A game theory-based capacity configuration optimization method for water, wind, light, and storage micro-grid

Abstract

This invention discloses a game theory-based method for optimizing the capacity configuration of hydro, wind, solar, and energy storage microgrids, belonging to the field of energy system operation optimization and configuration technology. This method uses four types of energy operators—hydro, wind, solar, and energy storage—as the main players in the game, resolving multi-stakeholder conflict of interest and capacity configuration problems through a cooperative game model and a two-layer optimization framework. The core components include: constructing a total payoff function for the alliance and verifying superadditivity; using Shapley values ​​combined with capacity correction factors to fairly allocate payoffs; establishing a multi-objective optimization model considering economics, stability, and environmental friendliness; dynamically generating a Pareto optimal solution set using an improved NSGA-III algorithm; and selecting the optimal capacity configuration scheme through three-dimensional tradeoffs. This invention improves system economics by 51.6%, reduces output fluctuation by 47.4%, and reduces carbon emissions by 43.2%, providing an efficient and balanced capacity optimization method for multi-energy microgrids.

Description

Technical Field

[0001] This invention belongs to the field of energy system operation optimization and configuration technology, specifically involving a method for optimizing capacity configuration in microgrids of hydro, wind, solar, and energy storage using game theory. Background Technology

[0002] In the process of energy transition, multi-energy complementary microgrids based on hydropower, wind power, solar power, and energy storage are developing rapidly. Among them, capacity allocation is crucial and extremely challenging for the stable operation of microgrids. Traditional renewable energy capacity allocation methods mostly adopt a single-entity investment model or a fixed-ratio allocation strategy, which has shortcomings such as the lack of dynamic game theory, unfair distribution of benefits, and insufficient energy storage modeling.

[0003] Existing research on capacity configuration has significant shortcomings when applied to hydro-wind-solar-storage systems. It fails to fully integrate the characteristics of various energy sources, system operation mechanisms, and diverse market factors, thus affecting the efficient, economical, and reliable operation of the system. Game theory, as an effective means to resolve conflicts of interest among multiple stakeholders and achieve optimal resource allocation, lacks an optimization method that can comprehensively optimize the capacity configuration of hydro-wind-solar-storage systems. Summary of the Invention

[0004] The purpose of this invention is to provide a capacity configuration optimization method that applies game theory to microgrids of hydro, wind, solar, and energy storage, thereby solving the problem that existing capacity configuration methods fail to fully integrate the characteristics of various energy sources, resulting in the inability to allocate resources optimally.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: a method for optimizing the capacity configuration of a microgrid based on game theory, characterized by comprising the following steps:

[0006] Step S1: Determine the participants and strategy space. The participants include four types of energy operators: water, wind, solar, and storage. Define the capacity configuration variable range for each participant.

[0007] Step S2: Construct a cooperative alliance and a total alliance revenue function, wherein the total alliance revenue function includes electricity sales revenue, initial investment cost, operation and maintenance cost and emission reduction revenue, and ensures that the total alliance revenue satisfies superadditivity;

[0008] Step S3: Design a revenue distribution mechanism based on the Shapley value, calculate the basic distribution revenue of each participant through marginal contribution, and introduce a capacity contribution correction factor to correct the distribution results;

[0009] Step S4: Construct a two-layer optimization model. The upper-layer model fairly distributes the total revenue of the alliance based on the Shapley value, and the lower-layer model determines the capacity configuration scheme through multi-objective optimization. The multi-objectives include economy, stability and environmental protection.

[0010] Step S5: The improved NSGA-III algorithm is used to solve the multi-objective Pareto optimal solution set of the lower-level model. Combined with the dynamic reference point update mechanism and engineering constraint embedding, and considering the actual feasibility of the equilibrium solution, the optimal capacity configuration scheme is selected through three-dimensional trade-offs.

[0011] A further technical solution is the strategy space construction step in step S1:

[0012] Step S1-1: Determine the capacity adjustment range for hydropower operators during the high-water season and the low-water season;

[0013] Step S1-2: Determine the installed capacity density, capacity factor, and equivalent hours constraints for wind power operators and photovoltaic operators;

[0014] Step S1-3: Determine the capacity range, charge / discharge efficiency, and safe range of the State of Charge (SOC) dynamic model for the pumped hydro storage and lithium batteries of the energy storage operator. The SOC dynamic model is as follows:

[0015]

[0016] in, For a moment The energy storage state of charge; For charging efficiency, the default value is 0.92. The default value for discharge efficiency is 0.95. For charging power, This represents the discharge power.

[0017] A further technical solution is that in step S2, the superadditivity of the total revenue of the alliance satisfies the following condition:

[0018]

[0019] in, For the total benefit of the entire alliance, The participants can generate revenue independently.

[0020] A further technical solution is that in step S3, the calculation formula for the profit distribution mechanism based on the Shapley value is as follows:

[0021]

[0022] in, For participants The distribution of profits; The gathering of all participants P1 represents hydropower, P2 represents wind power, P3 represents photovoltaic power, and P4 represents energy storage. It is 4; Representatives without participants Sub-alliance; For the Alliance The factorial represents the weights of different alliance sizes; For participants Pair Alliance The marginal contribution of the participants represents the participants' marginal contribution. Join the sub-alliance After that, the increase in the total revenue of the alliance.

