Nash negotiation-based method for balancing reserve benefits of cascade hydropower-wind power alliance
By adopting a reserve benefit balancing method for cascade hydropower-wind power alliances based on Nash negotiations, the problem of ineffective utilization of reserve management mechanisms under large-scale wind power grid connection was solved, maximizing wind power grid connection and minimizing total reservoir energy consumption, thereby improving the operational efficiency and alliance benefits of wind power and cascade hydropower.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SICHUAN ELECTRIC POWER IND ASSOC
- Filing Date
- 2022-12-08
- Publication Date
- 2026-07-21
AI Technical Summary
With large-scale grid connection of wind power, the existing reserve management mechanism is difficult to adapt to the coordination of safety and economy in the new power system, resulting in the ineffective use of some reserve capacity, which cannot meet the demand for full wind power consumption and may lead to wind curtailment and increased economic costs.
A cascade hydropower-wind power alliance reserve benefit balancing method based on Nash negotiation is adopted. By constructing a joint operation optimization scheduling model, establishing a Nash negotiation model, introducing the Alternating Direction Multiplier Method (ADMM), decomposing the model, and adopting the power-determined water mode, incremental reserve capacity is allocated to maximize wind power grid connection and minimize total reservoir energy consumption.
It has increased the amount of wind power connected to the grid, promoted the absorption of wind power, achieved a balance of benefits between cascade hydropower and wind power, improved the operating income of each entity and the overall benefits of the alliance, and ensured the stability and enthusiasm of cooperation.
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Figure CN116247721B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of power system automation technology, specifically relating to a method for balancing the reserve benefits of a cascade hydropower-wind power alliance based on Nash negotiations. Background Technology
[0002] In recent years, the scale of wind power grid connection has been increasing. Due to the volatility of wind power output, large-scale wind power grid connection will severely impact the power grid and threaten the safe operation of the system. Hydropower has advantages such as adjustable reservoir capacity, flexible start-up, and fast regulation speed. Cascade hydropower has a larger overall scale and stronger regulation capacity. When jointly operated and dispatched with wind power, hydropower units can provide spinning reserve capacity, ensuring reliable grid connection for wind power stakeholders. Joint operation of wind power and cascade hydropower stations is an effective way to solve the problem of large-scale wind power consumption. However, the participation of cascade hydropower in the regulation and dispatch of large-scale wind power consumption will inevitably harm its own interests. When the actual wind power output is lower than the predicted output, cascade hydropower can obtain greater grid connection capacity only from the perspective of power generation. However, due to the uncertainty of wind power, cascade hydropower often needs to provide ancillary services such as spinning reserve to cooperate with wind power consumption, resulting in losses for cascade hydropower. How to balance the interests between wind power and cascade hydropower in the process of hydropower participating in wind power consumption has become one of the key issues that need to be addressed in the joint operation of wind and hydropower. To address the uncertainties brought about by large-scale wind power grid integration, sufficient and economical reserve capacity is essential for increasing wind power grid-connected output. Traditional day-ahead reserve models typically select a fixed percentage of the maximum load or the maximum single-unit capacity as system reserve at the system level. However, because they do not consider the constraints of external transmission capacity, power flow congestion may occur when the reserved generators adjust their output. This results in some ineffective reserve capacity that cannot be fully utilized. When existing negative reserves are insufficient to meet the demand for full wind power consumption, the system struggles to balance wind power fluctuations during operation, potentially leading to wind curtailment, increased economic costs, and resource waste. Therefore, in the context of large-scale wind power grid integration, the current reserve management mechanism is ill-suited to coordinating the security and economy of the new power system. Summary of the Invention
[0003] The purpose of this invention is to provide a method for balancing the reserve benefits of a cascade hydropower-wind power alliance based on Nash negotiations, in order to solve the technical problems existing in the prior art. Under the condition of large-scale wind power grid connection, the current reserve management mechanism is difficult to adapt to the coordination of the security and economy of the new power system.
[0004] To achieve the above objectives, the technical solution of the present invention is as follows:
[0005] The backup benefit balancing method for cascade hydropower-wind power alliances based on Nash negotiations includes the following steps:
[0006] S1. Considering the uncertainty of wind power, a joint operation and scheduling strategy for cascade hydropower and wind power is proposed. A mathematical model for the joint operation and optimized scheduling of cascade hydropower and wind power systems is constructed to maximize the grid-connected power of wind power.
[0007] S2. Based on the optimization results of the previous stage, construct benefit models for cascade hydropower and wind power cooperation and non-cooperation respectively.
[0008] S3. Based on Nash negotiation theory, establish a Nash negotiation model for the cooperative operation of the cascade hydropower-wind power alliance, and determine the incremental reserve capacity and price of the incremental reserve capacity of the cascade hydropower-wind power alliance.
[0009] S4. Introduce the Alternating Direction Multiplier Method (ADMM) to decompose the model from the previous stage;
[0010] S5. Adopt the power-determined water supply model to allocate incremental reserve capacity to each cascade hydropower station within the cascade hydropower-wind power alliance, thereby minimizing the total energy consumption of cascade hydropower reservoirs during the dispatch period.
[0011] Furthermore, step S1 includes: considering the uncertainty of wind power, proposing a joint operation and scheduling strategy for cascade hydropower and wind power, constructing a mathematical model for the optimized scheduling of the joint operation of the cascade hydropower and wind power system, and maximizing the grid-connected power of wind power, specifically:
[0012] Taking the maximization of wind power grid connection as the optimization objective, the mathematical model is expressed as follows:
[0013]
[0014] Where E represents the wind power generation during the dispatch period T; This represents the total number of wind farms. Let w be the output power of the wind farm at time t; For scheduling periods;
[0015] Considering the uncertainty of wind power output, the constraints on wind power are modeled as follows:
[0016]
[0017]
[0018]
[0019]
[0020] in, , These represent the lower and upper limits of wind power output at time t, respectively. Let t be the predicted wind power output at time t; Let w be the fluctuation value of the wind farm's output deviating from the predicted value during time period t, and let t be the predicted value. ;
[0021] The constraints of cascade hydropower are modeled as follows:
[0022] (1) Power balance constraint
[0023]
[0024] in, Let be the power generation capacity of the h-th hydropower station at time t; Let t be the electrical load that the cascade hydropower needs to meet at time t; This represents the total number of cascade hydropower stations.
