Method for optimizing capacity configuration of water, wind and light storage micro-grid based on game theory

Abstract

The invention discloses a game theory-based capacity configuration optimization method for a water, wind and light storage micro-grid, and relates to the technical field of energy system operation optimization configuration. According to the method, four types of energy operators including water, wind, light and storage serve as game subjects, and the problems of multi-subject benefit conflict and capacity configuration are solved through a cooperative game model and a double-layer optimization framework. The method comprises the following steps: constructing an alliance total revenue function and verifying the super-additivity; fairly distributing earnings by adopting a Shapley value in combination with a capacity correction factor; an economical, stable and environment-friendly multi-objective optimization model is established, an improved NSGA-III algorithm is utilized to dynamically generate a Pareto optimal solution set, and an optimal capacity configuration scheme is selected through three-dimensional tradeoff. According to the invention, the economical efficiency of the system is improved by 51.6%, the output fluctuation is reduced by 47.4%, the carbon emission is reduced by 43.2%, and an efficient and balanced capacity optimization method is provided for the multi-energy microgrid.

Description

Technical Field

[0001] The present invention belongs to the technical field of energy system operation optimization configuration, and specifically relates to a capacity configuration optimization method using game theory in a water, wind, solar and storage microgrid. Background Art

[0002] In the energy transition, microgrids combining hydropower, wind power, solar power, and energy storage are rapidly developing. Capacity allocation is crucial for the stable operation of microgrids and is extremely challenging. Traditional methods for allocating renewable energy capacity often rely on single-party investment or fixed-ratio allocation strategies, which suffer from a lack of dynamic game-playing relationships, unfair distribution of benefits, and inadequate energy storage modeling.

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

[0004] The purpose of the present invention is to provide a capacity configuration optimization method for hydro-wind-solar-storage microgrids using game theory to solve the problem that existing capacity configuration methods fail to fully integrate the characteristics of various energy sources, resulting in inefficient resource allocation.

[0005] To solve the above technical problems, the present invention adopts the following technical solution: a method for optimizing the capacity configuration of a water-wind-solar-storage microgrid based on game theory, characterized by comprising 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: Constructing 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 the total alliance revenue satisfies superadditivity; Step S3: Design a profit distribution mechanism based on the Shapley value, calculate the basic distribution profit of each participant through marginal contribution, and introduce a capacity contribution correction factor to correct the distribution result; Step S4: Construct a two-layer optimization model. The upper layer model fairly distributes the total revenue of the alliance based on Shapley value, and the lower layer model determines the capacity allocation plan 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 model. Combined with the dynamic reference point update mechanism and engineering constraint embedding, combined with the practical feasibility of the equilibrium solution, the optimal capacity configuration scheme is selected through three-dimensional trade-off.

[0006] A further technical solution is the step of constructing the strategy space in step S1: Step S1-1: Determine the capacity adjustment range of the hydropower operator during the flood season and the dry season; Step S1-2: Determine the installed capacity density, capacity factor and equivalent hours constraints of wind power operators and photovoltaic operators; Step S1-3: Determine the capacity range, charge / discharge efficiency, and safety interval of the state of charge (SOC) dynamic model of the energy storage operator's pumped storage and lithium battery. The SOC dynamic model is: in, For the moment Energy storage state of charge; is the charging efficiency, the default value is 0.92, is the discharge efficiency, the default value is 0.95; is the charging power, is the discharge power.

[0007] A further technical solution is that in step S2, the superadditivity of the total alliance revenue satisfies the following conditions: in, is the total revenue of the entire alliance, Independent operating income for participants.

[0008] A further technical solution is that in step S3, the calculation formula of the profit distribution mechanism designed based on the Shapley value is: in, For participants the distribution of income; Represents the set of all participants , P1 represents hydropower, P2 represents wind power, P3 represents photovoltaic power, and P4 represents energy storage; is 4; Representatives do not include participants Sub-alliance of For sub-alliance The factorial of , which represents the weight of different alliance sizes; For participants Pair Alliance The marginal contribution of the participants Join a sub-alliance After that, the increase in the total revenue of the alliance.

[0009] A further technical solution is that in step S4, the lower-level model determines the capacity configuration scheme through multi-objective optimization as follows: Step S4-1: The economic goal is achieved by maximizing net benefits. The net benefits calculation formula is: in, is the electricity price, reflecting the electricity market revenue; For water, wind, solar and storage microgrid systems at all times Total output; The total life cycle cost, or LCOE, is the levelized cost of energy storage over the entire life cycle, including initial investment, operation and maintenance costs, and life depreciation costs. The calculation formula is: ,in, For the Total annual cost; For the Annual power generation; is the discount rate; is the operating period; Step S4-2: The stability goal is achieved by minimizing the system output fluctuation. The fluctuation calculation formula is: in, is the weight coefficient, reflecting the The degree to which the volatility of energy sources affects system stability; For the The standard deviation of the energy output and the output fluctuation are: ,in For the The actual output value of a certain energy at a certain point in time or within a certain period of time. For the The average output of the energy is calculated by the formula Calculate, where is the total number of time points in the time period, For the The actual output value at a time point; Step S4-3: Environmental protection goals are achieved by minimizing carbon emissions, calculated as follows: Carbon emissions = replaced thermal power × 0.82 tons / MWh Replacement of thermal power = renewable energy power generation + net energy storage discharge Among them, the net discharge of energy storage = energy storage discharge × discharge efficiency - energy storage charge × charge efficiency Renewable energy generation is the total power generation of hydropower, wind power and photovoltaic power.

