Virtual power plant distributed optimization and feasible region analysis method and system

Abstract

The invention discloses a virtual power plant distributed optimization and feasible region analysis method and system. The method comprises the following steps: establishing an interactive physical model of a virtual power plant and a power distribution network; based on an interactive physical model, relaxation decoupling is carried out on wide-area and neighborhood time coupling constraints caused by the state of charge of the energy storage system through a Lyapunov optimization theory, and a multi-period optimization problem of the virtual power plant is converted into a single-period optimization sub-problem; aiming at the single-period optimization sub-problem, adopting a particle swarm optimization algorithm HSIPSO improved based on a hybrid strategy and fusing the particle swarm optimization algorithm HSIPSO into an ADMM distributed optimization framework to form an ADMM-HSIPSO algorithm, and carrying out distributed solution on the single-period optimization sub-problem; converting a multi-period virtual power plant feasible region representation problem into a calculation problem of each scheduling period feasible region; a mathematical model of the feasible region of the virtual power plant is constructed, and an ADMM-HSIPSO algorithm is adopted for solving; the coordination and unification of the optimal distribution of the dispatching power of the power distribution network among the virtual power plants and the privacy protection in the virtual power plants are realized.

Description

Technical Field

[0001] This invention belongs to the field of virtual power plant optimization scheduling, and specifically relates to a method and system for distributed optimization and feasible domain analysis of virtual power plants. Background Technology

[0002] While the installed capacity of new energy sources continues to increase, the intermittent and fluctuating nature of their output poses significant challenges to the operation and management of distribution networks. Virtual power plants, by effectively aggregating distributed power sources, controllable loads, and energy storage into a virtual whole, provide an effective way for them to actively participate in distribution network dispatch and the electricity market. However, given the increasingly complex resource structure and rising privacy requirements, their internal dispatch and external interaction mechanisms still face problems such as low dispatch efficiency, poor response time, and weak privacy protection. Specifically, the current challenges mainly lie in the following two aspects: 1) Internal optimization and scheduling of virtual power plants: First, virtual power plants consist of multiple heterogeneous distributed energy units, each with unique energy characteristics and operational constraints. Existing optimization algorithms often face problems such as low computational efficiency and insufficient solution accuracy when dealing with large-scale complex problems. Second, the decisions and states at different times during the optimization process are interdependent. This time coupling characteristic requires the VPP to consider the interaction between variables simultaneously over the entire time series, which places higher demands on the optimization solution algorithm.

[0003] 2) Interaction between VPP and the Distribution Network: As a commercial entity, the VPP needs to actively interact with the distribution network to generate profits and ensure sustainable operation. Due to market competition, VPP operators are reluctant to disclose their internal models, making it difficult for the distribution network to accurately assess its dispatch capabilities. When the distribution network has additional dispatch needs during the day, it typically prioritizes interaction with traditional power plants to ensure grid security and power supply reliability. Therefore, the VPP needs to characterize its own feasible region and report it to the distribution network to achieve interaction. However, the feasible region is affected by the intermittency and time span of distributed energy output, exhibiting dynamic characteristics that change over time. This makes it difficult for the VPP to efficiently characterize a reliable feasible region, thus affecting the efficiency of the interaction between the VPP and the distribution network. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for distributed optimization and feasible domain analysis of virtual power plants, so as to solve the problems of leakage of important information, difficulty in parsing and characterizing the dispatchable boundary, and difficulty in meeting the timeliness of intraday dispatch of the distribution network when virtual power plants participate in the dispatch of the distribution network.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a method for distributed optimization and feasible region analysis of a virtual power plant, comprising: Establish an interactive physical model between the virtual power plant and the distribution network; Based on the interactive physical model, the Lyapunov optimization theory is used to relax and decouple the wide-area and neighborhood time coupling constraints caused by the state of charge of the energy storage system, transforming the multi-period optimization problem of the virtual power plant into a single-period optimization subproblem. For single-time-period optimization subproblems, the particle swarm optimization algorithm HSIPSO based on a hybrid strategy is adopted and integrated into the ADMM distributed optimization framework to form the ADMM-HSIPSO algorithm for distributed solution of single-time-period optimization subproblems. Based on the analysis of distribution network dispatch characteristics, the problem of representing the feasible region of virtual power plants in multiple time periods is transformed into the problem of calculating the feasible region of each dispatch period. Within each dispatch period, the feasible region of the virtual power plant after completing the original dispatch plan is represented by the spinning reserve capacity. A mathematical model of the feasible region of the virtual power plant is constructed and solved using the ADMM-HSIPSO algorithm. This achieves the coordination and unity between the optimal allocation of dispatch power in the distribution network among the virtual power plants and the protection of privacy within the virtual power plants.