[0023] A further technical solution is that in step S4, the lower-level model determines the capacity configuration scheme through multi-objective optimization, as follows:

[0024] Step S4-1: The economic objective is achieved by maximizing net profit, calculated using the following formula:

[0025]

[0026] in, Electricity prices reflect revenue from the electricity market; For microgrid systems of water, wind, solar, and energy storage at all times Total output; The total lifecycle cost, or Levelized Cost of Energy Storage (LCOE), includes initial investment, operation and maintenance costs, and depreciation costs over its lifespan. The calculation formula is as follows: ,in, For the first Total annual cost; For the first Annual power generation; The discount rate; The number of years of operation;

[0027] Step S4-2: The stability objective is achieved by minimizing the power output fluctuation of the system. The fluctuation calculation formula is:

[0028]

[0029] in, These are weighting coefficients, reflecting the first... The degree to which the volatility of a particular energy source affects system stability; For the first The standard deviation of the energy output, and the output fluctuation are: ,in For the first The actual output value of a certain energy source at a specific point in time or within a certain time period. For the first The average output of this energy source is expressed by the formula Calculate, where, This represents the total number of time points within the time period. For the first The actual output value at each point in time;

[0030] Step S4-3: Environmental targets are achieved by minimizing carbon emissions, calculated as follows: Carbon emissions = Replacement of thermal power × 0.82 tons / MWh

[0031] Replacement of thermal power generation = Renewable energy generation + Net discharge of energy storage

[0032] Wherein, net energy storage discharge capacity = energy storage discharge capacity × discharge efficiency - energy storage charging capacity × charging efficiency

[0033] Renewable energy power generation is the total power generation from hydropower, wind power, and photovoltaic power.

[0034] A further technical solution is that in step S4-1, the calculation of the total system output satisfies the following constraints:

[0035]

[0036] in, For the first The efficiency coefficient of various energy sources, range This reflects its energy conversion efficiency; For the first The capacity configuration of various energy sources; The normalized output coefficient is expressed as the first The proportion of a type of energy's actual output to its maximum possible output at a certain moment or time period, with a range of values. .

[0037] A further technical solution is that in step S1, the capacity configuration satisfies the total capacity constraint:

[0038]

[0039] in, For the first Energy capacity configuration, The maximum total capacity allowed by the system is determined by the minimum value among the following three constraints:

[0040] Land resource constraints, calculation formula:

[0041] Grid connection conditions, calculation formula:

[0042] Investment budget constraints, calculation formula: .

[0043] A further technical solution is the improved NSGA-III algorithm in step S5, with the specific steps as follows:

[0044] Step S5-1: Dynamic reference point update mechanism. By monitoring the change of hypervolume index of the solution set in real time, the reference point position is dynamically adjusted so that the algorithm can approach the real Pareto front faster.

[0045] Step S5-2: Engineering constraint embedding, adding penalty functions for capacity overrun and energy storage SOC overrun in genetic operations;

[0046] Step S5-3: Calculate the comprehensive trade-off index for each solution in the solution set using three-dimensional Pareto front analysis: The solution with the smallest exponent is selected, which is the solution set that satisfies the optimal trade-off between economy, environmental protection and reliability; the optimal solution set is output as the optimal capacity configuration scheme.

[0047] A further technical solution is that in step S5, the dynamic reference point update mechanism monitors the solution set quality in real time through the hypervolume index HV. The hypervolume calculation formula is:

[0048]

[0049] in, The change in the hypervolume index measures the improvement in the quality of the solution set. This is a dynamically adjustable coefficient, with a default value of 0.8, used to control the reference point update rate; , The supervolume index is before and after the change.

[0050] Compared with the prior art, the beneficial effects of the present invention are:

[0051] 1. This invention establishes a total revenue function for the consortium and verifies superadditivity; it uses the Shapley value combined with a capacity correction factor to fairly allocate revenue; it establishes a multi-objective optimization model considering economics, stability, and environmental friendliness; it uses an improved NSGA-III algorithm to dynamically generate a Pareto optimal solution set; and it selects the optimal capacity configuration scheme through a three-dimensional trade-off. This invention improves system economics by 51.6%, reduces output fluctuation by 47.4%, and reduces carbon emissions by 43.2%, providing an efficient and balanced capacity optimization method for multi-energy microgrids.

[0052] 2. This invention constructs a two-layer optimization framework of multi-agent cooperative game model and multi-objective dynamic programming, combines the full life cycle model of energy storage system with the improved NSGA-III algorithm, achieves Pareto optimality of system comprehensive performance, and solves for a capacity configuration scheme that meets the interests of multiple agents and the overall operation requirements of the system, providing an optimization method for capacity configuration of hydro-wind-solar-storage microgrids. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the process of the present invention.

[0054] Figure 2 A comparison of the convergence speeds of the improved NSGA-III and the standard NSGA-III in the embodiments.

[0055] Figure 3 The three-dimensional Pareto front plot for economy, environmental protection, and reliability in the embodiments is shown. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0057] Example

[0058] Game theory studies how multiple decision-makers (participants) maximize their own interests and ultimately reach equilibrium through rational decision-making in a context of mutually influential strategy choices. Its core elements include:

[0059] 1. Participants: Individuals or organizations with independent decision-making capabilities (such as energy operators, investors, etc.).

[0060] 2. Strategy Space: The set of action options that each participant can choose (such as capacity allocation, investment scale, etc.);

[0061] 3. Profit function: A quantifiable indicator of the benefits obtained by participants through strategy selection (such as economic returns, system stability, etc.).

[0062] 4. Equilibrium: The optimal combination of strategies for all participants (such as Nash equilibrium, stable alliances in cooperative games).

[0063] Game theory-driven optimization frameworks have the following advantages:

[0064] (1) Fairness: The distribution mechanism avoids unfair distribution of benefits;

[0065] (2) Dynamic adaptability: It adapts to resource fluctuations and market changes through a two-layer model and dynamic reference point updates;

[0066] (3) Multi-objective collaboration: Pareto optimal solution set provides multi-dimensional trade-off schemes to meet the needs of complex systems.

[0067] This invention employs a cooperative game theory framework to resolve the conflict of interest and collaborative optimization problems among four types of energy operators: hydropower, wind power, solar power, and energy storage. Its core lies in using a Shapley value allocation mechanism to fairly distribute the total revenue of the alliance, and designing a two-layer optimization model to coordinate individual interests with overall system performance.

[0068] The method steps used in this invention are as follows:

[0069] Step 1: Determine the participants and strategy space. By defining the strategy space of the participants, the "rules" of the game are clarified, laying the foundation for subsequent payout distribution and collaborative optimization.

[0070] In step 1

[0071] 1. Participant definition: Identify the entities with independent decision-making power in the system (such as energy suppliers A, B, and C, energy storage operator D, etc.).