[0010] A further technical solution is that in step S4-1, the total system output calculation satisfies the following constraints: in, For the Efficiency coefficient of energy, range , reflecting its energy conversion efficiency; For the Capacity configuration of various energy sources; is the normalized output coefficient The ratio of the actual output of a type of energy to its maximum possible output at a certain moment or time period, with a value range of .

[0011] A further technical solution is that in step S1, the capacity configuration satisfies the total capacity constraint: in, For the Energy capacity configuration, The maximum total capacity allowed by the system is the minimum value among the following three constraints: Land resource constraints, calculation formula: Grid access conditions, calculation formula: Investment budget constraint, calculation formula: .

[0012] A further technical solution is that the specific steps of the improved NSGA-III algorithm in step S5 are as follows: Step S5-1: Dynamic reference point update mechanism, which dynamically adjusts the reference point position by real-time monitoring of the change in the hypervolume index of the solution set, so that the algorithm can approach the true Pareto front faster; Step S5-2: Embed engineering constraints and add penalty functions for capacity over-limit and energy storage SOC out-of-bounds in genetic operations; Step S5-3: Calculate the comprehensive trade-off index of each solution in the solution set through three-dimensional Pareto front analysis: , select the solution with the smallest index, that is, the solution set that satisfies the optimal compromise among economy, environmental protection and reliability; the output of the optimal solution set is the optimal capacity configuration plan.

[0013] A further technical solution is that in step S5, the dynamic reference point update mechanism monitors the quality of the solution in real time through the hypervolume indicator HV. The hypervolume calculation formula is: in, is the change in the super volume index, which measures the improvement in the quality of the solution set; It is a dynamic adjustment coefficient with a default value of 0.8, which is used to control the reference point update rate; 、 is the hypervolume index before and after the change.

[0014] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention constructs a total alliance revenue function and verifies superadditivity; uses Shapley values combined with capacity correction factors to fairly distribute revenue; establishes a multi-objective optimization model for economic efficiency, stability, and environmental protection, dynamically generates a Pareto optimal solution set using an improved NSGA-III algorithm, and selects the optimal capacity allocation scheme through three-dimensional trade-offs. This invention improves system economic efficiency 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.

[0015] 2. This invention achieves the Pareto optimality of the system's comprehensive performance by constructing a two-level optimization framework of a multi-agent cooperative game model and multi-objective dynamic programming, combining the energy storage system's full life cycle model with an improved NSGA-III algorithm, and solving a capacity configuration scheme that meets the interests of multiple agents and the overall operation requirements of the system, providing an optimization method for the capacity configuration of hydropower, wind power, solar power, and storage microgrids. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a schematic diagram of the process of the present invention.

[0017] Figure 2 Convergence speed comparison chart of improved NSGA-III and standard NSGA-III in the embodiment.

[0018] Figure 3 It is a three-dimensional Pareto front diagram of economy, environmental protection and reliability in the embodiment. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present 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 only used to explain the present invention and are not intended to limit the present invention.

[0020] Example Game theory studies how multiple decision-makers (participants) maximize their own interests through rational decision-making in the context of mutually influential strategic choices and ultimately reach equilibrium. Its core elements include: 1. Participants: individuals or organizations with independent decision-making capabilities (such as energy operators, investors, etc.); 2. Strategy space: the set of action options available to each participant (e.g., capacity allocation, investment scale, etc.); 3. Benefit function: a quantitative indicator of the benefits obtained by participants through strategy selection (such as economic benefits, system stability, etc.); 4. Equilibrium: The optimal combination of strategies of all participants (such as Nash equilibrium and stable alliances in cooperative games).

[0021] The game theory-driven optimization framework has the following advantages: (1) Fairness: The distribution mechanism avoids unfair distribution of benefits; (2) Dynamic adaptability: Adapting to resource fluctuations and market changes through a two-layer model and dynamic reference point updates; (3) Multi-objective collaboration: The Pareto optimal solution set provides a multi-dimensional trade-off solution to meet the needs of complex systems.

[0022] This invention uses a cooperative game framework to address conflicts of interest and collaborative optimization issues among four energy operators: hydropower, wind power, solar power, and storage. Its core approach is to fairly distribute the alliance's total revenue through a Shapley value allocation mechanism and to design a two-tier optimization model to coordinate individual interests with overall system performance.

[0023] The method steps adopted by the present invention are as follows: Step 1: Identify the participants and strategy space. By defining the strategy space of the participants and clarifying the "rules" of the game, we lay the foundation for subsequent profit distribution and collaborative optimization.

[0024] In step 1 1. Participant definition: Identify the entities with independent decision-making power in the system (e.g., energy suppliers A, B, C, energy storage operator D, etc.).

[0025] 2. Strategy space construction: capacity configuration variables that can be adjusted by each participant (such as the optional capacity range of A and the charging and discharging range of D).

[0026] 3. Goal conflict analysis: Identify conflicts of interest between participants (e.g., A’s pursuit of high returns may conflict with D’s goal of stability).