[0025] (2) Output constraint
[0026]
[0027] in, , For the minimum and maximum output of the cascade hydropower station h;
[0028] (3) Climbing constraint
[0029]
[0030]
[0031] in, , These are the maximum upward and downward climbing rates of the cascade hydropower project, respectively.
[0032] (4) Water balance constraints
[0033]
[0034] in, Let h be the reservoir capacity of the h-th hydropower station at time t. Let be the power generation flow of the h-th hydropower station at time t; Let h be the natural inflow of the h-th hydropower station at time t: The time delay of water flow between the (h-1)th hydropower station and the hth hydropower station;
[0035] (5) Reservoir capacity constraints
[0036]
[0037] in, , These are the lower and upper limits of the reservoir capacity of the h-th hydropower station, respectively.
[0038] (6) Downflow constraint
[0039]
[0040] in, , These are the lower and upper limits of the discharge of the h-th hydropower station, respectively;
[0041] (7) Constraints on hydropower conversion relationship
[0042]
[0043] in, For hydroelectric conversion efficiency; Let h be the generating head of the h-th hydropower station at time t;
[0044] The rapid regulation characteristics of cascade hydropower units are used to provide spinning reserve capacity, as modeled below:
[0045]
[0046]
[0047]
[0048] in, , These refer to the upper and lower rotating reserve capacities provided by the cascade hydropower stations, respectively. This is the emergency standby capacity coefficient for hydropower units.
[0049] Furthermore, step S2 includes: based on the optimization results of the previous stage, constructing benefit models for cascade hydropower and wind power cooperation and non-cooperation, respectively, specifically:
[0050] Under the limitation of cross-sectional transmission capacity, a portion of the adjustable capacity of the cascade reservoir group is used as the incremental reserve capacity to support wind power in the region, and wind power purchases incremental reserve capacity from cascade hydropower.
[0051] Benefits of wind farms participating in cooperation Including revenue from selling electricity to the grid Operating costs include the cost of purchasing incremental reserve from cascade hydropower. and wind curtailment losses The model is as follows:
[0052]
[0053]
[0054]
[0055]
[0056] in, The electricity price sold by the wind farm; The price for wind farms to purchase incremental reserve capacity from cascaded hydropower stations; This refers to the incremental reserve capacity purchased by wind farms from cascade hydropower stations. Price as a penalty for wind curtailment; This refers to the amount of wind curtailed from wind farms. ,
[0057] This represents the maximum transmission capacity of the cross-section.
[0058] The benefits of cascade hydropower participating in cooperation include the benefits of selling electricity from the cascade hydropower to the grid. Cascade hydropower incremental reserve benefits Benefits of purchasing incremental reserve capacity for wind power The model is as follows:
[0059]
[0060]
[0061]
[0062] in, The electricity price for cascade hydropower; Reserve price for incremental hydropower generation;
[0063] Benefits of wind farms not participating in the cooperation To improve the profitability of electricity sales from wind farms wind curtailment losses The difference is modeled as follows:
[0064]
[0065]
[0066] Benefits of cascade hydropower without participation in cooperation Benefits of selling electricity from cascade hydropower to the grid With the incremental reserve benefits of cascade hydropower The sum is modeled as follows:
[0067] .
[0068] Furthermore, step S3 includes: establishing a Nash negotiation model for the cooperative operation of a cascade hydropower-wind power alliance based on Nash negotiation theory, and determining the incremental reserve capacity and price of the cascade hydropower-wind power alliance, specifically:
[0069] To ensure the stability of the alliance and promote the participation of cascade hydropower in wind power transmission, each participating entity hopes to reach a consensus through negotiation to maximize its own interests. Nash negotiation theory falls under the category of cooperative game theory, which can simultaneously consider individual and collective interests. Introducing Nash negotiation theory, we model the equilibrium of the benefits of the cascade hydropower-wind power alliance cooperation, using the maximum Nash product as the Nash negotiation solution. The mathematical model is expressed as:
[0070]
[0071] in, , These represent the optimal benefits of wind power and cascade hydropower when no cooperation was established, i.e., the breakdown point of the Nash negotiations;
[0072] The Nash negotiation model is transformed and decomposed into the sub-problem of maximizing the benefits of the wind power-cascade hydropower alliance and the sub-problem of negotiating incremental reserve capacity payments.
[0073] Substituting the day-ahead outputs of wind power and cascade hydropower from the results of step S1, we solve the subproblem of maximizing the benefits of the wind power-cascade hydropower alliance to obtain the optimal wind power benefit. and the optimal benefits of cascade hydropower To obtain incremental reserve capacity The mathematical model for maximizing the benefits of the wind power-cascade hydropower alliance sub-problem is expressed as:
[0074]
[0075] Substituting the optimal solution into the subproblem of maximizing the benefits of the wind power-cascade hydropower alliance , Benefits when not participating in cooperation , The mathematical model for the sub-problem of negotiating payments for incremental reserve capacity to balance the benefits of wind power and cascaded hydropower is as follows:
[0076] .
