S1: Find the equilibrium point of the upper game:

[0109] S1-1: Initialize the particle swarm. Set the decision ranges of the generator and MGCC, and randomly initialize the position and velocity of the particle swarm. Each particle represents a set of possible strategy combinations, i.e., a set of decisions of the generator and MGCC.

[0110] S1-2: Evaluate fitness. For each possible strategy combination, calculate the corresponding benefits of the generator and MGCC.

[0111] S1-3: Update individual and global optimal solutions. For each particle (strategy combination), update its individual optimal solution based on its payoff, saving the historical best position and corresponding payoff value. Then, find the global optimal solution (i.e., the optimal game strategy combination) within the entire particle swarm.

[0112] S1-4: Update particle position and velocity. Update the particle position and velocity based on the individual historical optimal position and the global optimal position.

[0113] S1-5: Convergence determination. Determine whether the maximum number of iterations has been reached. If not, return to S1-2 to continue iteration.

[0114] S1-6: Call the Cplex solver. Input the equilibrium point found by the particle swarm algorithm as the initial solution into the Cplex solver to obtain the game result.

[0115] S2: Find the equilibrium point of the lower-level game:

[0116] S2-1: Reinitialize the particle swarm. Set the decision ranges of the MGCC and the user, and randomly initialize the position and velocity of the particle swarm. Each particle represents a set of possible strategy combinations, i.e., a set of decisions of the MGCC and the user.

[0117] S2-2: Evaluate fitness. Calculate the objective function for each strategy. Input the results of the upper-level game as parameters to solve the lower-level game.

[0118] S2-3: Update individual and global optimal solutions. For each particle (strategy combination), update its individual optimal solution based on its payoff, saving the historical best position and corresponding payoff value. Then, find the global optimal solution (i.e., the optimal game strategy combination) within the entire particle swarm.

[0119] S2-4: Update particle position and velocity. Update the particle position and velocity based on the individual historical optimal position and the global optimal position.

[0120] S2-5: Convergence determination. Determine whether the maximum number of iterations has been reached. If not, return to S2-2 and continue iteration. S2-6: Invoke the Cplex solver. The equilibrium point found by the particle swarm algorithm is input into the Cplex solver as the initial solution to obtain the game result; each particle represents a set of MGCC and user decisions.

[0121] S3: Feedback and Integration: Feedback the results of the lower-level game to the upper-level game to readjust the upper-level strategy. Conduct comprehensive optimization of the upper and lower-level games to ensure that the final result meets the overall goal.

[0122] S4: Re-solve: Based on the feedback results and the adjusted parameters, repeat the solution process S1-S2 of the upper and lower level games.

[0123] S5: Verify whether the result after optimization adjustment is better. If it meets the requirements, the entire solution process is completed.

[0124] Through the game process, the optimal solutions of the upper and lower level games are obtained, including the optimal electricity sales price and power generation plan of the power generator, the optimal electricity purchase plan and electricity sales price of the MGCC, and the optimal electricity consumption plan of the user.

[0125] In step 3, the optimal two-way time-of-use electricity price optimization strategy specifically refers to: when the upper and lower level games reach a game equilibrium, the time-of-use electricity sales price of the power generator to the MGCC and the time-of-use electricity sales price of the MGCC to the user.

[0126] The present invention provides a multi-microgrid bidirectional time-of-use electricity price optimization method based on multi-level game, and the technical effects are as follows:

[0127] (1) Step 1 of the present invention proposes a two-way time-of-use electricity price incentive mechanism, which has the following advantages over traditional electricity price strategies:

[0128] a. Price flexibility: The two-way time-of-use electricity pricing mechanism adjusts electricity prices based on supply and demand conditions in different time periods. Traditional electricity pricing strategies usually adopt fixed electricity prices or simple peak and valley electricity prices without detailed time period divisions.

[0129] b. Optimize resource allocation: The two-way time-of-use electricity pricing mechanism more effectively matches electricity supply and demand, optimizes resource allocation, and reduces waste. Traditional electricity pricing strategies are often unable to dynamically adjust to actual demand changes.

