Virtual power plant operation method and system based on intelligent scheduling and market bidding optimization
Through the virtual power plant operation method of intelligent scheduling and market bidding optimization, the problems of low prediction accuracy and difficult to achieve diversified operation goals in the existing technology are solved, and higher prediction adaptability and multi-target optimization effects are achieved, reducing the risk of price wars.
Patent Information
- Application Number
- CN202510451280.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-11
- Publication Date
- 2025-05-13
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
When faced with complex and changing environments, the existing virtual power plant technology has low prediction accuracy and is difficult to achieve diversified operation goals. It lacks self-learning and self-adjustment capabilities, resulting in uncertainty in decision-making and economic losses.
A virtual power plant operation method based on intelligent scheduling and market bidding optimization is adopted, and the data is filled through linear differences, and a variety of external factors are considered comprehensively. The long-term and short-term memory network model is used to predict, and the operating status of DERs is dynamically adjusted through reinforcement learning algorithms. The bidding strategy based on Nash equilibrium is used to generate the optimal market bidding strategy.
It improves the comprehensiveness and adaptability of the prediction model, enhances the flexibility and robustness of the model, achieves multi-objective optimization, finds the optimal operating strategy, reduces the risk of price wars, and improves the economic benefits and environmental impact of virtual power plants.
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Figure CN119990693A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of virtual power plants, and in particular to a virtual power plant operation method and system based on intelligent scheduling and market bidding optimization. Background Art
[0002] Existing virtual power plant (VPP) technologies rely on centralized or distributed control architectures to aggregate and manage distributed energy resources (DERs). Traditional forecasting methods mainly rely on statistical models, such as time series analysis and regression analysis, but these methods often perform poorly in complex and changing environments. Although modern forecasting models have made significant progress compared to traditional methods, due to the highly random and intermittent characteristics of renewable energy, any forecast has a certain error range. Especially in the absence of sufficient historical data support, the forecast accuracy will be greatly reduced, affecting the reliability of subsequent decisions.
[0003] Most existing VPP management systems focus on single-objective optimization (such as cost minimization) and fail to fully consider diversified operational goals, such as improving service quality, enhancing grid stability, and reducing carbon emissions. At the same time, they also lack the ability to self-learn and self-adjust, and are unable to update strategies in a timely manner based on emerging information. Traditional data collection methods may rely on fixed sampling frequencies or specific sensor network layouts, which may result in certain key information not being captured, especially in the face of rapidly changing environmental conditions, such as the impact of sudden weather changes on renewable energy. Due to equipment aging, communication interruptions, or other technical failures, traditional data collection systems may generate a large amount of noisy data or erroneous data, affecting the accuracy of subsequent analysis and decision-making.
[0004] VPPs earn revenue by participating in electricity market transactions, which involves the design of complex bidding strategies. An ideal bidding strategy should not only take into account the costs and benefits of its own DERs, but also pay close attention to market price fluctuations and the behavior of competitors. Traditional optimization algorithms usually only consider a single goal (such as economic benefits), ignore other important factors, and are mostly based on fixed mathematical models, making it difficult to quickly respond to changes in the external environment, such as sudden changes in supply and demand caused by extreme weather events or sharp fluctuations in market prices. Once the actual situation deviates from the preset conditions, the original optimization plan may become invalid, causing economic losses. Summary of the invention
[0005] The present invention aims to solve at least one of the technical problems existing in the related art. To this end, the present invention provides a virtual power plant operation method and system based on intelligent scheduling and market bidding optimization, which fills data through linear difference to ensure data integrity; comprehensively considers various external factors, such as weather, market prices, policy changes, etc., to improve the comprehensiveness and adaptability of the prediction model; by continuously optimizing algorithm parameters, it adapts to different types of DERs and complex market conditions, and improves the flexibility and robustness of the model; on the basis of considering multiple goals such as cost, benefit, and environmental impact, dynamically adjusts the operating status of each DERs, finds the optimal operation strategy, takes into account the synergy between different DERs, and uses the Nash equilibrium concept in game theory to describe the optimal bidding strategy, ensuring that the maximum benefit is obtained in a highly competitive market environment while reducing the risk of price wars with other competitors.