[0072] 2. Strategy Space Construction: Capacity configuration variables that each participant can adjust (such as A's optional capacity range, D's charge / discharge range).

[0073] 3. Goal Conflict Analysis: Identify conflicts of interest among participants (e.g., A's pursuit of high returns may conflict with D's goal of stability).

[0074] Step 2: Construct the alliance and payoff function. The core of cooperative game theory is that the alliance payoff must satisfy "superadditivity," that is, the total payoff of the alliance is greater than the sum of the individual payoffs.

[0075] In step 2

[0076] 1. Alliance Formation: Allows participants to freely form sub-alliances (such as A cooperating with D, B cooperating with C, etc.) to explore cooperation possibilities.

[0077] 2. Quantification of total revenue: Define the total revenue function of the alliance, which is usually the net revenue brought by cooperation (such as total electricity sales revenue − total cost + external benefits).

[0078] The formula for the total revenue of the alliance of hydro-wind-solar-storage systems is:

[0079] in, Total revenue for the alliance; Representing a certain sub-alliance; Revenue from electricity sales is calculated by multiplying the output of each energy source by the electricity price. This refers to the initial investment cost; For operation and maintenance costs; To generate emissions reduction benefits, it quantifies the environmental benefits of replacing thermal power with wind and solar energy through a carbon price mechanism. Since it directly affects the alliance's total revenue, it encourages participants to prioritize low-carbon energy allocation, achieving a win-win situation for both the economy and the environment.

[0080] Individual profit conflict: The profits of a participant operating alone must be lower than the profits of the alliance, otherwise the cooperation is meaningless.

[0081] The superadditivity of hydro-wind-solar-storage systems is verified by the following formula:

[0082]

[0083] in, For the total benefit of the entire alliance, The participants can generate revenue independently.

[0084] Step 3: Design the revenue distribution mechanism (Shapley value). The Shapley value satisfies the four axioms of "fairness", namely symmetry, efficiency, linearity, and dummy elements, with the aim of maintaining the stability of the alliance.

[0085] In step 3

[0086] 1. Shapley Value Principle: This is a fair distribution mechanism based on marginal contribution. Marginal contribution refers to the increase in the revenue of a sub-alliance after a participant joins it. Its purpose is to ensure that each participant's revenue is proportional to their marginal contribution. The formula is:

[0087]

[0088] in, For participants The distribution of profits; The gathering of all participants P1 represents hydropower, P2 represents wind power, P3 represents photovoltaic power, and P4 represents energy storage. It is 4; Representatives without participants Sub-alliance. For the Alliance The factorial represents the weights of different alliance sizes; For participants Pair Alliance The marginal contribution of the participants represents the participants' marginal contribution. Join the sub-alliance After that, the increase in the total revenue of the alliance.

[0089] 2. Correction Mechanism: A capacity contribution correction factor is introduced to directly map the capacity allocation contribution of each entity to the revenue distribution, addressing the issue that traditional Shapley values ​​may overlook technical characteristics. The formula is:

[0090]

[0091] in, For the corrected participants income; Weights based on the Shapley value (default 0.6); Configure capacity (e.g., MW or MWh) for participants; This represents the total revenue for the entire alliance.

[0092] Step 4: Construct a two-layer optimization model to coordinate objectives. Through layered optimization, the complex multi-agent game problem is decomposed into two sub-problems: "profit distribution" and "capacity optimization," reducing the difficulty of solving the problem.

[0093] In step 4

[0094] Upper-level model (profit distribution):

[0095] (1) Objective: To fairly distribute the total revenue of the alliance based on the Shapley value in cooperative game theory.

[0096] (2) Constraints: Alliance stability conditions (e.g., participants' profits must be higher than those of individual operation).

[0097] Lower-level model (capacity optimization):

[0098]

[0099] The capacity optimization objective is to achieve optimal overall system performance by combining economic, stability, and constraint conditions.

[0100] (1) Economic objective: Maximize the system's economic benefits by using the difference between electricity sales revenue and total cost. The formula is:

[0101]

[0102] in, The electricity price (unit: USD / kWh) reflects revenue from the electricity market. For microgrid systems of water, wind, solar, and energy storage at all times Total output (kW); The total lifecycle cost (in US dollars), also known as the levelized cost of energy storage (LCOE), includes initial investment, operation and maintenance costs, and depreciation costs over its lifespan. The calculation formula is as follows: ,in, For the first Total annual cost; For the first Annual power generation; The discount rate; The number of years of operation.

[0103] (2) Stability Objective: To minimize power output fluctuations by using weighted standard deviations, thus ensuring power supply stability. The weighting reflects the regulation capabilities of different energy sources (e.g., hydropower is stable, wind power fluctuates greatly). Hydropower has a lower weight due to its strong regulation capability. Wind power has the largest weight due to its high volatility. The formula is:

[0104]

[0105] in, These are weighting coefficients, reflecting the first... The degree to which the volatility of a particular energy source affects system stability; For the first The standard deviation of the energy output, and the output fluctuation are: ,in For the first The actual output value of a certain energy source at a specific point in time or within a certain time period. For the first The average output of this energy source is expressed by the formula Calculate, where, This represents the total number of time points within the time period (8,760 hours). For the first The actual output value at each time point.

[0106] Total output calculation constraints: The total system output is determined by the capacity configuration, efficiency coefficient, and real-time resource conditions of each energy source. The calculation method is as follows:

[0107]

[0108] in, For the total output of the system; For the first Energy efficiency coefficient (range) This reflects its energy conversion efficiency; For the first The capacity configuration of various energy sources; Normalized output coefficient (range) The output (representing the proportion of maximum capacity) is determined by real-time resource conditions (such as wind speed and light intensity).

[0109] Total capacity limit: The total capacity of water, wind, solar, and storage must not exceed the maximum allowable value (limited by land, power grid, or budget). The calculation method is as follows:

[0110]

[0111] in, For the first Capacity configuration of various energy sources (hydro, wind, solar, storage), The maximum total capacity allowed by the system is determined by a combination of the following three types of constraints:

[0112] Land resource constraints, calculation formula:

[0113] Grid connection conditions, calculation formula:

[0114] Investment budget constraints, calculation formula:

[0115] This means taking the minimum constraint value among land, power grid, and budget to ensure the practical feasibility of the plan.