[0077] Furthermore, step S4 includes: introducing the Alternating Direction Multiplier Method (ADMM) to decompose the model from the previous stage, specifically as follows:
[0078] For the sub-problem of maximizing the benefits of the wind power-cascade hydropower alliance in the previous stage, an auxiliary variable of incremental reserve capacity is introduced. Solve the problem. To address the incremental reserve capacity expected from wind power purchases for cascade hydropower projects, Lagrange multipliers are introduced. and penalty factor The mathematical expression for the augmented Lagrange function is constructed as follows:
[0079]
[0080] According to the ADMM algorithm, the above expression can be decomposed as follows:
[0081] Wind power benefit model:
[0082]
[0083] Benefit model of cascade hydropower:
[0084]
[0085] The solution steps are as follows:
[0086] (11) Set the maximum number of iterations Convergence accuracy Punishment factor Initialize all parameters, including the initial Lagrange multipliers. ;
[0087] (12) Cascade hydropower receives incremental reserve capacity from wind power Solving the benefit model of cascade hydropower yields the expected incremental reserve capacity. ;
[0088] (13) Expected incremental reserve capacity for wind power reception Solving the wind power benefit model yields the incremental reserve capacity. ;
[0089] (14) Update the Lagrange multipliers ;
[0090] (15) Determine whether the convergence condition is met:
[0091]
[0092] The maximum number of convergence iterations may be reached; if not, return (12); if the convergence condition is met, the calculation ends and the result is output.
[0093] By solving the subproblem of maximizing the benefits of the wind power-cascade hydropower alliance, the optimal incremental reserve capacity is obtained. To address the sub-problem of incremental reserve capacity payment negotiations in the previous stage, the optimal operating efficiency of wind power and cascade hydropower when not participating in cooperation is introduced. , Introducing an auxiliary variable: incremental reserve capacity price Introducing Lagrange multipliers and penalty factor Construct the augmented Lagrange function, the mathematical expression of which is shown below:
[0094]
[0095] The purchase price should be lower than the grid connection price of wind power, that is... ;
[0096] According to the ADMM algorithm, the above expression can be decomposed as follows:
[0097] Negotiation and transaction model for wind power:
[0098]
[0099] Negotiation and transaction model for cascade hydropower:
[0100]
[0101] The solution steps are as follows:
[0102] (21) Set the maximum number of iterations Convergence accuracy Punishment factor Initialize all parameters, including the initial Lagrange multipliers. ;
[0103] (22) Price of incremental reserve capacity received by cascade hydropower from wind power Solving the negotiation and trading model for cascade hydropower yields the expected incremental reserve capacity price. ;
[0104] (23) Price of expected incremental reserve capacity for wind power reception Solving the wind power negotiation and trading model yields the incremental reserve capacity price. ;
[0105] (24) Update the Lagrange multipliers ;
[0106] (25) Determine whether the convergence condition is met.
[0107]
[0108] The maximum number of convergence attempts may be reached; if not, return (22); if the convergence condition is met, the calculation ends and the result is output.
[0109] Furthermore, step S5 includes: adopting an electricity-driven water allocation model to distribute incremental reserve capacity to each cascade hydropower station within the cascade hydropower-wind power alliance, thereby minimizing the total energy consumption of the cascade hydropower reservoirs during the dispatch period, specifically:
[0110] The water supply is determined by electricity demand, with the goal of minimizing the total energy consumption of the cascade hydropower reservoirs at the end of the scheduling period. The incremental reserve capacity is allocated to each cascade hydropower station, and the mathematical expression of the objective function is as follows:
[0111]
[0112] The constraints for the incremental reserve allocation model of cascade hydropower are modeled as follows:
[0113]
[0114]
[0115]
[0116] The remaining constraints are the same as those in step S1 for modeling the cascade hydropower constraints.
[0117] To summarize all the descriptions of the benefit equilibrium method for cascade hydropower-wind power alliances mentioned above, the benefit equilibrium problem was solved in the MATLAB environment at each stage using the YALMIP and CPLEX solvers.
[0118] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0119] This invention proposes a reserve benefit balancing method for cascade hydropower-wind power alliances based on Nash negotiation. The proposed joint operation and scheduling strategy for cascade hydropower and wind power can effectively promote wind power transmission, significantly increasing wind power grid connection compared to the situation without cooperation, and effectively promoting the consumption of new energy in the region. The proposed reserve benefit balancing method based on Nash negotiation theory can promote the benefit balance between cascade hydropower and wind power, encouraging the formation of alliances between cascade hydropower and wind power. The proposed reserve benefit balancing method for cascade hydropower-wind power alliances simultaneously considers individual rationality and overall rationality. Through cooperative operation, the operating benefits of each entity and the alliance benefits significantly increase compared to the situation without cooperation, making each entity more inclined to cooperate to obtain greater profits, ensuring the enthusiasm of each entity to participate in cooperation, and helping to maintain the stability of the alliance. The results of the implementation examples verify that through the cooperative operation of cascade hydropower-wind power, the operating benefits of each entity and the overall benefits of the cooperative alliance can be significantly improved. Attached Figure Description
[0120] Figure 1 Overall model solution flowchart.
[0121] Figure 2 System scenario diagram.
[0122] Figure 3 Schematic diagram of predicted wind power output.
[0123] Figure 4 Schematic diagram of incremental backup scheduling results in different scenarios.
[0124] Figure 5 A schematic diagram of wind power dispatch results when the wind power installed capacity increases by 0.75.
[0125] Figure 6 A schematic diagram of wind power dispatch results when the wind power installed capacity is increased by 1.0.
[0126] Figure 7 A schematic diagram of wind power dispatch results when the wind power installed capacity is increased by 2.0%.
[0127] Figure 8 Schematic diagram of incremental reserve price results for different scenarios.
[0128] Figure 9 Schematic diagram of a primary hydropower station.
[0129] Figure 10 Schematic diagram of a secondary hydropower station.