[0006] The present invention provides a virtual power plant operation method based on intelligent scheduling and market bidding optimization, comprising: S1: Collect the operating status data of each distributed energy resource in the virtual power plant in real time and pre-process it to obtain model input data; S2: Combining historical data and model input data, the future operating status data of each distributed energy resource in the virtual power plant is predicted through the long short-term memory network model; S3: Dynamically adjust the future operating status data of each distributed energy resource in the virtual power plant by comprehensively considering costs, benefits and environment to obtain multi-objective optimization results; S4: Based on the multi-objective optimization results, the Nash equilibrium-based bidding strategy is used to generate the optimal market bidding strategy.
[0007] According to a virtual power plant operation method based on intelligent scheduling and market bidding optimization provided by the present invention, the distributed energy resources also include solar panels, wind turbines, energy storage equipment, and electric vehicle charging stations.
[0008] According to a virtual power plant operation method based on intelligent scheduling and market bidding optimization provided by the present invention, the method also includes step S1, in which the operating status data of each distributed energy resource of the virtual power plant is preprocessed by a linear interpolation method.
[0009] According to a virtual power plant operation method based on intelligent scheduling and market bidding optimization provided by the present invention, the historical data also includes meteorological data, power grid load level and electricity price, and the meteorological data includes hourly wind speed, solar radiation intensity and temperature.
[0010] According to a virtual power plant operation method based on intelligent scheduling and market bidding optimization provided by the present invention, the step S2 includes: S21: Collect historical data, pre-process the historical data, and organize them into time series data; S22: Initialize the weight matrix and bias term of the long short-term memory network model according to the time series data; S23: Using the long short-term memory network model according to the weight matrix, bias term and model input data, calculate the future operating status data of each distributed energy resource in the virtual power plant.
[0011] According to a virtual power plant operation method based on intelligent scheduling and market bidding optimization provided by the present invention, the method also includes dynamically adjusting the future operating status data of each distributed energy resource based on a reinforcement learning algorithm in step S3.
[0012] According to a virtual power plant operation method based on intelligent scheduling and market bidding optimization provided by the present invention, the reinforcement learning algorithm also includes a proximal strategy optimization algorithm.
[0013] According to a virtual power plant operation method based on intelligent scheduling and market bidding optimization provided by the present invention, the step S3 includes: S31: Get the status of the virtual power plant And actions ,in, This includes current grid load levels, renewable energy availability, market electricity prices, the current status of energy storage equipment, and meteorological data; This includes power generation planning and controlling the charging and discharging rates of energy storage devices; S32: According to the status of the virtual power plant And actions Construct a reward function, the reward function is: in, For the strategy parameters The reward function under is the strategy parameter, is the probability of adopting the current strategy, is the trajectory of the current strategy, is the average probability of the current strategy appearing in all possible trajectories, for Length, For the status Take action Instant rewards; S33: The calculation expression of probability ratio is: in, is the probability ratio, For the current strategy in state Take action The probability of For the old policy in state Take action The probability of S34: The optimization goal is to maximize the reward function while keeping the new and old strategies close. The calculation expression of the objective function is: in, is the objective function, is the advantage function, is the clipping range, To find the minimum function, is the clipping function; S35: Optimize the objective function according to the synergy between distributed energy resources to obtain multi-objective optimization results.
[0014] According to the present invention, a virtual power plant operation method based on intelligent scheduling and market bidding optimization is provided, which also includes generating an optimal market bidding strategy based on a bidding strategy based on Nash equilibrium, obtaining the price of electricity that the virtual power plant is willing to sell within a certain period of time, and the net profit that can be obtained based on this price.