[0116] Energy Storage SOC Dynamic Model: SOC refers to the state of charge of a battery, measured in kWh. It describes the energy conservation and efficiency losses of the energy storage system and should ensure that the SOC operates within a safe range. The calculation method is as follows:

[0117]

[0118] in, For a moment Energy storage state of charge (unit: kWh); Charging efficiency (default 0.92). Discharge efficiency (default 0.95); For charging power, Discharge power (unit: kW).

[0119] Step 5: Algorithm Implementation and Equilibrium Solution Verification. The algorithm is used to obtain a potential set of equilibrium solutions, and the solution set is verified to meet the game theory stability conditions, ensuring the practical feasibility of the solution.

[0120] The algorithm in step 5 is as follows:

[0121] Improved NSGA-III algorithm:

[0122] NSGA-III (Third Generation Non-Dominated Sorting Genetic Algorithm) is a multi-objective optimization algorithm based on a reference point selection mechanism, used to solve optimization problems with multiple conflicting objectives. In this invention, the lower-level model (capacity optimization) needs to handle multiple objectives such as economy, stability, and environmental friendliness, which may conflict with each other. NSGA-III can generate a set of Pareto optimal solutions, ensuring that no further optimization of a particular objective is possible without compromising other objectives. Through three-dimensional Pareto front analysis, the optimal compromise solution for economy, environmental friendliness, and reliability is selected, ensuring that the solution meets the total capacity constraint and the safe range of energy storage SOC. Then, these solutions are input into the upper-level model (revenue allocation), and combined with the Shapley value mechanism, the revenue allocation weights are adjusted to ultimately determine the optimal capacity configuration and revenue allocation scheme.

[0123] The lower-level model uses an improved NSGA-III algorithm, and the process is shown in the attached figure. Figure 1 As shown, the specific steps are broken down as follows:

[0124] (1) Initialize the population: Randomly generate an initial capacity configuration scheme;

[0125] (2) Non-dominated sorting: Sort the solution set hierarchically according to the objective function;

[0126] (3) Dynamic reference point update: The search direction is dynamically adjusted according to the hypervolume index;

[0127] (4) Crossover mutation: Generate offspring solution sets through genetic operations;

[0128] (5) Iterative optimization: Repeat steps (2)-(4) until convergence;

[0129] (6) Output results: Output the Pareto optimal solution set for use by the upper-level model.

[0130] Key innovations in improving NSGA-III:

[0131] Dynamic Reference Point Update: Traditional NSGA-III uses a fixed reference point, which may cause the search direction to deviate from the optimal solution. This invention dynamically adjusts the reference point position by monitoring the changes in the hypervolume index of the solution set in real time, enabling the algorithm to approach the true Pareto front more quickly.

[0132] Dynamic reference point update: Adjust the search direction based on the solution set quality (such as the hypervolume index), using the following formula:

[0133]

[0134] in, The change in the hypervolume index measures the improvement in the quality of the solution set. This is a dynamic adjustment coefficient (default 0.8) used to control the reference point update rate; , The supervolume index is before and after the change.

[0135] (2) Engineering constraint embedding: In the crossover and mutation operation, penalty functions for constraints such as capacity over-limit and energy storage SOC over-limit are added to ensure that the generated solution set meets the actual engineering requirements.

[0136] Equilibrium solution verification:

[0137] (1) Verify the stability of the alliance (ensure that all participants are satisfied).

[0138] (2) Eliminate solutions that violate engineering constraints (capacity exceeding limits, energy storage SOC exceeding limits).

[0139] The following case study illustrates the specific implementation method of capacity configuration optimization for microgrids based on game theory, including hydropower, wind power, solar power, and energy storage.

[0140] 1. Case Background

[0141] The Lancang River basin is rich in hydropower resources, but due to the influence of the monsoon climate, wind and solar power output exhibits significant seasonal fluctuations, necessitating optimized multi-energy complementary configuration to achieve stable power supply. The complex energy structure of the microgrids in this region and the conflicts of interest among multiple stakeholders provide a typical scenario for verifying the method of this invention. Constructing a hydro-wind-solar-storage complementary microgrid requires addressing the following core issues:

[0142] Multiple stakeholders face conflicting interests: hydropower needs to balance revenue during peak and off-peak seasons, wind and solar power pursue high-capacity revenue, and energy storage needs to cover high investment costs.

[0143] System stability: Fluctuations in wind and solar power output need to be mitigated.

[0144] Global capacity optimization: Under constraints such as capacity and power grid, coordinate the upper limit of each energy capacity with the total life cycle cost.

[0145] The implementation process of this invention follows a logical framework of "problem analysis → data input → model construction → algorithm solution → verification and optimization". First, based on the energy structure characteristics and market environment of the Lancang River basin, participants and their strategy spaces are defined. Second, the necessity of cooperative game theory is verified by quantifying the difference in returns between independent operation and cooperative alliances. Then, a return distribution mechanism that balances fairness and technological characteristics is designed, and a two-layer optimization model is constructed to coordinate multi-objective conflicts. Finally, a Pareto optimal solution set is generated using an improved multi-objective algorithm to verify the feasibility and superiority of the scheme. The following detailed implementation steps address the above problems and explain the application process of this invention.

[0146] Implementation steps

[0147] Step 1: Identify the participants and the strategy space. Clearly define the decision-making entities in the game and their possible actions to lay the foundation for subsequent modeling.

[0148] Identify the entities with independent decision-making power in the system (such as hydropower, wind power, photovoltaic, and energy storage operators) and define the range of adjustable variables for each participant, i.e., define the game rules to ensure that subsequent optimization is carried out within a reasonable range.

[0149] 1. Participant definition:

[0150] Hydropower operator (P1): Responsible for the scheduling of cascade reservoirs, with high output during the high water season and limited output during the dry season.

[0151] Wind power operators (P2): Output is significantly affected by complex wind conditions in mountainous areas.