[0130] c. Promote demand response: Two-way time-of-use electricity prices encourage users to use electricity during periods of low electricity prices, reduce electricity consumption during peak periods, and promote demand response; traditional electricity pricing strategies lack this dynamic adjustment mechanism.

[0131] d. Improve power generation efficiency: The two-way time-of-use electricity pricing mechanism allows power generators to adjust their power generation plans based on electricity prices, thereby improving power generation efficiency. Traditional electricity pricing strategies cannot provide this flexibility.

[0132] e. Enhanced grid stability: The two-way time-of-use electricity pricing mechanism balances loads by adjusting electricity prices, enhancing grid stability. Traditional electricity pricing strategies may lead to power shortages or surpluses.

[0133] (2) Step 2 of the present invention proposes a multi-level differentiated game model. The bidirectional time-of-use electricity price incentive mechanism in step 1 is also designed based on this model. The specific advantages of this model are as follows:

[0134] 1) Simulating real market behavior: The game model can truly reflect the interaction and strategy selection between power producers, microgrid control centers (MGCCs) and users, and simulate the competition and cooperation behaviors in the actual market.

[0135] 2) Considering strategic interaction: The game model can handle the mutual influence and optimization of the strategies of all parties, making the design of electricity price strategy more in line with the dynamic adjustment needs in actual games.

[0136] 3) Multi-level decision optimization: Game models are suitable for handling multi-level decision-making problems. Through game analysis at different levels, power generation, sales and consumption strategies can be optimized, thereby optimizing electricity price settings more comprehensively.

[0137] Solving complex problems: Game models can handle complex strategic interactions and optimization problems, and are suitable for solving multi-party games and nonlinear optimization problems that are difficult to handle with traditional methods.

[0138] (3) Step 3 of the present invention specifically involves using a two-layer particle swarm optimization algorithm to solve the multi-level differentiated game model of step 2. The specific advantages of this algorithm are as follows:

[0139] ①. Efficient optimization: The particle swarm algorithm converges quickly by simulating group behavior and can efficiently find the optimal solution, making it suitable for handling complex multi-level game problems.

[0140] ②. Multi-level adaptability: The two-layer particle swarm algorithm can be optimized at different levels to ensure the coordination and optimization of upper and lower-level decisions.

[0141] Flexible processing: Able to handle nonlinear and multi-objective optimization problems and adapt to different electricity price strategy requirements.

[0142] ③. Dynamic adjustment: Adapt to market dynamics, continuously update strategies through an iterative process, and optimize electricity price settings.

[0143] ④. Global search capability: The particle swarm algorithm has strong global search capabilities, which can avoid local optimal solutions and improve the solution quality of the overall game model.

[0144] (4) The time-of-use electricity price optimization method proposed in the present invention can optimize energy management, reduce system operating costs and user electricity costs, improve the economic benefits of power generators and the environmental friendliness of multi-microgrid systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0145] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0146] Figure 1 This is a flow chart of the multi-microgrid bidirectional time-of-use electricity price optimization method based on multi-level game.

[0147] Figure 2 This is the optimized time-of-use electricity price diagram.

[0148] Figure 3 This is the load optimization result of microgrid user 1.

[0149] Figure 4 This is the load optimization result of microgrid user 2.

[0150] Figure 5 This is the load optimization result of microgrid user 3. DETAILED DESCRIPTION

[0151] The present invention will be further described in detail below with reference to the embodiments and the accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0152] Figure 1 This is a flow chart of the optimization method proposed in the present invention. First, in the electric energy transaction based on a multi-microgrid system, the present invention designs a two-way time-of-use electricity price incentive mechanism for both power generators and users. Secondly, a multi-level differentiated game model is established, which couples non-cooperative games and master-slave games with power generators, MGCCs, and microgrid users as the main bodies. Finally, a two-layer particle swarm algorithm is combined with a Cplex solver to solve the established multi-level game model and obtain the optimal two-way time-of-use electricity price optimization strategy. The time-of-use electricity price optimization method proposed in the present invention can optimize energy management, reduce system operating costs and user electricity costs, and improve the economic benefits of power generators.