[0006] Secondly, the present invention provides a virtual power plant distributed optimization and feasible domain analysis system, comprising: The model building module is used to build an interactive physical model of the virtual power plant and the distribution network; The problem transformation module is used to relax and decouple the wide-area and neighborhood time coupling constraints caused by the state of charge of the energy storage system based on the interactive physical model and Lyapunov optimization theory, transforming the multi-period optimization problem of the virtual power plant into a single-period optimization sub-problem. The solution module is used to solve single-time-period optimization subproblems by adopting the particle swarm optimization algorithm HSIPSO based on a hybrid strategy and integrating it into the ADMM distributed optimization framework to form the ADMM-HSIPSO algorithm. The feasible region calculation module is used to transform the feasible region representation problem of virtual power plants in multiple time periods into the calculation problem of feasible regions in each scheduling period based on the analysis of distribution network scheduling characteristics. Within each scheduling period, the feasible region of the virtual power plant after completing the original scheduling plan is represented by the spinning reserve capacity. A mathematical model of the feasible region of the virtual power plant is constructed and solved using the ADMM-HSIPSO algorithm. This achieves the coordination and unification of optimal allocation of distribution network scheduling power among virtual power plants and privacy protection within virtual power plants.

[0007] Thirdly, the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the virtual power plant distributed optimization and feasible domain analysis method.

[0008] Fourthly, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the virtual power plant distributed optimization and feasible domain analysis method.

[0009] Compared with the prior art, the present invention has the following technical effects: This invention utilizes Lyapunov optimization theory to relax and decouple the time coupling constraints within the VPP, transforming the multi-time-period optimization problem into multiple single-time-period subproblems and reducing problem complexity. Secondly, to improve computational efficiency and solution accuracy, a hybrid strategy-based improvement of the particle swarm optimization algorithm is adopted and embedded into the ADMM distributed optimization framework to achieve distributed solution of each single-time-period subproblem. Finally, a method for characterizing the feasible region of the VPP based on spinning reserve capacity is proposed, achieving efficient and reliable characterization of the feasible region to meet the requirements of timely interaction between the VPP and the distribution network and power supply reliability, while protecting the data privacy of the VPP. Attached Figure Description

[0010] Figure 1 This is a diagram of the virtual power plant resource composition of the present invention.

[0011] Figure 2 This is a diagram illustrating the interaction process between the virtual power plant and the distribution network in this invention.

[0012] Figure 3 This is the distributed optimization design diagram of the present invention.

[0013] Figure 4 This is a flowchart of the intraday optimization process for the virtual power plant of the present invention.

[0014] Figure 5 This is a schematic diagram of the solution method of the present invention.

[0015] Figure 6 This is a diagram showing the relationship between the optimized time periods of this invention.

[0016] Figure 7 This is a comparison diagram of population initialization in this invention.

[0017] Figure 8 This is a flowchart of the HSIPSO algorithm execution of the present invention.

[0018] Figure 9 This is a schematic diagram of the instruction time period analysis of the present invention.

[0019] Figure 10 It is the limit feasible region diagram of the virtual power plant.

[0020] Figure 11 This is a flowchart of the calculation of the feasible domain upper limit of the present invention.

[0021] Figure 12 This is the scheduling power allocation diagram of the present invention.

[0022] Figure 13 This is a diagram of the test system of the present invention.

[0023] Figure 14 The diagram shows the predicted values ​​of wind power and photovoltaic power for each VPP and the original dispatch plan diagram of the present invention. Detailed Implementation

[0024] The present invention will be further described below with reference to the accompanying drawings: Example 1, please refer to Figure 1 This invention provides a method for distributed optimization and feasible region analysis of virtual power plants, comprising: Establish an interactive physical model between the virtual power plant and the distribution network; Based on the interactive physical model, the Lyapunov optimization theory is used to relax and decouple the wide-area and neighborhood time coupling constraints caused by the state of charge of the energy storage system, transforming the multi-period optimization problem of the virtual power plant into a single-period optimization subproblem. For single-time-period optimization subproblems, the particle swarm optimization algorithm HSIPSO based on a hybrid strategy is adopted and integrated into the ADMM distributed optimization framework to form the ADMM-HSIPSO algorithm for distributed solution of single-time-period optimization subproblems. Based on the analysis of distribution network dispatch characteristics, the problem of representing the feasible region of virtual power plants in multiple time periods is transformed into the problem of calculating the feasible region of each dispatch period. Within each dispatch period, the feasible region of the virtual power plant after completing the original dispatch plan is represented by the spinning reserve capacity. A mathematical model of the feasible region of the virtual power plant is constructed and solved using the ADMM-HSIPSO algorithm. This achieves the coordination and unity between the optimal allocation of dispatch power in the distribution network among the virtual power plants and the protection of privacy within the virtual power plants.