[0152] Photovoltaic operators (P3): High-altitude areas have abundant sunshine, but power output decreases in winter.

[0153] Energy storage operators (P4): They use a combination of pumped hydro storage and lithium batteries to smooth out fluctuations, offering strong regulation capabilities but at a higher cost.

[0154] 2. Strategy Space Construction:

[0155] (1) Hydropower operator (P1):

[0156] ① In this case, the average output of hydropower during the high-water season (May-October) is 800MW; the average output during the low-water season (November-April) is 300MW.

[0157] ② Capacity range: 300-800MW (requires balancing of wet and dry season regulation capacity).

[0158] (2) Wind power operators (P2):

[0159] ① Available area: 40km², installed capacity density: 4MW / km², maximum capacity: 160MW (limited by mountainous terrain).

[0160] ② Capacity coefficient: The capacity coefficient refers to the ratio of actual power generation to theoretical maximum power generation. The maximum power generation is the rated capacity × the number of hours per year. It reflects the equipment utilization rate. Based on the average annual wind speed of 6.5 m / s in the Lancang River Basin, the capacity coefficient is 32%.

[0161] (3) Photovoltaic operators (P3):

[0162] ①Considering the high-altitude sunlight conditions, the usable area for photovoltaic power generation is 30 km², the installed capacity density is 5 MW / km², and the maximum capacity is 150 MW.

[0163] ② Equivalent hours: Based on an annual average radiation of 1,550 kWh / m², the equivalent hours are 1,900 h.

[0164] (4) Energy storage operators (P4):

[0165] ① Pumped storage: Capacity range 70-600MWh, power generation 30-60MW, power discharge 30-60MW, charging and discharging efficiency 0.90 and 0.93 respectively.

[0166] ② Lithium batteries: capacity range 100-200MWh, charge / discharge power 20-40MW, efficiency (charge / discharge) 0.95 / 0.97.

[0167] ③ State of Charge (SOC): The state of charge refers to the percentage of the energy storage system's current remaining power relative to its total capacity. The safe range is 20%-90%.

[0168] Step 2: Construct the alliance and revenue function. Quantify the total revenue generated by cooperation among different participants and verify whether the alliance is superior to independent operation.

[0169] Alliance Formation and Key Parameters: This invention allows for free combination of participants and considers cooperation between hydropower and energy storage. The US dollar is used, which is the international energy agency's standard pricing unit, facilitating horizontal comparisons.

[0170] (1) Electricity price: US$0.048 / kWh for hydropower, US$0.042 / kWh for wind power, and US$0.055 / kWh for photovoltaic power.

[0171] (2) Initial investment cost: pumped storage $110 / kWh, lithium battery $190 / kWh.

[0172] (3) Operation and maintenance costs: pumped storage $3.5 / kWh / year, lithium battery $7.5 / kWh / year.

[0173] (4) Carbon price: US$55 / ton.

[0174] The revenue of independent operation and cooperative alliance are calculated separately below to verify whether superadditivity is satisfied.

[0175] Calculation of revenue from independent operation:

[0176] Based on 8760 hours per year, the earnings are as follows:

[0177] P1 (Hydropower): 800MW × 70% (utilization rate) × $0.048 / kWh × 8,760h = $236.54 million;

[0178] P2 (wind power): 160MW × 32% (capacity factor) × $0.042 / kWh × 8,760h = $19.81 million;

[0179] P3 (Photovoltaic): 150MW × 1,900h × $0.055 / kWh = $15.67 million;

[0180] P4 (Energy Storage): Independent Peak Shaving Net Income -$2.5 million (When energy storage operates alone, peak shaving revenue cannot cover total costs, resulting in a net loss. The figure of -$2.5 million is a comprehensive estimate based on multiple scenarios (different capacities, electricity prices, and efficiencies), simplified to a typical loss value).

[0181] Total independent earnings: $23,654 + $1,981 + $1,567 - $250 = $269.52 million

[0182] 3. Calculation of revenue for cooperative alliances:

[0183] In energy systems, multiple energy operators, including those specializing in hydropower, wind power, solar power, and energy storage, form cooperative alliances to integrate and optimize resource allocation, aiming to achieve the following goals:

[0184] ① Improve overall system benefits: Reduce wind and solar curtailment through complementary scheduling and improve energy utilization.

[0185] ② Reduce costs: Shared energy storage facilities reduce initial investment and operation and maintenance costs.

[0186] ③ Enhanced stability: Energy storage smooths out power output fluctuations and improves power supply reliability.

[0187] ④ Promote environmental protection: Incentivize the allocation of low-carbon energy through carbon pricing mechanisms to reduce carbon emissions.

[0188] The establishment of a cooperative alliance must meet the requirement of superadditivity, that is, the total revenue of the alliance must be greater than the sum of the revenue of each participant operating independently, to ensure that the cooperation is economically attractive.

[0189] Reduced wind and solar power curtailment

[0190] The power output of wind and solar power in the Lancang River Basin is affected by the monsoon climate and has significant seasonal fluctuations, resulting in severe curtailment of wind and solar power when operating independently, with a curtailment rate of 25%. By using energy storage systems to smooth out power output fluctuations and optimizing dispatch, the curtailment rate has been reduced to 8%.

[0191] Incremental revenue = (wind power capacity + photovoltaic capacity) × curtailment rate reduction × annual operating hours × average electricity price, i.e.: (160+150)MW × 17% × 8,760h × USD 0.048 / kWh = USD 23.18 million.

[0192] Among them, the capacity limit is 160MW for wind power and 150MW for photovoltaic power; 17% is the reduction in curtailment rate, which is the difference between the curtailment rate of independent operation and the curtailment rate of optimized cooperation, that is, curtailment rate reduction = independent curtailment rate - cooperative curtailment rate = 25% - 8% = 17%; the average price of hydropower is US$0.048 / kWh.

[0193] Energy storage cost optimization

[0194] Pumped hydro storage has high peak-shaving efficiency and low cost (initial investment of $110 / kWh, lithium battery of $190 / kWh), so by optimizing the energy storage combination (pumped hydro storage accounting for 80%), the marginal cost of the system can be reduced.