[0153] Figure 2 is the optimized time-of-use electricity price diagram. Figure 2As can be seen, generators set time-of-use (TOU) schedules based on power generation demand, while MGCCs set TOU schedules based on user load. Therefore, the generator's TOU schedule differs from the MGCC electricity sales price and the MGCC interactive electricity price. In the early morning hours (00:00-4:00), power demand after demand response increases compared to before optimization. PV output is zero, and there is no available energy in the energy storage system. During this time, the generator's power generation plan is relatively high, and the generator's electricity sales price is within the peak period. From 4:00-9:00, PV equipment gradually begins operating, and the energy storage system performs its low-charge, high-discharge scheduling function. The generator's power generation plan is somewhat lower than during peak periods, resulting in a TOU electricity sales price within the normal period. From 10:00-16:00, PV output reaches its peak, and user load after demand response tends to stabilize. During this period, MGCC's demand for power from the generator is relatively low, and the TOU electricity price is within the off-peak period. During the period of 18:00-21:00, photovoltaic equipment stops generating electricity, and the output of MGCC's distributed power sources, gas turbines, etc. is insufficient to cover user demand, so the power generation plan of the power generator is relatively high, and the time-of-use electricity price is in the peak period. During the period of 0:00-7:00 and 20:00-23:00, the user load is relatively low, so the MGCC electricity sales price and the MGCC interactive electricity price are both in the valley period. During the period of 7:00-11:00 and 16:00-20:00, the output of photovoltaic equipment, wind power equipment and gas turbines is insufficient to cover user demand, and MGCC needs to buy electricity from power generators. At this time, the power generation price of power generators is high, and the power purchase cost of MGCC increases, so the power sales price of MGCC also increases. During the period of 11:00-16:00, the output of photovoltaic equipment increases, and the power purchase cost of MGCC decreases, so the power sales price of MGCC is in the valley period.

[0154] Figures 3 to 5 They are the load optimization results of microgrid users 1, 2 and 3 respectively. Figures 3 to 5 Analysis shows that user loads in all three microgrids were reduced during optimization. Demand response was implemented during the period of higher electricity prices (10:00 AM to 10:00 PM), shifting some load to lower-price hours. This reduced peak load and minimized peak-to-valley variations, thereby saving energy costs. This optimization strategy not only alleviated pressure on the grid but also improved the economic benefits for both the MGCC and microgrid users.

[0155] Table 1 Multi-scheme system optimization results

[0156]

[0157] Table 1 shows the results of multi-scheme system optimization. In order to verify the economic and environmental performance of the proposed method, four schemes were set up for comparative analysis.

[0158] Option 1 does not consider the game process, and both the generator and the MGCC set a fixed time-of-use electricity price;

[0159] Option 2 considers the power generator and MGCC to participate in the game process, and a fixed time-of-use electricity price is set between MGCC and users;

[0160] Option 3 considers the game process between MGCC and users, and sets a fixed time-of-use electricity price between the power generator and MGCC;

[0161] Solution 4 considers that the power generator, MGCC and users all participate in the game process, which is the method proposed in the present invention.

[0162] A comprehensive comparison of Schemes 1 and 4 reveals that Scheme 1 lacks a game-playing process, resulting in the generator's electricity price being almost identical to the MGCC's time-of-use period. However, Scheme 4 exhibits a multi-level game-playing process. When the game equilibrium is reached, the generator's electricity price exhibits a pattern of high prices when electricity sales are high and low prices when electricity sales are low, with reduced peak-to-valley price fluctuations. Scheme 4 reduces gas turbine costs by 8,111.6 yuan, a 25.6% decrease; environmental protection costs by 222.8 yuan, a 19.1% decrease; MGCC total benefits by 15,343.7 yuan, a 54.3% increase; generator revenue by 12,951.3 yuan, a 27.3% increase; microgrid user costs by 43,028.6 yuan, a 31.6% decrease; and overall user satisfaction by 0.627.