[0130] Figure 11 Schematic diagram of a three-level hydropower station. Detailed Implementation
[0131] 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 only for explaining the invention and are not intended to limit the invention; that is, the described embodiments are merely some embodiments of the invention, and not all embodiments. The components of the embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.
[0132] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention. It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations.
[0133] Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.
[0134] Example: Figure 1 As shown, a method for balancing the reserve benefits of a cascade hydropower-wind power alliance based on Nash negotiations is proposed, including the following steps:
[0135] S1. Considering the uncertainty of wind power, a joint operation and scheduling strategy for cascade hydropower and wind power is proposed. A mathematical model for the joint operation and optimized scheduling of cascade hydropower and wind power systems is constructed to maximize the grid-connected power of wind power.
[0136] S2. Based on the optimization results of the previous stage, construct benefit models for cascade hydropower and wind power cooperation and non-cooperation respectively.
[0137] S3. Based on Nash negotiation theory, establish a Nash negotiation model for the cooperative operation of the cascade hydropower-wind power alliance, and determine the incremental reserve capacity and price of the incremental reserve capacity of the cascade hydropower-wind power alliance.
[0138] S4. Introduce the Alternating Direction Multiplier Method (ADMM) to decompose the model from the previous stage;
[0139] S5. Adopt the power-determined water supply model to allocate incremental reserve capacity to each cascade hydropower station within the cascade hydropower-wind power alliance, thereby minimizing the total energy consumption of cascade hydropower reservoirs during the dispatch period.
[0140] Furthermore, step S1 includes: considering the uncertainty of wind power, proposing a joint operation and scheduling strategy for cascade hydropower and wind power, constructing a mathematical model for the optimized scheduling of the joint operation of the cascade hydropower and wind power system, and maximizing the grid-connected power of wind power, specifically:
[0141] Taking the maximization of wind power grid connection as the optimization objective, the mathematical model is expressed as follows:
[0142]
[0143] Where E represents the wind power generation during the dispatch period T; This represents the total number of wind farms. Let w be the output power of the wind farm at time t; For scheduling periods;
[0144] Considering the uncertainty of wind power output, the constraints on wind power are modeled as follows:
[0145]
[0146]
[0147]
[0148]
[0149] in, , These represent the lower and upper limits of wind power output at time t, respectively. Let t be the predicted wind power output at time t; Let w be the fluctuation value of the wind farm's output deviating from the predicted value during time period t, and let t be the predicted value. ;
[0150] The constraints of cascade hydropower are modeled as follows:
[0151] (1) Power balance constraint
[0152]
[0153] in, Let be the power generation capacity of the h-th hydropower station at time t; Let t be the electrical load that the cascade hydropower needs to meet at time t; This represents the total number of cascade hydropower stations.
[0154] (2) Output constraint
[0155]
[0156] in, , For the minimum and maximum output of the cascade hydropower station h;
[0157] (3) Climbing constraint
[0158]
[0159]
[0160] in, , These are the maximum upward and downward climbing rates of the cascade hydropower project, respectively.
[0161] (4) Water balance constraints
[0162]
[0163] in, Let h be the reservoir capacity of the h-th hydropower station at time t. Let be the power generation flow of the h-th hydropower station at time t; Let h be the natural inflow of the h-th hydropower station at time t: The time delay of water flow between the (h-1)th hydropower station and the hth hydropower station;
[0164] (5) Reservoir capacity constraints
[0165]
[0166] in, , These are the lower and upper limits of the reservoir capacity of the h-th hydropower station, respectively.
[0167] (6) Downflow constraint
[0168]
[0169] in, , These are the lower and upper limits of the discharge of the h-th hydropower station, respectively;
[0170] (7) Constraints on hydropower conversion relationship
[0171]
[0172] in, For hydroelectric conversion efficiency; Let h be the generating head of the h-th hydropower station at time t;
[0173] The rapid regulation characteristics of cascade hydropower units are used to provide spinning reserve capacity, as modeled below:
[0174]
[0175]
[0176]
[0177] in, , These refer to the upper and lower rotating reserve capacities provided by the cascade hydropower stations, respectively. This is the emergency standby capacity coefficient for hydropower units.
[0178] Furthermore, step S2 includes: based on the optimization results of the previous stage, constructing benefit models for cascade hydropower and wind power cooperation and non-cooperation, respectively, specifically:
[0179] Under the limitation of cross-sectional transmission capacity, a portion of the adjustable capacity of the cascade reservoir group is used as the incremental reserve capacity to support wind power in the region, and wind power purchases incremental reserve capacity from cascade hydropower.
[0180] Benefits of wind farms participating in cooperation Including revenue from selling electricity to the grid Operating costs include the cost of purchasing incremental reserve from cascade hydropower. and wind curtailment losses The model is as follows:
[0181]
[0182]
[0183]
[0184]
[0185] in, The electricity price sold by the wind farm; The price for wind farms to purchase incremental reserve capacity from cascaded hydropower stations; This refers to the incremental reserve capacity purchased by wind farms from cascade hydropower stations. Price as a penalty for wind curtailment; This refers to the amount of wind curtailed from wind farms. ,
[0186] This represents the maximum transmission capacity of the cross-section.
[0187] The benefits of cascade hydropower participating in cooperation include the benefits of selling electricity from the cascade hydropower to the grid. Cascade hydropower incremental reserve benefits Benefits of purchasing incremental reserve capacity for wind power The model is as follows:
[0188]
[0189]
[0190]
[0191] in, The electricity price for cascade hydropower; Reserve price for incremental hydropower generation;
[0192] Benefits of wind farms not participating in the cooperation To improve the profitability of electricity sales from wind farms wind curtailment losses The difference is modeled as follows:
[0193]
[0194]
[0195] Benefits of cascade hydropower without participation in cooperation Benefits of selling electricity from cascade hydropower to the grid With the incremental reserve benefits of cascade hydropower The sum is modeled as follows:
[0196] .