[0027] Step 2: Construct the alliance and benefit function. The core of the cooperative game is that the alliance benefit must satisfy the "superadditivity" property, that is, the total alliance benefit is greater than the sum of the individual benefits.

[0028] In step 2 1. Alliance formation: Allow participants to freely form sub-alliances (such as A and D cooperating, B and C cooperating, etc.) to explore cooperation possibilities.

[0029] 2. Quantification of total benefits: Define the total benefit function of the alliance, which is usually the net benefit brought by the cooperation (such as total electricity sales revenue − total costs + external benefits).

[0030] The total revenue formula of the water, wind, solar and storage system alliance is: in, is the total revenue of the alliance; Representing a sub-alliance; The income from electricity sales is calculated by multiplying the output of each energy source by the electricity price; is the initial investment cost; Operation and maintenance costs; In order to achieve emission 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 total revenue of the alliance, it encourages participants to give priority to low-carbon energy configurations and achieve a win-win situation for economy and environmental protection.

[0031] Conflict of individual benefits: The benefits of individual participants operating independently must be lower than the benefits of the alliance, otherwise cooperation is meaningless.

[0032] The superadditivity of the water-wind-solar-storage system is verified by the following formula: in, is the total revenue of the entire alliance, Independent operating income for participants.

[0033] Step 3: Design a profit distribution mechanism (Shapley value). The Shapley value satisfies the four axioms of fairness, namely symmetry, efficiency, linearity, and dummy variables, with the goal of maintaining alliance stability.

[0034] In the step 3, 1. Shapley Value Principle: It is a fair distribution mechanism based on marginal contribution. Marginal contribution refers to the incremental 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: in, For participants the distribution of income; Represents the set of all participants , P1 represents hydropower, P2 represents wind power, P3 represents photovoltaic power, and P4 represents energy storage; is 4; Representatives do not include participants Sub-alliance. For sub-alliance The factorial of , which represents the weight of different alliance sizes; For participants Pair Alliance The marginal contribution of the participants Join a sub-alliance After that, the increase in the total revenue of the alliance.

[0035] 2. Correction mechanism: Introduce a capacity contribution correction factor to directly map each entity's capacity configuration contribution to the revenue distribution, solving the problem that the traditional Shapley value may ignore technical characteristics. The formula is: in, For the corrected participants income; The weight of the basic Shapley value (default 0.6); The capacity configuration of the participant (e.g. MW or MWh); is the total income of the entire alliance.

[0036] Step 4: Construct a two-layer optimization model to coordinate objectives. Through hierarchical optimization, the complex multi-agent game problem is decomposed into two sub-problems: "revenue distribution" and "capacity optimization," reducing the difficulty of solving the problem.

[0037] In the step 4, Upper model (income distribution): (1) Objective: To fairly distribute the total revenue of the alliance based on the Shapley value in cooperative game theory.

[0038] (2) Constraints: Alliance stability conditions (e.g., participants’ profits must be higher than their individual operating profits).

[0039] Lower layer model (capacity optimization): The capacity optimization goal is to achieve the best overall system performance by combining economic efficiency, stability goals and constraints. (1) Economic objective: Maximize the economic benefits of the system by using the difference between electricity sales revenue and total cost. The formula is: in, is the electricity price (unit: US dollars / kWh), reflecting the electricity market revenue; For water, wind, solar and storage microgrid systems at all times Total output (kW); is the total life cycle cost (unit: US dollars), that is, the levelized cost of energy storage (LCOE) over the entire life cycle, including initial investment, operation and maintenance costs and life depreciation costs. The calculation formula is: ,in, For the Total annual cost; For the Annual power generation; is the discount rate; The operating period.

[0040] (2) Stability target: By weighting the standard deviation, the system output fluctuation is minimized to ensure the stability of power supply. The weight distribution reflects the regulation ability of different energy sources (such as hydropower is stable, wind power has large fluctuations). Hydropower has a lower weight due to its strong regulation ability. , wind power has the largest weight due to its high volatility, The formula is: in, is the weight coefficient, reflecting the The degree to which the volatility of energy sources affects system stability; For the The standard deviation of the energy output and the output fluctuation are: ,in For the The actual output value of a certain energy at a certain point in time or within a certain period of time. For the The average output of the energy is calculated by the formula Calculate, where is the total number of time points in the time period (taken as 8,760 hours), For the The actual output value at a time point.

[0041] 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: in, is the total output of the system; For the Efficiency coefficient of energy (range ), reflecting its energy conversion efficiency; For the Capacity configuration of various energy sources; is the normalized output coefficient (range , indicating the proportion of output to maximum capacity), which is determined by real-time resource conditions (such as wind speed and light intensity).

[0042] Total capacity limit: The total capacity of water, wind, solar, and storage must not exceed the maximum allowed (limited by land, grid, or budget). The calculation method is as follows: in, For the capacity configuration of various energy sources (water, wind, light, storage), The maximum total capacity allowed by the system, whose specific value is determined by the following three types of constraints: Land resource constraints, calculation formula: Grid access conditions, calculation formula: Investment budget constraint, calculation formula: That is, the minimum constraint value among land, power grid and budget is taken to ensure that the plan is actually feasible.