[0015] The present invention also provides a virtual power plant operation system based on intelligent scheduling and market bidding optimization, which is used to execute the above-mentioned virtual power plant operation method based on intelligent scheduling and market bidding optimization, including: A collection and preprocessing module, which collects the operating status data of each distributed energy resource of the virtual power plant in real time and performs preprocessing to obtain model input data; A prediction module, which combines historical data and model input data to predict future operating status data of each distributed energy resource of the virtual power plant through a long short-term memory network model; A multi-objective optimization module, which dynamically adjusts the future operating state data of each distributed energy resource of the virtual power plant by comprehensively considering costs, benefits and the environment to obtain a multi-objective optimization result; The market bidding module generates an optimal market bidding strategy based on a bidding strategy based on Nash equilibrium according to the multi-objective optimization results.
[0016] The above one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects: The present invention provides a virtual power plant operation method and system based on intelligent scheduling and market bidding optimization, which fills data through linear difference to ensure data integrity. Comprehensively consider a variety of external factors, such as weather, market prices, policy changes, etc., to improve the comprehensiveness and adaptability of the prediction model; by continuously optimizing algorithm parameters, adapt to different types of DERs and complex market conditions, improve the flexibility and robustness of the model; on the basis of considering multiple goals such as cost, benefit, and environmental impact, dynamically adjust the operating status of each DERs to find the optimal operating strategy, consider the synergy between different DERs, and use the Nash equilibrium concept in game theory to describe the optimal bidding strategy, ensuring maximum benefits in a highly competitive market environment while reducing the risk of price wars with other competitors.
[0017] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS
[0018] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.
[0019] Figure 1 It is a flow chart of a virtual power plant operation method based on intelligent scheduling and market bidding optimization provided by the present invention.
[0020] Figure 2 It is a structural schematic diagram of a virtual power plant operation system based on intelligent scheduling and market bidding optimization provided by the present invention.
[0021] Reference numerals: 101. Collection and preprocessing module; 102. Prediction module; 103. Multi-objective optimization module; 104. Market bidding module. DETAILED DESCRIPTION
[0022] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme in the present invention will be clearly and completely described below. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection of the present invention. The following embodiments are used to illustrate the present invention, but cannot be used to limit the scope of the present invention.
[0023] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the embodiment of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.
[0024] Combine the following Figure 1 to Figure 2 The present invention describes a virtual power plant operation method and system based on intelligent scheduling and market bidding optimization.
[0025] like Figure 1 As shown, a virtual power plant operation method based on intelligent scheduling and market bidding optimization includes: S1: Collect the operating status data of each distributed energy resource in the virtual power plant in real time and pre-process it to obtain model input data; The distributed energy resources include solar panels, wind turbines, energy storage devices, and electric vehicle charging stations; The linear interpolation method is used to preprocess the operating status data of each distributed energy resource of the virtual power plant. The calculation expression is: in, For the The model input data at this moment, For the The operating status data of distributed energy resources at all times, For the The operating status data of distributed energy resources at all times, For the The horizontal axis of the operating status data of distributed energy resources at the moment, For the The horizontal axis of the operating status data of distributed energy resources at the moment, For the The horizontal axis of the operating status data of distributed energy resources at each moment.
[0026] In a specific embodiment of the present invention, a virtual power plant located in North China, which mainly relies on wind power and solar power generation, is equipped with an energy storage system. The operating status data of each distributed energy resource of the virtual power plant is collected in real time to obtain a time series data set. , linear interpolation method is used to fill the time series data set, and the calculation expression is: in, For the The model input data at this moment, For the The operating status data of distributed energy resources at all times, For the The operating status data of distributed energy resources at all times, For the The horizontal axis of the operating status data of distributed energy resources at the moment, For the The horizontal axis of the operating status data of distributed energy resources at the moment, For the The horizontal axis of the operating status data of distributed energy resources at each moment.
[0027] The padded data is used to ensure the integrity of the subsequent prediction model input data. In this embodiment, due to inaccurate weather forecasts, some data was lost. These data were successfully restored through the above interpolation method, thereby improving the accuracy of the model input data.