[0197] Furthermore, step S3 includes: establishing a Nash negotiation model for the cooperative operation of a cascade hydropower-wind power alliance based on Nash negotiation theory, and determining the incremental reserve capacity and price of the cascade hydropower-wind power alliance, specifically:
[0198] To ensure the stability of the alliance and promote the participation of cascade hydropower in wind power transmission, each participating entity hopes to reach a consensus through negotiation to maximize its own interests. Nash negotiation theory falls under the category of cooperative game theory, which can simultaneously consider individual and collective interests. Introducing Nash negotiation theory, we model the equilibrium of the benefits of the cascade hydropower-wind power alliance cooperation, using the maximum Nash product as the Nash negotiation solution. The mathematical model is expressed as:
[0199]
[0200] in, , These represent the optimal benefits of wind power and cascade hydropower when no cooperation was established, i.e., the breakdown point of the Nash negotiations;
[0201] The Nash negotiation model is transformed and decomposed into the sub-problem of maximizing the benefits of the wind power-cascade hydropower alliance and the sub-problem of negotiating incremental reserve capacity payments.
[0202] Substituting the day-ahead outputs of wind power and cascade hydropower from the results of step S1, we solve the subproblem of maximizing the benefits of the wind power-cascade hydropower alliance to obtain the optimal wind power benefit. and the optimal benefits of cascade hydropower To obtain incremental reserve capacity The mathematical model for maximizing the benefits of the wind power-cascade hydropower alliance sub-problem is expressed as:
[0203]
[0204] Substituting the optimal solution into the subproblem of maximizing the benefits of the wind power-cascade hydropower alliance , Benefits when not participating in cooperation , The mathematical model for the sub-problem of negotiating payments for incremental reserve capacity to balance the benefits of wind power and cascaded hydropower is as follows:
[0205] .
[0206] Furthermore, step S4 includes: introducing the Alternating Direction Multiplier Method (ADMM) to decompose the model from the previous stage, specifically as follows:
[0207] For the sub-problem of maximizing the benefits of the wind power-cascade hydropower alliance in the previous stage, an auxiliary variable of incremental reserve capacity is introduced. Solve the problem. To address the incremental reserve capacity expected from wind power purchases for cascade hydropower projects, Lagrange multipliers are introduced. and penalty factor The mathematical expression for the augmented Lagrange function is constructed as follows:
[0208]
[0209] According to the ADMM algorithm, the above expression can be decomposed as follows:
[0210] Wind power benefit model:
[0211]
[0212] Benefit model of cascade hydropower:
[0213]
[0214] The solution steps are as follows:
[0215] (11) Set the maximum number of iterations Convergence accuracy Punishment factor Initialize all parameters, including the initial Lagrange multipliers. ;
[0216] (12) Cascade hydropower receives incremental reserve capacity from wind power Solving the benefit model of cascade hydropower yields the expected incremental reserve capacity. ;
[0217] (13) Expected incremental reserve capacity for wind power reception Solving the wind power benefit model yields the incremental reserve capacity. ;
[0218] (14) Update the Lagrange multipliers ;
[0219] (15) Determine whether the convergence condition is met:
[0220]
[0221] The maximum number of convergence iterations may be reached; if not, return (12); if the convergence condition is met, the calculation ends and the result is output.
[0222] By solving the subproblem of maximizing the benefits of the wind power-cascade hydropower alliance, the optimal incremental reserve capacity is obtained. To address the sub-problem of incremental reserve capacity payment negotiations in the previous stage, the optimal operating efficiency of wind power and cascade hydropower when not participating in cooperation is introduced. , Introducing an auxiliary variable: incremental reserve capacity price Introducing Lagrange multipliers and penalty factor Construct the augmented Lagrange function, the mathematical expression of which is shown below:
[0223]
[0224] The purchase price should be lower than the grid connection price of wind power, that is... ;
[0225] According to the ADMM algorithm, the above expression can be decomposed as follows:
[0226] Negotiation and transaction model for wind power:
[0227]
[0228] Negotiation and transaction model for cascade hydropower:
[0229]
[0230] The solution steps are as follows:
[0231] (21) Set the maximum number of iterations Convergence accuracy Punishment factor Initialize all parameters, including the initial Lagrange multipliers. ;
[0232] (22) Price of incremental reserve capacity received by cascade hydropower from wind power Solving the negotiation and trading model for cascade hydropower yields the expected incremental reserve capacity price. ;
[0233] (23) Price of expected incremental reserve capacity for wind power reception Solving the wind power negotiation and trading model yields the incremental reserve capacity price. ;
[0234] (24) Update the Lagrange multipliers ;
[0235] (25) Determine whether the convergence condition is met.
[0236]
[0237] The maximum number of convergence attempts may be reached; if not, return (22); if the convergence condition is met, the calculation ends and the result is output.
[0238] Furthermore, step S5 includes: adopting an electricity-driven water allocation model to distribute incremental reserve capacity to each cascade hydropower station within the cascade hydropower-wind power alliance, thereby minimizing the total energy consumption of the cascade hydropower reservoirs during the dispatch period, specifically:
[0239] The water supply is determined by electricity demand, with the goal of minimizing the total energy consumption of the cascade hydropower reservoirs at the end of the scheduling period. The incremental reserve capacity is allocated to each cascade hydropower station, and the mathematical expression of the objective function is as follows:
[0240]
[0241] The constraints for the incremental reserve allocation model of cascade hydropower are modeled as follows:
[0242]
[0243]
[0244]
[0245] The remaining constraints are the same as those in step S1 for modeling the cascade hydropower constraints.