[0163] The above data analysis shows that because the generator, MGCC, and users all participate in the game in Scheme 4, users' energy consumption behavior is guided by electricity prices to respond to demand, reducing electricity costs. The generator's power generation plan has achieved higher profits after adjustment. Compared with Scheme 1, Scheme 4 reduces all costs by about 20%, and the generator's profit and the overall benefit of MGCC are greatly improved, demonstrating the absolute advantages of Scheme 4 in terms of economy and environmental protection.

Claims

1. A multi-microgrid bidirectional time-of-use electricity price optimization method based on multi-level game theory is characterized by The following steps are involved: Step 1: In the context of power trading in a multi-microgrid system, a two-way time-of-use electricity price incentive mechanism is designed for both generators and users. Step 2: A multi-level differentiated game model was established, which couples non-cooperative game and master-slave game with power generators, microgrid control center (MGCC) and microgrid users as the main bodies. Step 3: Use a two-layer particle swarm optimization algorithm combined with a solver to solve the multi-level differentiation game model established in step 2 and obtain the optimal two-way time-of-use electricity price optimization strategy; The multi-level differentiated game model solution includes the following steps: S1: Find the equilibrium point of the upper game: S1-1: Initialize the particle swarm; set the decision range of the generator and MGCC, and randomly initialize the position and velocity of the particle swarm; each particle represents a set of possible strategy combinations, that is, a set of decisions of the generator and MGCC; S1-2: Evaluate fitness; for each possible strategy combination, calculate the corresponding generator and MGCC benefits; S1-3: Update individual and global optimal solutions. For each particle, update its individual optimal solution based on the payoff, i.e. save the historical best position and the corresponding payoff value. Then, find the global optimal solution, i.e. the optimal game strategy combination, in the entire particle swarm. S1-4: Update particle position and velocity; update the particle position and velocity based on the individual historical optimal position and the global optimal position; S1-5: Convergence judgment: judge whether the maximum number of iterations has been reached; if not, return to S1-2 to continue iteration; S1-6: Call the Cplex solver; input the equilibrium point found by the particle swarm algorithm as the initial solution into the Cplex solver to obtain the game result; S2: Find the equilibrium point of the lower-level game: S2-1: Set the decision range of MGCC and user, and randomly initialize the position and velocity of the particle swarm; each particle represents a set of possible strategy combinations, that is, a set of MGCC and user decisions; S2-2: Calculate the objective function of each strategy; input the results of the upper-level game as parameters to solve the lower-level game; S2-3: For each particle, update its individual optimal solution based on the payoff, that is, save the historical best position and the corresponding payoff value; then, find the global optimal solution in the entire particle swarm, that is, the optimal game strategy combination; S2-4: Update the position and velocity of the particle based on the individual historical optimal position and the global optimal position; S2-5: Determine whether the maximum number of iterations has been reached; if not, return to S2-2 to continue iterating; S2-6: Input the equilibrium point found by the particle swarm algorithm as the initial solution into the Cplex solver to obtain the game result; S3: Feedback and integration: Feedback the results of the lower-level game to the upper-level game to readjust the upper-level strategy; Conduct comprehensive optimization of upper and lower-level games to ensure that the final result meets the overall goal; S4: Re-solve: Based on the feedback results and the adjusted parameters, repeat the solution process S1-S2 of the upper and lower game; S5: Verify whether the result after optimization adjustment is better. If it meets the requirements, the entire solution process is completed; Through the game process, the optimal solutions of the upper and lower level games are obtained, including the optimal electricity sales price and power generation plan of the power generator, the optimal electricity purchase plan and electricity sales price of the MGCC, and the optimal electricity consumption plan of the user.