[0028] S2: Combine weather forecasts, historical data, and model input data to predict the future operating status data of each distributed energy resource in the virtual power plant through the long short-term memory network model; Historical data includes meteorological data, grid load levels and electricity prices. Meteorological data includes hourly wind speed, solar radiation intensity and temperature.
[0029] S21: Collect historical data, pre-process the historical data, and organize them into time series data; S22: Initialize the weight matrix and bias term of the long short-term memory network model according to the time series data; S23: Using the long short-term memory network model according to the weight matrix, bias term and model input data, calculate the future operating status data of each distributed energy resource in the virtual power plant.
[0030] The Long Short-Term Memory (LSTM) network controls the flow of information through a gating mechanism. The LSTM calculation formula is as follows: Input gate: determines which information should be added to the current memory; in, For the The state of the input gate at a certain moment determines which information should be added to the current memory. The sigmoid activation function compresses the input to between 0 and 1 to control the information flow. For the Hidden state at the moment With the current input The amount of splicing, is the input gate bias term, is the input gate weight matrix; Forget gate: determines which states should be taken from old memory; in, For the The forget gate state at that moment, is the forget gate weight matrix, is the forget gate bias term; Output gate: determines which information should be output to the next time step; in, For the The output gate state at the time, is the output gate weight matrix, is the output gate bias term; Current Memory : in, For the The memory of the moment, is the hyperbolic tangent activation function, is the candidate memory equity matrix, is a candidate memory bias term, Hidden state: in, For the The hidden state of the moment.
[0031] In a specific embodiment of the present invention, in a virtual power plant (VPP) environment, the goal is to predict wind power generation and electricity demand within the next 24 hours.
[0032] First, collect historical data, including hourly wind speed, solar radiation intensity, temperature and other meteorological data, as well as external factors such as grid load level and electricity price. Organize these data into time series format and perform necessary preprocessing (such as missing value filling, normalization, etc.).
[0033] Secondly, use the collected historical data as a training set to initialize the weight matrix of the LSTM model and the bias term For each time step, the formula is used to calculate , , , , and will Passed to the next time step.
[0034] Finally, after the model training is completed, the trained model is used to predict future wind power generation and electricity demand. According to the prediction results, a corresponding scheduling plan is formulated, such as adjusting the charging and discharging rate of energy storage equipment or optimizing the output power of power generation equipment. The accuracy of the prediction results is regularly evaluated, and the model parameters are dynamically adjusted according to the actual situation to improve the prediction accuracy.
[0035] S3: Dynamically adjust the future operating status data of each distributed energy resource in the virtual power plant by comprehensively considering costs, benefits and environment to obtain multi-objective optimization results; Dynamically adjust the future operating status data of each distributed energy resource based on a reinforcement learning algorithm, which includes a proximal strategy optimization algorithm; S31: Get the status of the virtual power plant And actions ,in, This includes current grid load levels, renewable energy availability, market electricity prices, the current status of energy storage equipment, and meteorological data; This includes power generation planning and controlling the charging and discharging rates of energy storage devices; S32: According to the status of the virtual power plant And actions Construct a reward function, the reward function is: in, For the strategy parameters The reward function under is the strategy parameter, is the probability of adopting the current strategy, is the trajectory of the current strategy, is the average probability of the current strategy appearing in all possible trajectories, for Length, For the status Take action Instant rewards; S33: The calculation expression of probability ratio is: in, is the probability ratio, For the current strategy in state Take action The probability of For the old policy in state Take action The probability of S34: The optimization goal is to maximize the reward function while keeping the new and old strategies close. The calculation expression of the objective function is: in, is the objective function, is the advantage function, is the clipping range, To find the minimum function, is the clipping function; S35: Optimize the objective function according to the synergy between distributed energy resources to obtain multi-objective optimization results.