[0246] To summarize all the descriptions of the benefit equilibrium method for cascade hydropower-wind power alliances mentioned above, the benefit equilibrium problem was solved in the MATLAB environment at each stage using the YALMIP and CPLEX solvers.
[0247] Case Analysis:
[0248] The system was tested using a cascade hydropower system consisting of three hydropower stations and a cascade hydropower-wind power cooperation alliance consisting of large-scale wind farms. The system scenario is as follows: Figure 2 As shown. The cross-sectional constraint is 2250MW; the on-grid tariff for wind power is 420 yuan / MW, the on-grid tariff for cascade hydropower is 350 yuan / MW, and the wind curtailment penalty tariff is 515 yuan / MW. The dispatch cycle is 24 hours, and the dispatch period is 1 hour. The installed capacity of the wind farm is 2000MW, and the wind power forecast data is as follows. Figure 3As shown, based on this wind power installed capacity, different wind power installed capacities were set up by reducing the capacity by 0.75 times and increasing it by 2 times. Nine different cooperative operation scenarios were set up for comparison with different hydropower water seasons and different wind power installed capacities.
[0249] To verify the feasibility and effectiveness of the proposed Nash negotiation-based benefit balancing method for the cascade hydropower-wind power alliance among its stakeholders, Table 1 presents the benefit comparison results before and after the cooperative operation of cascade hydropower and wind power. Table 1 shows that when operating independently, due to the limitation of cross-sectional transmission capacity, the on-grid electricity generated by wind power is roughly the same for the same installed capacity, resulting in roughly the same benefits. During cooperative operation, although wind power purchases incremental reserve capacity from cascade hydropower, the reduction in wind curtailment and the increase in on-grid electricity generated by wind power improve wind power revenue. While the provision of reserve capacity by cascade hydropower to wind power results in a loss of revenue for cascade hydropower, the cost of incremental reserve capacity paid by wind power exceeds the revenue from direct on-grid connection of cascade hydropower, thus improving the overall benefit of cascade hydropower. This demonstrates that through cooperation between cascade hydropower and wind power, the individual interests of each stakeholder are significantly enhanced, while simultaneously considering both individual and overall interests, achieving a benefit balance between wind power and cascade hydropower.
[0250]
[0251] Furthermore, to verify the feasibility and effectiveness of the proposed Nash negotiation-based benefit balancing method for the cascade hydropower-wind power alliance, a comparison of the benefits before and after cooperation is presented in Table 2. Table 2 shows that in all scenarios, the alliance benefits significantly increase. Both cascade hydropower and wind power benefit from cooperation, and the alliance members are more inclined to cooperate in electricity sales to obtain greater profits, ensuring the stability of the alliance. Comparing different water season scenarios for cascade hydropower with the same wind power installed capacity expansion ratio, the operational benefit gain of cascade hydropower is: high-water season gain < low-water season gain < normal-water season gain. During the high-water season, to avoid water wastage, it is difficult to provide upstream and downstream spinning reserves, and cascade hydropower lacks wind power absorption capacity, resulting in the worst benefit and smallest gain after cooperation between hydropower and wind power. During the normal-water season, by scheduling cascade hydropower units to provide upstream and downstream spinning reserves and incremental reserves to wind power, the cascade hydropower units have the ability to absorb wind power, resulting in the largest benefit. Due to limited hydropower generation capacity, the downstream reserve capacity provided by cascade hydropower is relatively small during the dry season. While hydropower units possess some wind power absorption capacity during this period, it is less than during the normal water season, resulting in lower gains. Comparing different wind power capacity expansion ratios during the same hydropower cascade water season, it can be concluded that the larger the wind power expansion ratio, the greater the benefits for both cascade hydropower and wind power. Comparing scenarios 2, 5, and 8, scenario 2 is least affected by cross-sectional limitations, with most wind power reaching the grid, less curtailment, and the lowest benefit, making the cooperative operation effect insignificant. In scenario 5, due to the expanded installed capacity, the amount of wind power reaching the grid increases compared to scenario 2, thus the wind power benefit before cooperation is greater than that before cooperation in scenario 2. Due to cross-sectional limitations, wind curtailment increases in scenario 5; after cooperation, wind curtailment decreases, increasing the wind power benefit. In scenario 8, due to cross-sectional constraints, wind curtailment is the largest, resulting in the smallest benefit before cooperation and the largest benefit. Since the incremental reserve capacity that cascade hydropower can provide is limited, the operating benefits of wind power after cooperation are basically the same.
[0252]
[0253] To analyze the incremental reserve capacity scheduling results after the cooperation of cascade hydropower-wind power alliances, and to compare the optimized scheduling results of incremental reserve capacity after the cooperation of cascade hydropower-wind power alliances with different wind power installed capacities and different water inflow periods, such as... Figure 4 As shown in the figure, the incremental reserve capacity deployed is in the order of wet season < dry season < normal season. During the wet season, cascade hydropower stations, in order to avoid or reduce water wastage, have difficulty providing reserve capacity, resulting in small incremental reserve capacity and poor wind power absorption capacity. During the normal season, cascade hydropower stations provide the largest incremental reserve capacity for wind power, which can absorb most of the wind power. Due to the low natural water inflow, the dispatchable spinning reserve of hydropower is limited during the dry season, resulting in a small incremental reserve capacity that can only absorb a portion of the wind power after cooperation.