[0043] Energy storage SOC dynamic model: SOC is the battery's state of charge, measured in kWh. It describes the energy conservation and efficiency loss of the energy storage system and should ensure that the state of charge (SOC) operates within a safe range. The calculation method is as follows: in, For the moment Energy storage state of charge (kWh); is the charging efficiency (default 0.92), is the discharge efficiency (default 0.95); is the charging power, is the discharge power (unit: kW).

[0044] Step 5: Algorithm implementation and equilibrium solution verification. Use the algorithm to obtain a set of potential equilibrium solutions and verify that the solution set meets the game theory stability conditions to ensure the practical feasibility of the solution.

[0045] The algorithm in step 5 is: Improved NSGA-III algorithm: 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) must address multiple objectives, such as economy, stability, and environmental protection, which may conflict with each other. NSGA-III generates a set of Pareto-optimal solutions, where no objective can be further optimized without compromising other objectives. Through three-dimensional Pareto front analysis, it selects the optimal compromise between economy, environmental protection, and reliability, ensuring that the solution satisfies the total capacity constraints and the energy storage SOC safety range. These solutions are then input into the upper-level model (revenue distribution), which, combined with the Shapley value mechanism, adjusts the revenue distribution weights to ultimately determine the optimal capacity configuration and revenue distribution scheme.

[0046] The lower model uses the improved NSGA-III algorithm, and the process is as shown in the attached Figure 1 The specific steps are as follows: (1) Initialize the population: randomly generate an initial capacity configuration plan; (2) Non-dominated sorting: hierarchical sorting of the solution set according to the objective function; (3) Dynamic reference point update: Dynamically adjust the search direction according to the hypervolume index; (4) Crossover mutation: Generate offspring solution sets through genetic operations; (5) Iterative optimization: Repeat steps (2) to (4) until convergence; (6) Output results: Output the Pareto optimal solution set for use by the upper model.

[0047] The core innovations of NSGA-III are: Dynamic reference point update: The traditional NSGA-III has 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 change in the hypervolume index of the solution set in real time, allowing the algorithm to approach the true Pareto front more quickly.

[0048] Dynamic reference point update: adjust the search direction according to the solution quality (such as the hypervolume index), the formula is: in, is the change in the super volume index, which measures the improvement in the quality of the solution set; It is a dynamic adjustment coefficient (default 0.8) used to control the reference point update rate; 、 is the hypervolume index before and after the change.

[0049] (2) Engineering constraint embedding: In the cross-mutation operation, penalty functions for constraints such as capacity exceeding the limit and energy storage SOC exceeding the limit are added to ensure that the generated solution set meets the actual engineering requirements.

[0050] Equilibrium solution verification: (1) Verify alliance stability (ensure all participants are satisfied).

[0051] (2) Eliminate solutions that violate engineering constraints (capacity exceeds limit, energy storage SOC exceeds the limit).

[0052] The following case study illustrates the specific implementation method of capacity configuration optimization of hydro-wind-solar-storage microgrid based on game theory.

[0053] 1. Case Background The Lancang River Basin boasts abundant hydropower resources, but the monsoon climate causes significant seasonal fluctuations in wind and solar output, necessitating a stable power supply through multi-energy complementary optimization. The complex energy structure and conflicting interests of multiple stakeholders in this region's microgrids provide a typical scenario for validating the proposed method. To build a hydro-wind-solar-storage complementary microgrid, the following core issues must be addressed: Conflicts of interest among multiple entities: hydropower needs to balance revenue during wet and dry seasons, wind and solar power pursue high capacity returns, and energy storage needs to cover high investment costs.

[0054] System stability: Fluctuations in wind and solar power output need to be smoothed out.

[0055] Global capacity optimization: Coordinate the upper limit of each energy capacity with the full life cycle cost under constraints such as capacity and power grid.

[0056] The implementation process of the method of the present invention follows the 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, the participants and their strategy space are defined; secondly, by quantifying the difference in income between independent operation and cooperative alliance, the necessity of cooperative game is verified; then, a profit distribution mechanism that takes into account both fairness and technical characteristics is designed, and a two-layer optimization model is constructed to coordinate multi-objective conflicts; finally, a Pareto optimal solution set is generated through an improved multi-objective algorithm to verify the feasibility and superiority of the solution. The following combines specific implementation steps to solve the above problems and explains in detail the application process of the method of the present invention.

[0057] Implementation steps Step 1: Identify the players and strategy space. Identify the decision-makers in the game and their possible actions to lay the foundation for subsequent modeling.

[0058] Identify the entities in the system with independent decision-making power (such as hydropower, wind power, photovoltaic, and energy storage operators) and define the range of adjustable variables for each participant, that is, define the rules of the game to ensure that subsequent optimization is carried out within a reasonable range.

[0059] 1. Definition of Participants: Hydropower Operator (P1): Responsible for the scheduling of cascade reservoirs, with high output during the flood season and limited output during the dry season.

[0060] Wind power operator (P2): Output is affected by complex wind conditions in mountainous areas and is subject to significant fluctuations.

[0061] Photovoltaic operator (P3): There is sufficient sunlight in the plateau area, but the output decreases in winter.

[0062] Energy storage operator (P4): Fluctuations are smoothed through hybrid energy storage of pumped storage and lithium batteries. This has strong regulation capabilities but is relatively costly.

[0063] 2. Strategy space construction: (1) Hydropower Operator (P1): ① In this case, the average hydropower output during the flood season (May-October) is 800MW; the average hydropower output during the dry season (November-April) is 300MW.