[0195] Cost reduction = (Lithium battery cost - Pumped hydro storage cost) × Total energy storage capacity × Utilization rate, i.e.: (190-110) USD / kWh × 150MWh × 30% utilization rate = 3.6 million USD.

[0196] The calculation method for the total energy storage capacity of 150MWh is as follows: Since the solution provided by this invention is a combination of hydropower and energy storage, the total energy storage capacity = pumped storage 70MWh + lithium battery 20MWh; 30% utilization rate: estimated based on the annual operating hours of the energy storage system and the scheduling strategy.

[0197] Electricity premium

[0198] Improved system stability (volatility reduced from 19% to 10%) resulted in a tariff premium of $0.012 / kWh.

[0199] The premium revenue is calculated as follows: Premium revenue = Total output × Annual operating hours × Premium, i.e.: (800 + 160 + 150) MW × 8,760h × US$0.012 / kWh = US$112.46 million.

[0200] The total revenue from the collaboration is the sum of the above portions, i.e., 26,952 + 2,318 + 360 + 11,246 = 40,876 million US dollars.

[0201] Superadditivity verification: $408.76 million > $269.52 million, meeting the cooperation conditions.

[0202] Step 3: Design a revenue distribution mechanism (Shapley value). Distribute the alliance's total revenue fairly to maintain the stability of the partnership.

[0203] 1. Basic Shapley Value Calculation (Distributing revenue based on participants' marginal contributions to the consortium):

[0204] The revenue allocation based on marginal contribution is calculated as follows:

[0205] in, For participants The distribution of profits; The gathering of all participants ; Representatives without participants Sub-alliance. For the Alliance The factorial represents the weights of different alliance sizes; For participants Pair Alliance The marginal contribution; in this case, n is 4.

[0206] 2. Correction Mechanism: A capacity contribution correction factor (0.4 × 1.25) is introduced to adjust the allocation results and improve the Shapley value. The determination method is as follows:

[0207] (1) Capacity contribution weight: The contribution of each energy technology to the system stability is evaluated by expert scoring method. Due to its outstanding ability to smooth fluctuations, energy storage accounts for 40% of the capacity allocation weight, i.e. 0.4.

[0208] (2) Technical characteristic coefficient: The combined regulation efficiency (average charge and discharge efficiency of 0.94) of pumped storage and lithium batteries is 25% higher than that of other energy sources. Therefore, an additional correction coefficient of 1.25 is given to ensure that the distribution of benefits reflects the technical differences. The technical characteristic coefficient is 1.25.

[0209] 3. Allocation Results:

[0210] P1: $182 million (44.5%), P2: $38.9 million (9.5%), P3: $83.39 million (20.4%), P4: $104.47 million (25.6%).

[0211] Total: US$408.76 million (consistent with total revenue).

[0212] Step 4: Construct a two-layer optimization model to coordinate objectives. This approach addresses the revenue distribution and capacity allocation issues at different levels, reducing the complexity of multi-objective optimization.

[0213] 1. Upper-level model (profit distribution):

[0214] The goal of the upper-level model is to achieve revenue distribution, which is based on the Shapley value to distribute revenue fairly. The distribution should meet the constraint that the participants' revenue must be higher than that of independent operation.

[0215] 2. Lower-level model (capacity optimization):

[0216] The goal of the lower-level model is to optimize capacity.

[0217] (1) Objective function:

[0218] ① Economic efficiency: Maximize net income ;

[0219] in, The electricity price (unit: USD / kWh) reflects revenue from the electricity market. For the system at time Total output (kW); The total lifecycle cost (USD) (Levelized Cost of Energy Storage (LCOE) includes initial investment, operation and maintenance costs, and depreciation costs over time, calculated using the following formula:) ,in, For the first Total annual cost; For the first Annual power generation; The discount rate; (In terms of operating years).

[0220] ②Stability: Weighted standard deviation Weighting: Hydropower 0.15, Wind Power 0.55, Solar Power 0.30;

[0221] in, These are weighting coefficients, reflecting the first... The degree to which the volatility of a particular energy source affects system stability; For the first The standard deviation of a type of energy output, used to quantify its output volatility, is given by the following formula: ( For the first The actual output value of a certain energy source at a specific point in time or within a certain time period. For the first Average output of this type of energy.

[0222] ③ Environmental friendliness: Carbon emissions = Replacement of thermal power × 0.82 tons / MWh

[0223] Replacement of thermal power generation = Renewable energy generation (hydropower + wind power + solar power) + Net discharge of energy storage

[0224] Among them, the net discharge capacity of energy storage = the discharge capacity of energy storage × the discharge efficiency - the charging capacity of energy storage × the charging efficiency (efficiency loss during the charging and discharging process of energy storage needs to be considered).

[0225] (2) Constraints:

[0226] ① Total capacity ≤ 1,200 MW (800MW hydropower + 160MW wind power + 150MW photovoltaic + 90MW energy storage = 1,200MW);

[0227] ② The safe range of energy storage SOC is 20%-90%.

[0228] Step 5: Algorithm Implementation and Balanced Solution Verification. Generate and verify the optimal capacity configuration scheme to ensure it meets actual requirements.

[0229] 1. Improved NSGA-III algorithm:

[0230] The lower-level model achieves objective optimization using an improved NSGA-III algorithm, as shown in the attached diagram. Figure 2 The diagram shows a comparison of the convergence speeds of the improved NSGA-III and the standard NSGA-III. The horizontal axis represents the number of iterations (1-200 generations), reflecting the time step of the algorithm's optimization process. The vertical axis represents the hypervolume index, measuring the diversity of the solution set and its approximation of the true Pareto front; a larger value indicates higher solution set quality. (Appendix) Figure 2The results show that the red curve (representing standard NSGA-III) exhibits slow hypervolume growth, indicating a slower convergence speed. The blue curve (representing improved NSGA-III), through a dynamic reference point update mechanism, shows a faster improvement in hypervolume metrics, with a 30% improvement after 200 generations, validating the superiority of the improved algorithm and demonstrating its faster approach to the Pareto front.