2. The multi-microgrid bidirectional time-of-use electricity price optimization method based on multi-level game according to claim 1 is characterized by: In step 1, the bidirectional time-of-use electricity price incentive mechanism includes two parts: bidirectional time-of-use electricity price period division and bidirectional time-of-use electricity price optimization decision model; wherein, the bidirectional time-of-use electricity price period division is specifically as follows: The time-of-use electricity price for MGCC sales needs to be clustered based on the amount of electricity purchased by the MGCC to determine the peak, flat, and valley time periods on the power generation side. The time-of-use electricity price for microgrid users needs to be clustered based on the amount of electricity purchased by the users. Since the amount of electricity purchased is one-dimensional data, the k-means clustering algorithm is used to determine the time periods. The objective function of the k-means clustering algorithm is the sum of the mean square error between the data and the cluster center to which it belongs. The clustering labels of the purchased electricity are obtained based on the k-means clustering algorithm. The peak, flat and valley time periods are determined according to the clustering labels. The expression is as follows: ； ； ； ； Where, is the cluster label vector of the purchased electricity; for Cluster marking of electricity purchase and power generation during the time period; 、 、 They are cluster marks for peak, flat and valley time periods respectively; 、 、 They are respectively the peak, flat and valley time periods of the electricity purchased; The construction of a two-way time-of-use electricity price optimization decision model takes into account the minimization of load peaks and peak-to-valley differences, while considering the economic benefit constraints of both supply and demand sides to ensure a balance of interests between the two sides; When deciding the electricity price for power generators, the objective function includes: (1) Minimize the peak value of the generator's power generation curve ; (2) Maximizing the valley value of the generator’s power generation curve ; (3) Minimize the peak-to-valley difference of the generator’s power generation curve , The specific objective function is as follows: ； ； ； In the above formula, The amount of electricity generated for power generators; Indicates the maximum power generation of a generator in a single period of 24 hours; indicates a period of 24 hours; When deciding the MGCC electricity price, the objective function is: (1) Minimize the peak value of microgrid user load curve ; (2) Maximizing the valley value of microgrid user load curve ; (3) Minimize the peak-valley difference of microgrid user load , The specific objective function is as follows: ； ； ； In the above formula, For the The amount of electricity purchased by microgrid users from MGCC; It is expressed as the maximum amount of electricity purchased by the user from MGCC in a single period of 24 hours; It is expressed as the minimum value of electricity purchased from MGCC in a single period of 24 hours.

3. The multi-microgrid bidirectional time-of-use electricity price optimization method based on multi-level game according to claim 2 is characterized by: The constraints of the game equilibrium include the generator's revenue, MGCC benefits, and user comprehensive satisfaction. The constraints are as follows: ； ； ； ； ； In the above formula, represents the revenue of the power generator after the electricity price adjustment, It represents the revenue of power generators before electricity price adjustment; The operation and maintenance costs of power generators after electricity price adjustment; The operation and maintenance costs of power generators before electricity price adjustment; is the profit of MGCC after electricity price adjustment, is the revenue of MGCC before electricity price adjustment; The comprehensive satisfaction of users with electricity consumption after the electricity price adjustment. It is the comprehensive satisfaction of users with electricity consumption before the electricity price adjustment; The amount of electricity purchased by microgrid users from MGCC after the electricity price adjustment. The amount of electricity purchased by microgrid users from MGCC before the electricity price adjustment; Mode ,Mode Japanese style It means that the objective function of each subject should be optimized after adjustment; Mode It indicates that power generators’ operation and maintenance costs need to be reduced after the electricity price adjustment; Mode It means that the user’s unit electricity purchase cost cannot increase after the electricity price adjustment.