[0254] To analyze the effect of the proposed benefit balancing method of the cascade hydropower-wind power alliance based on Nash negotiations on promoting wind power transmission, the wind power output under different wind power installed capacities and different water inflow periods of cascade hydropower was compared, such as... Figure 5 , 6 As shown in Figures 7 and 8, under the same scenario, the grid-connected wind power after cooperation is greater than that before cooperation. Through the cooperation of cascade hydropower and wind power, the grid-connected wind power volume increases significantly, promoting the transmission of wind power outside the region. When the wind power installed capacity expansion ratio is 2.0, the wind power output after cooperation in scenarios 7, 8, and 9 is almost the same. Due to cross-sectional limitations and the need for cascade hydropower to fulfill its own scheduling plan, it can only promote the transmission of wind power to a certain extent. When the wind power installed capacity expansion ratio is 0.75, due to the relatively small impact of cross-sectional limitations on this scenario, the difference between the wind power output after cooperation and the output before cooperation is not significant, and the improvement effect after cooperation is not obvious.
[0255] To analyze whether the price of incremental reserve capacity within the cascade hydropower-wind power alliance meets price constraints under different wind power installed capacities and different hydropower inflow periods, price comparisons are made as follows: Figure 8 As shown. By Figure 8 It can be seen that in all scenarios, the incremental reserve price is within the range of [350, 390], which is less than the grid connection price of wind power (420 yuan) but higher than the grid connection price of cascade hydropower (350 yuan). For both wind power and cascade hydropower, the price is acceptable, which promotes the enthusiasm of cascade hydropower and wind power to participate in cooperation.
[0256] In addition, to analyze the reserve allocation results within the cascade hydropower alliance, the reserve allocation results of primary, secondary, and tertiary hydropower were compared when the wind power installed capacity expansion ratio was 1.0. Figure 9 , 10 As shown in Figure 11. Figure 9 It can be seen that, for the same hydropower station, the incremental reserve capacity is: normal water period > dry season > wet season. During the wet season, the available reserve capacity is the least to ensure power generation. Due to the lower natural water inflow, the dispatchable spinning reserve of hydropower is limited during the dry season, resulting in a smaller incremental reserve capacity compared to the normal water period. Comparing the same water periods, the scheduling result of incremental reserve is: primary hydropower > tertiary hydropower > secondary hydropower. Primary hydropower has the largest inflow and the largest adjustable output capacity, thus providing the largest incremental reserve capacity. Since the reservoir capacity of secondary hydropower is smaller than that of tertiary hydropower, after optimization with the goal of minimizing water consumption, to save more water energy for power generation, the reserve capacity provided by secondary hydropower is less than that of tertiary hydropower.
[0257] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.
Claims
1. A method for balancing the reserve benefits of a cascade hydropower-wind power alliance based on Nash negotiations, characterized in that, Under the constraint of cross-sectional transmission capacity, a portion of the adjustable capacity of the cascade reservoir group is used as incremental reserve capacity to support wind power in the region. Wind power purchases incremental reserve capacity from cascade hydropower, including the following steps: S1. Considering the uncertainty of wind power, a joint operation and scheduling strategy for cascade hydropower and wind power is proposed. A mathematical model for the joint operation and optimized scheduling of cascade hydropower and wind power systems is constructed to maximize the grid-connected power of wind power. S2. Based on the optimization results of the previous stage, construct benefit models for cascade hydropower and wind power cooperation and non-cooperation respectively. S3. Based on Nash negotiation theory, establish a Nash negotiation model for the cooperative operation of the cascade hydropower-wind power alliance, and determine the incremental reserve capacity and price of the incremental reserve capacity of the cascade hydropower-wind power alliance. S4. Introduce the Alternating Direction Multiplier Method (ADMM) to decompose the model from the previous stage; S5. Adopt the power-determined water supply model to allocate incremental reserve capacity to each cascade hydropower station within the cascade hydropower-wind power alliance, thereby minimizing the total energy consumption of cascade hydropower reservoirs during the dispatch period.
2. The method for balancing the reserve benefits of a cascade hydropower-wind power alliance based on Nash negotiation as described in claim 1, characterized in that, Step S1 specifically involves: Taking the maximization of wind power grid connection as the optimization objective, the mathematical model is expressed as follows: Where E represents the wind power generation during the dispatch period T; This represents the total number of wind farms. Let w be the output power of the wind farm at time t; For scheduling periods; Considering the uncertainty of wind power output, the constraints on wind power are modeled as follows: in, , These represent the lower and upper limits of wind power output at time t, respectively. Let t be the predicted wind power output at time t; Let w be the fluctuation value of the wind power plant's output deviating from the predicted value during time period t, and let the predicted value be denoted as w. ; The constraints of cascade hydropower are modeled as follows: (1) Power balance constraint in, Let h be the power generation capacity of the h-th hydropower station at time t; Let t be the electrical load that the cascade hydropower needs to meet at time t; This represents the total number of cascade hydropower stations. (2) Output constraint in, , For the minimum and maximum output of the cascade hydropower station h; (3) Climbing constraint in, , These are the maximum upward and downward climbing rates of the cascade hydropower project, respectively. (4) Water balance constraints in, Let h be the reservoir capacity of the h-th hydropower station at time t. Let be the power generation flow of the h-th hydropower station at time t; Let h be the natural inflow of the h-th hydropower station at time t: The time delay of water flow between the (h-1)th hydropower station and the hth hydropower station; (5) Reservoir capacity constraints in, , These are the lower and upper limits of the reservoir capacity of the h-th hydropower station, respectively. (6) Downflow constraint in, , These are the lower and upper limits of the discharge of the h-th hydropower station, respectively; (7) Constraints on hydropower conversion relationship in, For hydroelectric conversion efficiency; Let h be the generating head of the h-th hydropower station at time t; The rapid regulation characteristics of cascade hydropower units are used to provide spinning reserve capacity, as modeled below: in, , These refer to the upper and lower rotating reserve capacities provided by the cascade hydropower stations, respectively. This is the emergency standby capacity coefficient for hydropower units.