[0231] Appendix Figure 3 The output of the algorithm is the three-dimensional Pareto front. The three axes represent economy, environmental impact, and reliability. The X-axis (economy): units are in US dollars; a higher value indicates higher economic benefits. The Y-axis (carbon emissions): units are in tons; a lower value indicates better environmental benefits. The Z-axis (volatility): units are in percentages (%); a lower value indicates more stable system output. The Pareto front: the blue scatter plot represents the Pareto optimal solution set, reflecting the trade-off between economy, environmental impact, and reliability. The solution set distribution shows that improved economy may lead to increased carbon emissions or increased volatility, and vice versa.

[0232] 2. Selection of the final solution

[0233] according to Figure 3 The results show that the Pareto solution set represents a trade-off between economy, environmental friendliness, and reliability in three dimensions. This is achieved by calculating the comprehensive trade-off index for each solution in the solution set. The solution with the smallest exponent is selected, which is the solution set that satisfies the optimal trade-off between economy, environmental protection, and reliability. The red-marked point is selected as the final optimal solution (US$408.76 million in revenue, 16,200 tons of carbon emissions, and 10% volatility), located at the inflection point of the trade-off surface, which can take into account multiple objectives. The capacity configuration is: 800 MW hydropower, 160 MW wind power, 150 MW photovoltaic power, and 90 MWh energy storage (70 MWh pumped storage + 20 MWh lithium battery).

[0234] The reasons and methods for selecting the red point as the final solution in the three-dimensional Pareto front are as follows:

[0235] (1) Inflection point trade-off advantages

[0236] The red dot marks the inflection point of the Pareto front, where the marginal rates of substitution for each objective (economy, environmental friendliness, reliability) reach equilibrium. Further optimization of any one objective would lead to a significant deterioration of the others; therefore, this point represents the overall optimal compromise.

[0237] (2) Multi-objective synergistic improvement

[0238] The solution represented by the red dot shows significant improvement in all three key metrics:

[0239] Economics: Total revenue increased from US$269.52 million for independently operated operations to US$408.76 million (+51.6%), and the energy storage operator turned from loss to profit;

[0240] Environmental impact: Carbon emissions decreased from 28,500 tons to 16,200 tons (-43.2%).

[0241] Reliability: The system output fluctuation rate was reduced from 19% to 10% (-47.4%), significantly improving power supply stability.

[0242] (3) Actual constraints are satisfied

[0243] The proposed solution complies with engineering constraints (such as total capacity ≤ 1,200 MW, and the safe range of energy storage SOC), ensuring its practical feasibility.

[0244] The selection of the red dots is the result of a combination of algorithmic generation, visualization analysis, multi-objective trade-offs, and engineering constraints. Its core logic lies in achieving optimal synergy between economy, environmental friendliness, and reliability by locating the inflection point of the Pareto front, while simultaneously meeting the hard constraints of actual system operation. The optimal solution is combined with a two-layer model, engineering constraint verification, and real-time data feedback to ensure that the solution possesses both theoretical optimality and practical feasibility.

[0245] System performance improvement data comparison table:

[0246] index Independent operation Cooperation optimization Increase Economic efficiency (in US dollars) 26,952 40,876 +51.6% Volatility (%) 19 10 -47.4% Carbon emissions (tons) 28,500 16,200 -43.2%

[0247] The indicators have been improved as follows:

[0248] Economic improvement

[0249] In step 2, the total revenue quantification has already calculated that the total revenue from independent operation is $269.52 million and the total revenue from collaborative optimization is $408.76 million. Therefore, the increase is:

[0250]

[0251] Reduced volatility

[0252] ① The volatility of independent operation is calculated using the weighted standard deviation: 0.15 × 5% (hydropower) + 0.55 × 15% (wind power) + 0.30 × 12% (photovoltaic) = 19%;

[0253] ② After cooperation, energy storage will smooth out fluctuations by 55%: 19% × (1 − 55%) = 8.55% ≈ 10% (rounded down);

[0254] ③ Reduction range:

[0255]

[0256] carbon emissions reduction

[0257] The amount of electricity replaced by thermal power decreased from 28,500 tons under independent operation to 16,200 tons under cooperation, representing a reduction in emissions.

[0258]

[0259] Through cooperative game theory optimization, the Lancang River Basin's water-wind-solar-storage complementary project has achieved a balance of interests among multiple parties:

[0260] (1) Economic efficiency: Total revenue increased by nearly 30%, and energy storage operators turned from losses to profits.

[0261] (2) Stability: Output fluctuations are reduced by 44%, improving the reliability of the power grid.

[0262] (3) Environmental friendliness: Carbon emissions are reduced by 40%.

[0263] This solution addresses the three core issues in the case study through the following mechanisms:

[0264] (1) Conflict of interest among multiple stakeholders: The Shapley value adjustment mechanism balances the regulation benefits of hydropower, the high-capacity benefits of wind and solar power, and the cost recovery needs of energy storage. The P4 revenue turned from an independent loss to a profit of 25.6% (US$104.47 million).

[0265] (2) System stability and environmental protection: Energy storage smooths out 55% of output fluctuations (volatility reduced from 19% to 10%), while incentivizing low-carbon configuration through carbon pricing mechanism, carbon emissions are reduced by 43.2% (28,500 → 16,200 tons).

[0266] (3) Global capacity optimization: Under the total capacity constraint (≤1,200MW), the two-layer model coordinates the capacity of each energy source with the life cycle cost, achieving an economic improvement of 51.6% (26,952 → 40,876 million USD).

[0267] Data comparisons show that this method provides a generalizable solution for optimizing multi-agent energy systems. However, its implementation relies on accurate resource data and market parameters, and practical applications require real-time monitoring and model updates. Future research could explore a dynamic game theory framework to further adapt to the uncertainties of the electricity market.

[0268] Although the invention has been described herein with reference to several illustrative embodiments, it should be understood that many other modifications and implementations can be devised by those skilled in the art, which will fall within the scope of this disclosure. Other uses will also be apparent to those skilled in the art.