4. The multi-microgrid bidirectional time-of-use electricity price optimization method based on multi-level game according to claim 1 is characterized by: In step 2, the multi-level game mechanism is as follows: In the multi-level game mechanism, there is a non-cooperative game between the power generator and the MGCC, and a master-slave game relationship between the MGCC and the microgrid users; the power generator sets the power sales price based on the power demand of each microgrid, taking into account the fixed cost of power generation and the operation and maintenance cost; the MGCC conducts day-ahead planning and dispatching, giving priority to consuming the renewable energy output and energy storage within the microgrid. If there is still demand, it will purchase electricity from other microgrids and finally from the power generator; the MGCC considers its own benefits and sets the load-side time-of-use electricity price; users adjust their electricity consumption behavior in different time periods based on the load-side time-of-use electricity price and psychological expectations; the three stakeholders, the power generator, the MGCC and the user, influence each other by deciding the on-grid time-of-use electricity price, the load-side time-of-use electricity price and the time-of-use electricity consumption behavior, and find the optimal equilibrium solution through game theory.

5. The multi-microgrid bidirectional time-of-use electricity price optimization method based on multi-level game according to claim 4 is characterized by: The game specifically includes the following steps: Step 2.1: The power generator sets the initial on-grid time-of-use electricity price on the power generation side; Step 2.2: MGCC formulates power purchase strategy and load-side TOU electricity price based on TOU electricity price and power demand; Step 2.3: Microgrid users independently shift or reduce loads based on the load-side time-of-use electricity price; Step 2.4: MGCC updates the dispatch strategy and power purchase plan based on the user's time-of-use load demand; Step 2.5: The power generator adjusts its power generation plan and updates the on-grid time-of-use electricity price based on the MGCC's power purchase plan; Step 2.6: Repeat steps 2.2 to 2.5 until the generator's on-grid TOU price, the MGCC's power purchase strategy, the load-side TOU price, and the user's electricity consumption plan remain stable, reaching a game equilibrium. Step 2.7: Energy trading is performed with the game equilibrium solution as the final result.