3. The method for balancing the reserve benefits of a cascade hydropower-wind power alliance based on Nash negotiation as described in claim 2, characterized in that, Step S2 specifically involves: Benefits of wind farms participating in cooperation Including revenue from selling electricity to the grid Operating costs include the cost of purchasing incremental reserve from cascade hydropower. and wind curtailment losses The model is as follows: in, The electricity price sold by the wind farm; The price for wind farms to purchase incremental reserve capacity from cascaded hydropower stations; This refers to the incremental reserve capacity purchased by wind farms from cascade hydropower stations. Price as a penalty for wind curtailment; This refers to the amount of wind curtailed from wind farms. , This represents the maximum transmission capacity of the cross-section. The benefits of cascade hydropower participating in cooperation include the benefits of selling electricity from the cascade hydropower to the grid. Cascade hydropower incremental reserve benefits Benefits of purchasing incremental reserve capacity for wind power The model is as follows: in, The electricity price for cascade hydropower; Reserve price for incremental hydropower generation; Benefits of wind farms not participating in the cooperation To improve the profitability of electricity sales from wind farms wind curtailment losses The difference is modeled as follows: Benefits of cascade hydropower without participation in cooperation Benefits of selling electricity from cascade hydropower to the grid With the incremental reserve benefits of cascade hydropower The sum is modeled as follows: 。 4. The method for balancing the reserve benefits of a cascade hydropower-wind power alliance based on Nash negotiation as described in claim 3, characterized in that, Step S3 specifically involves: Introducing Nash negotiation theory, we model the benefit equilibrium of the cascade hydropower-wind power alliance, taking the maximum Nash product as the Nash negotiation solution. The mathematical model is expressed as: in, , These represent the optimal benefits of wind power and cascade hydropower when no cooperation was established, i.e., the breakdown point of the Nash negotiations; The Nash negotiation model is transformed and decomposed into the sub-problem of maximizing the benefits of the wind power-cascade hydropower alliance and the sub-problem of negotiating incremental reserve capacity payments. Substituting the day-ahead outputs of wind power and cascade hydropower from the results of step S1, we solve the subproblem of maximizing the benefits of the wind power-cascade hydropower alliance to obtain the optimal wind power benefit. and the optimal benefits of cascade hydropower To obtain incremental reserve capacity The mathematical model for maximizing the benefits of the wind power-cascade hydropower alliance sub-problem is expressed as: Substituting the optimal solution into the subproblem of maximizing the benefits of the wind power-cascade hydropower alliance , Benefits when not participating in cooperation , The mathematical model for the sub-problem of negotiating payments for incremental reserve capacity to balance the benefits of wind power and cascaded hydropower is as follows: 。 5. The method for balancing the reserve benefits of a cascade hydropower-wind power alliance based on Nash negotiation as described in claim 4, characterized in that, Step S4 specifically involves: For the sub-problem of maximizing the benefits of the wind power-cascade hydropower alliance in the previous stage, an auxiliary variable of incremental reserve capacity is introduced. Solve the problem. To address the incremental reserve capacity expected from wind power purchases for cascade hydropower projects, Lagrange multipliers are introduced. and penalty factor The mathematical expression for the augmented Lagrange function is constructed as follows: According to the ADMM algorithm, the above expression can be decomposed as follows: Wind power benefit model: Benefit model of cascade hydropower: The solution steps are as follows: (11) Set the maximum number of iterations Convergence accuracy Punishment factor Initialize all parameters, including the initial Lagrange multipliers. ; (12) Cascade hydropower receives incremental reserve capacity from wind power Solving the benefit model of cascade hydropower yields the expected incremental reserve capacity. ; (13) Expected incremental reserve capacity for wind power reception Solving the wind power benefit model yields the incremental reserve capacity. ; (14) Update the Lagrange multipliers ; (15) Determine whether the convergence condition is met: Or it may reach the maximum number of convergences; If the condition cannot be met, return to (12); if the convergence condition is met, the calculation ends and the result is output. By solving the subproblem of maximizing the benefits of the wind power-cascade hydropower alliance, the optimal incremental reserve capacity is obtained. To address the sub-problem of incremental reserve capacity payment negotiations in the previous stage, the optimal operating efficiency of wind power and cascade hydropower when not participating in cooperation is introduced. , Introducing an auxiliary variable: incremental reserve capacity price Introducing Lagrange multipliers and penalty factor Construct the augmented Lagrange function, the mathematical expression of which is shown below: The purchase price should be lower than the grid connection price of wind power, that is... ; According to the ADMM algorithm, the above expression can be decomposed as follows: Negotiation and transaction model for wind power: Negotiation and transaction model for cascade hydropower: The solution steps are as follows: (21) Set the maximum number of iterations Convergence accuracy Punishment factor Initialize all parameters, including the initial Lagrange multipliers. ; (22) Price of incremental reserve capacity received by cascade hydropower from wind power Solving the negotiation and trading model for cascade hydropower yields the expected incremental reserve capacity price. ; (23) Price of expected incremental reserve capacity for wind power reception Solving the wind power negotiation and trading model yields the incremental reserve capacity price. ; (24) Update the Lagrange multipliers ; (25) Determine whether the convergence condition is met. Or it may reach the maximum number of convergences; If the condition cannot be met, return (22); if the convergence condition is met, the calculation ends and the result is output.
6. The method for balancing the reserve benefits of a cascade hydropower-wind power alliance based on Nash negotiation as described in claim 5, characterized in that, Step S5 specifically involves: The water supply is determined by electricity demand, with the goal of minimizing the total energy consumption of the cascade hydropower reservoirs at the end of the scheduling period. The incremental reserve capacity is allocated to each cascade hydropower station, and the mathematical expression of the objective function is as follows: The constraints for the incremental reserve allocation model of cascade hydropower are modeled as follows: The remaining constraints are the same as those in step S1 for modeling the cascade hydropower constraints.