[0064] ②Capacity range: 300-800MW (needs to balance the regulation capacity during wet and dry seasons).

[0065] (2) Wind power operator (P2): ①Usable area: 40km², installed density: 4MW / km², and upper capacity limit: 160MW (limited by mountainous terrain).

[0066] ②Capacity coefficient: The capacity coefficient refers to the ratio of actual power generation to theoretical maximum power generation, where the maximum power generation is rated capacity × number of hours per year. It reflects the equipment utilization rate. Based on the Lancang River basin's average annual wind speed of 6.5m / s, the capacity coefficient is 32%.

[0067] (3) Photovoltaic Operator (P3): ① Photovoltaic takes into account the plateau lighting conditions, with an available area of 30km², an installed density of 5MW / km², and a maximum capacity of 150MW.

[0068] ②Equivalent hours: Based on the annual average radiation of 1,550kWh / m², the equivalent hours are 1,900h.

[0069] (4) Energy storage operator (P4): ① Pumped storage: capacity range 70-600MWh, generation power 30-60MW, discharge power 30-60MW, charging and discharging efficiency of 0.90 and 0.93.

[0070] ②Lithium battery: capacity range 100-200MWh, charge and discharge power 20-40MW, efficiency (charge / discharge) 0.95 / 0.97.

[0071] ③ State of Charge (SOC): The state of charge refers to the percentage of the energy storage system's current remaining power to its total capacity, with a safety range of 20%-90%.

[0072] Step 2: Construct an alliance and revenue function. Quantify the total revenue from collaboration among different participants and verify whether the alliance is superior to independent operation.

[0073] Alliance formation and key parameters: Participants are allowed to freely combine, and this invention considers cooperation between hydropower and energy storage. The US dollar is used as the International Energy Agency's universal pricing standard to facilitate horizontal comparison.

[0074] (1) Electricity price: hydropower: USD 0.048 / kWh, wind power: USD 0.042 / kWh, photovoltaic power: USD 0.055 / kWh.

[0075] (2) Initial investment cost: pumped storage: USD 110 / kWh; lithium battery: USD 190 / kWh.

[0076] (3) Operation and maintenance costs: pumped storage: US$3.5 / kWh / year; lithium battery: US$7.5 / kWh / year.

[0077] (4) Carbon price: US$55 / ton.

[0078] The following calculates the benefits of independent operation and cooperative alliance respectively to verify whether superadditivity is satisfied.

[0079] Calculation of independent operating income: Based on 8760 hours per year, the income is as follows: P1 (hydropower): 800MW × 70% (utilization rate) × $0.048 / kWh × 8,760h = $236.54 million; P2 (wind power): 160MW × 32% (capacity factor) × $0.042 / kWh × 8,760h = $19.81 million; P3 (photovoltaic): 150MW x 1,900h x $0.055 / kWh = $15.67 million; P4 (Energy Storage): Net revenue from independent peak regulation is -$2.5 million. (When energy storage operates independently, peak regulation revenue cannot cover total costs, resulting in a net loss. The -$2.5 million is a comprehensive estimate of multiple scenarios (different capacities, electricity prices, and efficiencies), simplified to a typical loss value.)

[0080] Total independent income: $23,654 + $1,981 + $1,567 − $250 = $269.52 million 3. Calculation of cooperative alliance income: In the energy system, operators of multiple energy sources, including water, wind, solar, and storage, form cooperative alliances to integrate resources and optimize their allocation, aiming to achieve the following goals: ① Improve the overall benefits of the system: reduce wind and solar power curtailment through complementary scheduling and improve energy utilization.

[0081] ② Reduce costs: Share energy storage facilities to reduce initial investment and operation and maintenance costs.

[0082] ③ Enhanced stability: Energy storage can smooth out output fluctuations and improve power supply reliability.

[0083] ④ Promote environmental protection: Encourage low-carbon energy allocation and reduce carbon emissions through the carbon pricing mechanism.

[0084] The establishment of a cooperative alliance must meet superadditivity, that is, the total income of the alliance must be greater than the sum of the independent operating income of each participant to ensure that the cooperation is economically attractive.

[0085] Reduced wind and solar curtailment The output of wind and solar power in the Lancang River Basin is affected by the monsoon climate and has significant seasonal fluctuations, resulting in serious wind and solar power curtailment during independent operation, with a curtailment rate of 25%. The output fluctuations are smoothed by the energy storage system, and the curtailment rate is reduced to 8% after optimized scheduling.

[0086] Incremental revenue = (wind power capacity + photovoltaic capacity) × reduction in curtailment rate × annual operating hours × average electricity price, that is: (160+150)MW×17%×8,760h×0.048 US dollars / kWh=US$23.18 million.

[0087] Among them, the capacity limit for wind power is 160MW and for photovoltaic power is 150MW; 17% is the reduction in the curtailment rate, which is the difference between the independent operation curtailment rate and the optimized cooperation curtailment rate, that is, the reduction in the curtailment rate = independent operation curtailment rate − cooperation curtailment rate = 25% − 8% = 17%; the average hydropower price is US$0.048 / kWh.

[0088] Energy storage cost optimization Pumped storage has high peak-shaving efficiency and low cost (initial investment is US$110 / kWh, lithium batteries are US$190 / kWh), so by optimizing the energy storage combination (pumped storage accounts for 80%), the marginal cost of the system can be reduced.