[0036] S4: According to the multi-objective optimization results, the bidding strategy based on Nash equilibrium is used to generate the optimal market bidding strategy; the optimal market bidding strategy is generated according to the bidding strategy based on Nash equilibrium to obtain the price of electricity that the virtual power plant is willing to sell within a certain period of time, and the net profit that can be obtained based on this price.
[0037] In some specific embodiments of the present invention, the optimal market bidding strategy is automatically generated according to the optimization results. Taking into account factors such as market price fluctuations and competitor behavior, the Nash equilibrium concept in game theory is used to describe the optimal bidding strategy.
[0038] Assume that there are N participants in the market. The net profit based on this price Depends on the bids of all participants , then the Nash equilibrium condition is: in, For participants The best bid, For All other bid combinations except is the price of electricity that the virtual power plant is willing to sell within a certain period of time, For participants The net profit that can be obtained based on this price.
[0039] By simulating the effects of different bidding strategies, it is found that the use of a bidding strategy based on Nash equilibrium can reduce the risk of price wars with other competitors while ensuring profits.
[0040] The execution and feedback mechanism ensures that the system can continuously optimize the model parameters according to the actual execution situation and improve the overall performance of the system. This is achieved by establishing a closed-loop control system, in which the feedback signal is used to correct the prediction error. Specify an error term: in, For the The error term at time, For the Actual values at the moment, such as actual power consumption, For the The predicted value at the moment, Use proportional-integral-derivative controller (PID) to adjust parameters: in, For the Feedback signal at all times, is the proportional gain, is the integral gain, is the differential gain, which is used to adjust the response speed and stability of the controller.
[0041] In some specific embodiments of the present invention, in the actual operation of VPP, It is used to adjust the charge and discharge rate of energy storage equipment or the output power of power generation equipment to minimize errors and optimize system performance. During a summer peak electricity consumption period, the charge and discharge rate of energy storage equipment was dynamically adjusted through the PID controller, which effectively alleviated the load pressure on the power grid and reduced the occurrence of power outages.
[0042] like Figure 2 As shown, a virtual power plant operation system based on intelligent scheduling and market bidding optimization is used to execute the above-mentioned virtual power plant operation method based on intelligent scheduling and market bidding optimization, including: The collection and preprocessing module 101 collects the operating status data of each distributed energy resource of the virtual power plant in real time and performs preprocessing to obtain model input data; The prediction module 102 combines historical data and model input data to predict the future operating status data of each distributed energy resource in the virtual power plant through a long short-term memory network model; The multi-objective optimization module 103 comprehensively considers the cost, benefit and environment to dynamically adjust the future operation status data of each distributed energy resource of the virtual power plant to obtain a multi-objective optimization result; The market bidding module 104 generates an optimal market bidding strategy based on a bidding strategy based on Nash equilibrium according to the multi-objective optimization results.
[0043] Through the collaborative work of the above modules, data is filled by linear interpolation to ensure data integrity; a variety of external factors, such as weather, market prices, policy changes, etc., are comprehensively considered to improve the comprehensiveness and adaptability of the prediction model; by continuously optimizing algorithm parameters, it adapts to different types of DERs and complex market conditions, thereby improving the flexibility and robustness of the model; on the basis of considering multiple objectives such as cost, benefit, and environmental impact, the operating status of each DER is dynamically adjusted to find the optimal operating strategy, and considering the synergy between different DERs, the concept of Nash equilibrium in game theory is used to describe the optimal bidding strategy to ensure maximum benefits in a highly competitive market environment while reducing the risk of price wars with other competitors.
[0044] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A virtual power plant operation method based on intelligent scheduling and market bidding optimization, characterized in that: include: S1: Collect the operating status data of each distributed energy resource in the virtual power plant in real time and pre-process it to obtain model input data; S2: Combining historical data and model input data, the future operating status data of each distributed energy resource in the virtual power plant is predicted through the long short-term memory network model; S3: Dynamically adjust the future operating status data of each distributed energy resource in the virtual power plant by comprehensively considering costs, benefits and environment to obtain multi-objective optimization results; S4: Based on the multi-objective optimization results, the Nash equilibrium-based bidding strategy is used to generate the optimal market bidding strategy.