6. The multi-microgrid bidirectional time-of-use electricity price optimization method based on multi-level game according to claim 5 is characterized by: In step 2, the multi-level differentiated game model includes: (1): Non-cooperative game model: The multi-level game proposed in this paper includes a non-cooperative game between the power generator and the MGCC, and a master-slave game between the MGCC and the user. The two parties involved in the non-cooperative game use the grid time-of-use electricity price and the power purchase plan as game items, respectively, to establish a non-cooperative game economic optimization model based on multiple microgrids. 1) Participant collection: ； Where, represents the power generator; Indicates the A microgrid control center; Indicates the first microgrid control center; Indicates the second microgrid control center; represents the Mth microgrid control center; 2) Strategy Collection: The strategy set of the generator is expressed as: ； ； Where, express The power generation of the generators during the period; represents the strategy set of the generator; 、 Respectively represent the upper and lower limits of power generation; express Time-of-use electricity prices sold by power generators during certain time periods; 、 They represent the upper and lower limits of the electricity sales price of power generators respectively; No. The policy set of a MGCC is expressed as: ； Where, express Time period The amount of electricity purchased by each MGCC from the power generator; Indicates the A set of MGCC strategies; 、 Respectively represent the upper and lower limits of the amount of electricity purchased; 3) Utility function: Power generators pursue their own benefits in the game process The maximum is expressed as follows: ； Where, For the benefit of the generator; is the electricity purchase cost of MGCC and the electricity sales revenue of the generator; Operation and maintenance costs for power generators; Environmental protection costs for power generators; MGCC pursues benefits in the game process The maximum is expressed as follows: ； Where, For the The total revenue of MGCC in each microgrid system; For microgrids The user's electricity cost is equivalent to the The electricity sales revenue of each MGCC; The operation and maintenance costs of photovoltaic equipment; Operation and maintenance costs of wind power equipment; Power generation and operation and maintenance costs for gas turbines; Charging and discharging operation and maintenance costs for energy storage equipment; Cost of electricity purchased for MGCC; is the interaction cost between microgrids; Environmental protection costs of MGCC; 4) Nash equilibrium: When the game reaches equilibrium, the generator and MGCC need to meet the following conditions: ； ； ； Where, It represents the revenue of the generator after the generator's power generation, the electricity price set by the generator, and the amount of electricity purchased by the m-th MGCC from the generator reach a game equilibrium; represents the power generation of the generator when the game reaches equilibrium; It represents the electricity price set by the generator when the game reaches equilibrium; It represents the amount of electricity purchased by the mth MGCC from the generator when the game reaches equilibrium; It represents the revenue of the generator only when the electricity price set by the generator and the amount of electricity purchased by the mth MGCC from the generator reach the game equilibrium; It represents the power generation of the generator when the game equilibrium is not reached; It represents the revenue of the generator only when the power generation of the generator and the power purchase amount of the mth MGCC from the generator reach the game equilibrium; It represents the electricity price set by the power generator when the game equilibrium is not reached; It represents the revenue of the generator only when the power generation of the generator and the electricity price set by the generator reach the equilibrium of the game; It represents the amount of electricity purchased by the mth MGCC from the generator when the game equilibrium is not reached; (2): Master-slave game model: The master-slave game model is a decision-making process in which MGCC and microgrid users participate in the game as leaders and followers, pursuing the optimal goal of each other. The master-slave game model is expressed as: 1) Participant collection: ； Where, Indicates the MGCCs; Indicates the microgrid users; 2) Strategy Collection: The strategy of the leader MGCC is , represents the strategy set of the mth MGCC; The strategy of the follower microgrid user is , represents the strategy set of the m-th microgrid user; in, 、 Respectively represent the upper and lower limits of MGCC’s electricity sales price; 、 They are the upper and lower limits of the amount of electricity that microgrid users can purchase; 3) Utility function: As the leader, MGCC seeks to maximize its own benefits during the game, as shown in the following expression: ； Microgrid users pursue the highest comprehensive satisfaction with electricity consumption during the game, which can be expressed as follows: ； ； ； Where, Indicates user satisfaction with electricity usage behavior; Indicates user satisfaction with electricity costs; Measured the overall user satisfaction; 、 represent the weight coefficients of user satisfaction with electricity consumption behavior and user satisfaction with electricity costs, respectively, and ; is the original load before demand response; 、 They are the user electricity efficiency coefficients, and their values ​​are , ; is the original electricity price before demand response; 4) Stcakelberg equilibrium: When the follower microgrid users make the best response according to the leader MGCC's strategy and MGCC also accepts this response, the game reaches the Stcakelberg equilibrium; if When it is the equilibrium solution of the master-slave game, it must satisfy: ； ； Where, It represents the revenue of MGCC when the time-of-use electricity price set by MGCC and the amount of electricity purchased by microgrid users from MGCC reach the game equilibrium; It represents the time-of-use electricity price set by MGCC when the game equilibrium is reached; It represents the revenue of MGCC only when the time-of-use electricity price set by MGCC reaches the game equilibrium; represents the strategy set of the mth MGCC; represents the strategy set of the m-th microgrid user; After the master-slave game between MGCC and microgrid users reaches an equilibrium solution, neither party can obtain greater benefits by unilaterally changing its strategy.

7. The multi-microgrid bidirectional time-of-use electricity price optimization method based on multi-level game according to claim 1 is characterized by: In step 3, a two-layer particle swarm optimization algorithm is combined with a Cplex solver to solve the established multi-level differentiated game model. The upper-level game is a non-cooperative game between the power generator and the MGCC, and the game objectives include maximizing the profits of the power generator and the MGCC, and determining the power generation price and power generation plan of the power generator. The lower-level game is a master-slave game between the MGCC and the user, and the game objectives include maximizing the benefits of the MGCC and the overall satisfaction of the user, and determining the MGCC power purchase plan and power sales price, as well as the user's power consumption plan.

8. The multi-microgrid bidirectional time-of-use electricity price optimization method based on multi-level game according to claim 1 is characterized by: In step 3, the optimal two-way time-of-use electricity price optimization strategy specifically refers to: when the upper and lower level games reach a game equilibrium, the time-of-use electricity sales price of the power generator to the MGCC and the time-of-use electricity sales price of the MGCC to the user.

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