[0089] Cost reduction = (lithium battery cost - pumped storage cost) × total storage capacity × utilization rate, that is: (190-110) US dollars / kWh × 150MWh × 30% utilization rate = US$3.6 million.

[0090] The calculation method for the total energy storage capacity of 150MWh is as follows: Since the solution provided by this invention combines hydropower and energy storage, the total energy storage capacity = 70MWh of pumped storage + 20MWh of lithium batteries; 30% utilization rate: an estimate based on the annual operating hours of the energy storage system and the scheduling strategy.

[0091] Electricity price premium Improved system stability (volatility reduced from 19% to 10%) resulted in a price premium of $0.012 / kWh.

[0092] The premium income is calculated as follows: Premium income = total output × annual operating hours × premium, that is: (800+160+150)MW×8,760h×0.012 US dollars / kWh=US$112.46 million. The total cooperation income is the sum of the above parts, that is, 26,952+2,318+360+11,246=408.76 million US dollars Superadditivity verification: US$408.76 million > US$269.52 million, meeting cooperation conditions.

[0093] Step 3: Design a profit distribution mechanism (Shapley value) to fairly distribute the total alliance profit and maintain cooperative stability.

[0094] 1. Basic Shapley value calculation (distributing benefits based on participants' marginal contributions to the alliance): The calculation of profit distribution based on contribution margin is as follows: in, For participants the distribution of income; Represents the set of all participants ; Representatives do not include participants Sub-alliance. For sub-alliance The factorial of , which represents the weight of different alliance sizes; For participants Pair Alliance marginal contribution; in this case, n is 4.

[0095] 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: (1) Capacity contribution weight: The contribution of each energy technology to system stability is evaluated through the expert scoring method. Energy storage has an outstanding ability to smooth fluctuations, and its capacity configuration weight accounts for 40%, or 0.4.

[0096] (2) Technical characteristic coefficient: The comprehensive regulation efficiency of pumped storage and lithium batteries (the average charge and discharge efficiency is 0.94) 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.

[0097] 3. Allocation results: P1: $182 million (44.5%), P2: $38.9 million (9.5%), P3: $83.39 million (20.4%), P4: $104.47 million (25.6%); Total: $408.76 million (in line with total proceeds).

[0098] Step 4: Construct a two-tier optimization model to coordinate objectives. This layered approach solves the revenue distribution and capacity allocation problems, reducing the complexity of multi-objective optimization.

[0099] 1. Upper model (income distribution): The goal of the upper model is to achieve profit distribution, and to fairly distribute profits based on Shapley values. The distribution should meet the constraints, that is, the participants' profits must be higher than independent operation.

[0100] 2. Lower layer model (capacity optimization): The goal of the lower-level model is capacity optimization.

[0101] (1) Objective function: ①Economical: Maximizing net benefits ; in, is the electricity price (unit: US dollars / kWh), reflecting the electricity market revenue; For the system at time Total output (kW); is the total life cycle cost (USD) (the levelized cost of energy storage over the entire life cycle (LCOE) includes initial investment, operation and maintenance costs, and life depreciation costs, and is calculated as follows: ,in, For the Total annual cost; For the Annual power generation; is the discount rate; is the operating period).

[0102] ② Stability: Weighted standard deviation , weight distribution: hydropower 0.15, wind power 0.55, photovoltaic 0.30; in, is the weight coefficient, reflecting the The degree to which the volatility of energy sources affects system stability; For the The standard deviation of the energy output is used to quantify its output volatility. The formula is: ( For the The actual output value of a certain energy at a certain point in time or within a certain period of time. For the average output of each energy source).

[0103] ③ Environmental protection: Carbon emissions = replaced thermal power × 0.82 tons / MWh Replacement of thermal power = renewable energy power generation (hydropower + wind power + photovoltaic power) + net energy storage discharge Among them, the net energy storage discharge amount = energy storage discharge amount × discharge efficiency - energy storage charge amount × charging efficiency (the efficiency loss during the energy storage charging and discharging process needs to be considered).

[0104] (2) Constraints: ① Total capacity ≤ 1,200 MW (800 MW hydropower + 160 MW wind power + 150 MW photovoltaic power + 90 MW energy storage = 1,200 MW); ② Energy storage SOC safety range is 20%-90%.

[0105] Step 5: Algorithm implementation and balanced solution verification: Generate and verify the optimal capacity configuration plan to ensure it meets actual needs.

[0106] 1. Improved NSGA-III algorithm: The lower model realizes the target optimization by using the improved NSGA-III algorithm, as shown in the attached Figure 2 The figure shows the convergence speed comparison between the improved NSGA-III and the standard NSGA-III. The horizontal axis is the number of iterations (1-200 generations), which reflects the time step of the algorithm optimization process. The vertical axis is the hypervolume index, which measures the diversity of the solution set and the degree of approximation to the true Pareto front. The larger the value, the higher the quality of the solution set. Figure 2 The red curve (representing standard NSGA-III) shows a slow growth in hypervolume, indicating a slow convergence rate. The blue curve (improved NSGA-III), through the dynamic reference point update mechanism, shows a faster improvement in hypervolume, with a 30% increase after 200 generations. This verifies the superiority of the improved algorithm and indicates that it approaches the Pareto front faster.