2. A virtual power plant operation method based on intelligent scheduling and market bidding optimization according to claim 1, characterized in that: The distributed energy resources include solar panels, wind turbines, energy storage devices, and electric vehicle charging stations.
3. A virtual power plant operation method based on intelligent scheduling and market bidding optimization according to claim 1, characterized in that: In step S1, the linear interpolation method is used to preprocess the operating status data of each distributed energy resource in the virtual power plant.
4. A virtual power plant operation method based on intelligent scheduling and market bidding optimization according to claim 1, characterized in that: The historical data includes meteorological data, power grid load level and electricity price. The meteorological data includes hourly wind speed, solar radiation intensity and temperature.
5. The method for operating a virtual power plant based on intelligent scheduling and market bidding optimization according to claim 1 is characterized in that: The S2 step includes: S21: Collect historical data, pre-process the historical data, and organize them into time series data; S22: Initialize the weight matrix and bias term of the long short-term memory network model according to the time series data; S23: Using the long short-term memory network model according to the weight matrix, bias term and model input data, calculate the future operating status data of each distributed energy resource in the virtual power plant.
6. A virtual power plant operation method based on intelligent scheduling and market bidding optimization according to claim 1, characterized in that: In step S3, the future operating status data of each distributed energy resource is dynamically adjusted based on the reinforcement learning algorithm.
7. A virtual power plant operation method based on intelligent scheduling and market bidding optimization according to claim 6, characterized in that: The reinforcement learning algorithm includes a proximal strategy optimization algorithm.
8. A virtual power plant operation method based on intelligent scheduling and market bidding optimization according to claim 7, characterized in that: The S3 steps include: S31: Get the status of the virtual power plant And actions ,in, This includes current grid load levels, renewable energy availability, market electricity prices, the current status of energy storage equipment, and meteorological data; This includes power generation planning and controlling the charging and discharging rates of energy storage devices; S32: According to the status of the virtual power plant And actions The proximal strategy optimization algorithm is used to construct the reward function, which is: in, For the strategy parameters The reward function under is the strategy parameter, is the probability of adopting the current strategy, is the trajectory of the current strategy, is the average probability of the current strategy appearing in all possible trajectories, for Length, For the status Take action Instant rewards; S33: The calculation expression of probability ratio is: in, is the probability ratio, For the current strategy in state Take action The probability of For the old policy in state Take action probability; S34: The optimization goal is to maximize the reward function while keeping the new and old strategies close. The calculation expression of the objective function is: in, is the objective function, is the advantage function, is the clipping range, To find the minimum function, is the clipping function; S35: Optimize the objective function according to the synergy between distributed energy resources to obtain multi-objective optimization results.
9. The method for operating a virtual power plant based on intelligent scheduling and market bidding optimization according to claim 1, characterized in that: The optimal market bidding strategy is generated based on the Nash equilibrium bidding strategy to obtain the price of electricity that the virtual power plant is willing to sell within a certain period of time, as well as the net profit that can be obtained based on this price.
10. A virtual power plant operation system based on intelligent scheduling and market bidding optimization, characterized in that: A method for operating a virtual power plant based on intelligent scheduling and market bidding optimization as claimed in any one of claims 1 to 9, comprising: A collection and preprocessing module, which collects the operating status data of each distributed energy resource of the virtual power plant in real time and performs preprocessing to obtain model input data; A prediction module, which combines historical data and model input data to predict future operating status data of each distributed energy resource of the virtual power plant through a long short-term memory network model; A multi-objective optimization module, which dynamically adjusts the future operating state data of each distributed energy resource of the virtual power plant by comprehensively considering costs, benefits and the environment to obtain a multi-objective optimization result; The market bidding module generates an optimal market bidding strategy based on a bidding strategy based on Nash equilibrium according to the multi-objective optimization results.
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