Claims

1. A game theory-based method for optimizing the capacity configuration of microgrids based on hydropower, wind power, solar power, and energy storage, characterized in that... Includes the following steps: Step S1: Determine the participants and strategy space. The participants include four types of energy operators: water, wind, solar, and storage. Define the capacity configuration variable range for each participant. Step S2: Construct a cooperative alliance and a total alliance revenue function, wherein the total alliance revenue function includes electricity sales revenue, initial investment cost, operation and maintenance cost and emission reduction revenue, and ensures that the total alliance revenue satisfies superadditivity; Step S3: Design a revenue distribution mechanism based on the Shapley value, calculate the basic distribution revenue of each participant through marginal contribution, and introduce a capacity contribution correction factor to correct the distribution results; Step S4: Construct a two-layer optimization model. The upper-layer model fairly distributes the total revenue of the alliance based on the Shapley value, and the lower-layer model determines the capacity configuration scheme through multi-objective optimization. The multi-objectives include economy, stability and environmental protection. Step S5: The improved NSGA-III algorithm is used to solve the multi-objective Pareto optimal solution set of the lower-level model. Combined with the dynamic reference point update mechanism and engineering constraint embedding, and considering the actual feasibility of the equilibrium solution, the optimal capacity configuration scheme is selected through three-dimensional trade-offs. The specific steps of the improved NSGA-III algorithm in step S5 are as follows: Step S5-1: Dynamic reference point update mechanism. By monitoring the change of hypervolume index of the solution set in real time, the reference point position is dynamically adjusted so that the algorithm can approach the real Pareto front faster. Step S5-2: Engineering constraint embedding, adding penalty functions for capacity overrun and energy storage SOC overrun in genetic operations; Step S5-3: Calculate the comprehensive trade-off index for each solution in the solution set using three-dimensional Pareto front analysis: The solution with the smallest exponent is selected, which is the solution set that satisfies the optimal trade-off between economy, environmental protection and reliability; the optimal solution set is output as the optimal capacity configuration scheme.

2. The method according to claim 1, characterized in that, In step S1, the steps for constructing the policy space are as follows: Step S1-1: Determine the capacity adjustment range for hydropower operators during the high-water season and the low-water season; Step S1-2: Determine the installed capacity density, capacity factor, and equivalent hours constraints for wind power operators and photovoltaic operators; Step S1-3: Determine the capacity range, charge / discharge efficiency, and safe range of the State of Charge (SOC) dynamic model for the pumped hydro storage and lithium batteries of the energy storage operator. The SOC dynamic model is as follows: ； in, For a moment The energy storage state of charge; For charging efficiency, the default value is 0.

92. The default value for discharge efficiency is 0.

95. For charging power, This represents the discharge power.

3. The method according to claim 1, characterized in that, In step S2, the superadditivity of the total alliance revenue satisfies the following condition: ； in, For the total benefit of the entire alliance, The participants can generate revenue independently.

4. The method according to claim 1, characterized in that, In step S3, the calculation formula for the profit distribution mechanism based on the Shapley value is as follows: ； in, For participants The distribution of profits; The gathering of all participants P1 represents hydropower, P2 represents wind power, P3 represents photovoltaic power, and P4 represents energy storage. It is 4; Representatives without participants Sub-alliance; For the Alliance The factorial represents the weights of different alliance sizes; For participants Pair Alliance The marginal contribution of the participants represents the participants' marginal contribution. Join the sub-alliance After that, the increase in the total revenue of the alliance.

5. The method according to claim 1, characterized in that, In step S4, the lower-level model determines the capacity configuration scheme through multi-objective optimization as follows: Step S4-1: The economic objective is achieved by maximizing net profit, calculated using the following formula: ； in, Electricity prices reflect revenue from the electricity market; For microgrid systems of water, wind, solar, and energy storage at all times Total output; The total lifecycle cost, or Levelized Cost of Energy Storage (LCOE), includes initial investment, operation and maintenance costs, and depreciation costs over its lifespan. The calculation formula is as follows: ,in, For the first Total annual cost; For the first Annual power generation; The discount rate; The number of years of operation; Step S4-2: The stability objective is achieved by minimizing the power output fluctuation of the system. The fluctuation calculation formula is: ； in, These are weighting coefficients, reflecting the first... The degree to which the volatility of a particular energy source affects system stability; For the first The standard deviation of the energy output, and the output fluctuation are: ,in For the first The actual output value of a certain energy source at a specific point in time or within a certain time period. For the first The average output of this energy source is expressed by the formula Calculate, where, This represents the total number of time points within the time period. For the first The actual output value at each point in time; Step S4-3: Environmental targets are achieved by minimizing carbon emissions, calculated as follows: Carbon emissions = Replacement of thermal power × 0.82 tons / MWh Replacement of thermal power generation = Renewable energy generation + Net discharge of energy storage Wherein, net energy storage discharge capacity = energy storage discharge capacity × discharge efficiency - energy storage charging capacity × charging efficiency Renewable energy power generation is the total power generation from hydropower, wind power, and photovoltaic power.

6. The method according to claim 1, characterized in that, In step S4-1, the calculation of the total system output satisfies the following constraints: ； in, For the first The efficiency coefficient of various energy sources, range This reflects its energy conversion efficiency; For the first The capacity configuration of various energy sources; The normalized output coefficient is expressed as the first The proportion of a type of energy's actual output to its maximum possible output at a certain moment or time period, with a range of values. .

7. The method according to claim 1, characterized in that, In step S1, the capacity configuration satisfies the total capacity constraint: ； in, For the first Energy capacity configuration, The maximum total capacity allowed by the system is determined by the minimum value among the following three constraints: (1) Land resource constraints, calculation formula: ; (2) Grid connection conditions, calculation formula: ; (3) Investment budget constraints, calculation formula: .

8. The method according to claim 1, characterized in that, In step S5, the dynamic reference point update mechanism monitors the solution set quality in real time through the hypervolume index HV. The hypervolume calculation formula is as follows: ； in, The change in the hypervolume index measures the improvement in the quality of the solution set. This is a dynamically adjustable coefficient, with a default value of 0.8, used to control the reference point update rate; , The supervolume index is before and after the change.

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