[0107] Attachment Figure 3 This is the algorithm's three-dimensional Pareto front output. The three coordinates represent economic efficiency, environmental protection, and reliability. The X-axis (Economy) is measured in US$10,000, with larger values indicating higher economic returns. The Y-axis (Carbon Emissions) is measured in tons, with smaller values indicating greater environmental benefits. The Z-axis (Volatility) is measured in percentages (%), with smaller values indicating more stable system output. The Pareto Frontier shows that the blue scattered points represent the Pareto optimal solution set, reflecting the trade-off between economic efficiency, environmental protection, and reliability. The distribution of the solution sets indicates that improved economic efficiency may lead to increased carbon emissions or higher volatility, and vice versa.

[0108] 2. Final solution selection according to Figure 3 As a result, the Pareto solution set presents a compromise relationship in the three-dimensional space of economy, environmental protection, and reliability. By calculating the comprehensive trade-off index of each solution in the solution set: , selecting the solution with the smallest index—the solution set that achieves the optimal compromise between economic efficiency, environmental protection, and reliability. The red point represents the final optimal solution (US$408.76 million in revenue, 16,200 tons of carbon emissions, and 10% volatility). This solution lies at the inflection point of the trade-off curve and balances multiple objectives. The capacity configuration is: 800 MW of hydropower, 160 MW of wind power, 150 MW of photovoltaic power, and 90 MWh of energy storage (70 MWh of pumped storage and 20 MWh of lithium batteries).

[0109] The reasons and methods for selecting the red point as the final solution in the 3D Pareto front are as follows: (1) Inflection point trade-off advantages The red dot is located at the inflection point of the Pareto frontier, where the marginal rates of substitution of the various objectives (economy, environmental protection, and reliability) reach equilibrium. Further optimizing any one objective would significantly deteriorate the others, so this point represents the optimal compromise.

[0110] (2) Multi-objective collaborative improvement The solutions corresponding to the red dots have significant improvements in three key indicators: Economics: Total revenue increased from $269.52 million in standalone operations to $408.76 million (+51.6%), with the energy storage operator transitioning from losses to profitability. Environmental performance: Carbon emissions dropped from 28,500 tons to 16,200 tons (-43.2%); Reliability: System output fluctuation dropped from 19% to 10% (-47.4%), significantly improving power supply stability.

[0111] (3) Actual constraint satisfaction This solution complies with engineering constraints (such as total capacity ≤ 1,200 MW, energy storage SOC safety range, etc.), ensuring practical feasibility.

[0112] The selection of red dots is the result of a combination of algorithm generation, visual analysis, multi-objective trade-offs, and engineering constraints. The core logic is to achieve optimal synergy between economy, environmental protection, and reliability by locating the inflection point on the Pareto frontier, while also meeting the rigid 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 achieves both theoretical optimality and practical feasibility.

[0113] System performance improvement data comparison table: index Independent operation Collaboration Optimization Improvement Economic efficiency (10,000 US dollars) 26,952 40,876 +51.6% Volatility (%) 19 10 -47.4% Carbon emissions (tons) 28,500 16,200 -43.2% The indicators have been improved as follows: Improved economic efficiency In the total revenue quantification in step 2, it was calculated that the total revenue from independent operation was US$269.52 million, and the total revenue from collaborative optimization was US$408.76 million. The improvement is: Reduced volatility ① Standalone operating volatility is calculated using the weighted standard deviation: 0.15 × 5% (hydropower) + 0.55 × 15% (wind power) + 0.30 × 12% (photovoltaic) = 19%; ② After the cooperation, energy storage can smooth out 55% of the fluctuation: 19% × (1 − 55%) = 8.55% ≈ 10% (rounded up); ③Reduction rate: Reduced carbon emissions The amount of electricity replaced by thermal power dropped from 28,500 tons in independent operation to 16,200 tons after cooperation, with emission reductions of: Through cooperative game optimization, the water, wind, solar and storage complementary project in the Lancang River Basin has achieved a balance of interests among multiple parties: (1) Economic efficiency: Total revenue increased by nearly 30%, and energy storage operators turned from losses to profits.

[0114] (2) Stability: Output fluctuation is reduced by 44%, improving grid reliability.

[0115] (3) Environmental protection: Carbon emissions are reduced by 40%.

[0116] This solution addresses three core issues in the case context through the following mechanisms: (1) Conflict of interests among multiple entities: The Shapley value correction 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 income has turned from an independent loss to a profit of 25.6% (US$104.47 million).

[0117] (2) System stability and environmental friendliness: Energy storage mitigates 55% of output fluctuations (fluctuations are reduced from 19% to 10%), while also incentivizing low-carbon configurations through a carbon pricing mechanism, reducing carbon emissions by 43.2% (28,500 → 16,200 tons).

[0118] (3) Global capacity optimization: The two-tier model coordinates the energy capacity and life cycle cost under the total capacity constraint (≤1,200MW), achieving a 51.6% improvement in economic efficiency (US$26,952 → US$40,876 million).

[0119] Data comparisons indicate that this approach provides a scalable solution for multi-agent energy system optimization. However, its implementation relies on accurate resource data and market parameters, and real-time monitoring and model updates are necessary for practical applications. Future research could explore dynamic game frameworks to further adapt to power market uncertainty.

[0120] Although the present invention has been described herein with reference to a number of illustrative embodiments of the present invention, it will be appreciated that those skilled in the art may devise numerous other modifications and embodiments that fall within the scope of this disclosure. Other uses will also be apparent to those skilled in the art.

Claims

1. A method for optimizing the capacity configuration of a hydro-wind-solar-storage microgrid based on game theory, characterized in that: The following steps are involved: 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: Constructing 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 the total alliance revenue satisfies superadditivity; Step S3: Design a profit distribution mechanism based on the Shapley value, calculate the basic distribution profit of each participant through marginal contribution, and introduce a capacity contribution correction factor to correct the distribution result; Step S4: Construct a two-layer optimization model. The upper layer model fairly distributes the total revenue of the alliance based on Shapley value, and the lower layer model determines the capacity allocation plan 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 model. Combined with the dynamic reference point update mechanism and engineering constraint embedding, combined with the practical feasibility of the equilibrium solution, the optimal capacity configuration scheme is selected through three-dimensional trade-off.

2. The method according to claim 1, characterized in that In step S1, the strategy space is constructed as follows: Step S1-1: Determine the capacity adjustment range of the hydropower operator during the flood season and the dry season; Step S1-2: Determine the installed capacity density, capacity factor and equivalent hours constraints of wind power operators and photovoltaic operators; Step S1-3: Determine the capacity range, charge / discharge efficiency, and safety interval of the state of charge (SOC) dynamic model of the energy storage operator's pumped storage and lithium battery. The SOC dynamic model is: in, For the moment Energy storage state of charge; is the charging efficiency, the default value is 0.92, is the discharge efficiency, the default value is 0.95; is the charging power, is 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 conditions: in, is the total revenue of the entire alliance, Independent operating income for participants.

4. The method according to claim 1, wherein In step S3, the calculation formula for designing the profit distribution mechanism based on the Shapley value is: in, For participants the distribution of income; Represents the set of all participants , P1 represents hydropower, P2 represents wind power, P3 represents photovoltaic power, and P4 represents energy storage; is 4; Representatives do not include participants Sub-alliance of For sub-alliance The factorial of , which represents the weight of different alliance sizes; For participants Pair Alliance The marginal contribution of the participants Join a sub-alliance After that, the increase in the total revenue of the alliance.

5. The method according to claim 1, wherein In step S4, the lower-level model determines the capacity configuration scheme through multi-objective optimization as follows: Step S4-1: The economic goal is achieved by maximizing net benefits. The net benefits calculation formula is: in, is the electricity price, reflecting the electricity market revenue; For water, wind, solar and storage microgrid systems at all times Total output; The total life cycle cost, or LCOE, is the levelized cost of energy storage over the entire life cycle, including initial investment, operation and maintenance costs, and life depreciation costs. The calculation formula is: ,in, For the Total annual cost; For the Annual power generation; is the discount rate; is the operating period; Step S4-2: The stability goal is achieved by minimizing the system output fluctuation. The fluctuation calculation formula is: in, is the weight coefficient, reflecting the The degree to which the volatility of energy sources affects system stability; For the The standard deviation of the energy output and the output fluctuation are: ,in For the The actual output value of a certain energy at a certain point in time or within a certain period of time. For the The average output of the energy is calculated by the formula Calculate, where is the total number of time points in the time period, For the The actual output value at a time point; Step S4-3: Environmental protection goals are achieved by minimizing carbon emissions, calculated as follows: Carbon emissions = replaced thermal power × 0.82 tons / MWh Replacement of thermal power = renewable energy power generation + net energy storage discharge Among them, the net discharge of energy storage = energy storage discharge × discharge efficiency - energy storage charge × charge efficiency Renewable energy generation is the total power generation of hydropower, wind power and photovoltaic power.

6. The method according to claim 1, characterized in that In step S4-1, the total system output calculation satisfies the following constraints: in, For the Efficiency coefficient of energy, range , reflecting its energy conversion efficiency; For the Capacity configuration of various energy sources; is the normalized output coefficient The ratio of the actual output of a type of energy to its maximum possible output at a certain moment or time period, with a value range of .

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

8. The method according to claim 1, characterized in that The specific steps of the improved NSGA-III algorithm in step S5 are as follows: Step S5-1: Dynamic reference point update mechanism, which dynamically adjusts the reference point position by real-time monitoring of the change in the hypervolume index of the solution set, so that the algorithm can approach the true Pareto front faster; Step S5-2: Embed engineering constraints and add penalty functions for capacity over-limit and energy storage SOC out-of-bounds in genetic operations; Step S5-3: Calculate the comprehensive trade-off index of each solution in the solution set through three-dimensional Pareto front analysis: , select the solution with the smallest index, that is, the solution set that satisfies the optimal compromise among economy, environmental protection and reliability; the output of the optimal solution set is the optimal capacity configuration plan.

9. The method according to claim 8, characterized in that In step S5, the dynamic reference point update mechanism monitors the quality of the solution in real time through the hypervolume indicator HV. The hypervolume calculation formula is: in, is the change in the super volume index, which measures the improvement in the quality of the solution set; It is a dynamic adjustment coefficient with a default value of 0.8, which is used to control the reference point update rate; 、 is the hypervolume index before and after the change.

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