[0025] Example 2: This invention provides a method for distributed optimization and feasible region analysis of a virtual power plant, comprising: Step 1: Establish an interactive physical model of the virtual power plant and the distribution network.

[0026] Step 2: Use Lyapunov optimization theory to relax and decouple the time coupling constraints within the virtual power plant; transform the multi-time period optimization problem into multiple single-time period optimization subproblems. Step 3: Based on the improved particle swarm optimization algorithm with hybrid strategy, integrate it into the ADMM distributed optimization framework to form the ADMM-HSIPSO algorithm with high search capability, so as to realize the distributed solution of single-time optimization sub-problems; Step 4: Based on the analysis of the distribution network dispatch characteristics, the problem of representing the feasible region of VPP in multiple time periods is transformed into the problem of calculating the feasible region of each dispatch period; Step 5: In each scheduling period, the rotating reserve capacity is used to characterize the feasible region of VPP after completing the original scheduling plan. By analyzing the impact mechanism of wind and solar fluctuations on reserve capacity, a mathematical model of the feasible region of VPP is constructed. Step 6: In each scheduling period, the rotating reserve capacity is used to characterize the feasible region of VPP after completing the original scheduling plan. By analyzing the impact mechanism of wind and solar fluctuations on reserve capacity, a mathematical model of the feasible region of VPP is constructed. Step 7: Based on the feasible domain of the virtual power plant, a multi-VPP-distribution network collaborative optimization strategy is proposed to achieve the coordination and unification of optimal power allocation for distribution network dispatch and VPP privacy protection.

[0027] Specifically: Step 1: With Figure 1 The example shown is a virtual power plant (VPP) consisting of wind turbines, photovoltaics, gas turbines, energy storage, and load shedding. It operates according to a pre-defined plan with the distribution network during the day. The VPP's coordination and control center manages resources centrally. While fully absorbing wind and solar power generation, it prioritizes using gas turbines to supplement any shortfall, utilizes energy storage for peak shaving, and reduces load when total power output is insufficient to minimize overall operating costs. If the plan still cannot be met, it reports the power deficit and accepts economic penalties. When there is surplus power, it feeds the surplus into the grid. Its physical interaction model with the distribution network is as follows.

[0028] Objective function: (1) (2) In the formula: VPP day-ahead operating costs; Number of time periods within a day; , , , , , , They are respectively from the day before Operating costs for wind power, photovoltaic power, energy storage batteries, gas turbines, demand response, off-load penalty, and surplus power to the grid; , , , , , These are the wind power operating cost coefficient, photovoltaic operating cost coefficient, energy storage battery operating cost coefficient, demand response compensation cost coefficient, load shedding penalty coefficient (100 times the time-of-use price), and surplus electricity grid connection price. , This is the operating cost coefficient for gas turbines; , , , , , , They are respectively Wind power output, photovoltaic power output, energy storage battery output, gas turbine output, load reduction output, off-load power, and surplus power fed into the grid during specific time periods; The duration of a time period.

[0029] Constraints: Virtual power plant power balance constraints (3) In the formula: These are new dispatch instructions to be issued by the distribution network within a certain period of time in the future. The load is the one that has been determined by the distribution network dispatch command.

[0030] Energy storage battery operating constraints (4) In the formula: , For energy storage batteries Discharge power and charging power during the time period; , This represents the charge / discharge state of the energy storage battery, and is a 0-1 variable. , This represents the maximum charging and discharging power of the energy storage battery. , For the charging and discharging efficiency of energy storage batteries; This refers to the rated capacity of the energy storage battery. For energy storage batteries State of charge at the end of the time period; , These represent the minimum and maximum permissible states of charge of the energy storage battery, respectively. , These represent the initial and final states of charge of the energy storage battery during a day, respectively.

[0031] Gas turbine operating constraints (5) In the formula: It is a 0-1 variable, representing the start-up and shutdown status of the gas turbine; , These are the minimum and maximum power outputs of the gas turbine, respectively. , These represent the downward and upward ramp rates of the gas turbine, respectively.

[0032] Reduced load operating constraints (6) In the formula: for The maximum output power of the load can be reduced during certain periods.

[0033] Electricity sales constraints (7) In the formula: These represent the upper limit of the power that a virtual power plant can sell to the grid.

[0034] Furthermore, in step 2, the time coupling constraints within the virtual power plant are mainly reflected in the energy storage system. Since the energy storage system itself does not have the ability to generate energy, its energy source is highly dependent on external input, and the current power level is directly affected by the charging and discharging decisions of the previous period. Therefore, significant neighborhood time coupling is formed in the intraday VPP multi-period rolling optimization. (Accumulation of the state of charge in the energy storage, a hard constraint). Furthermore, to ensure the periodic operation of the energy storage, its state of charge typically needs to remain consistent at the beginning and end of a cycle, which introduces wide-area time coupling. (Improve the flexibility of energy storage resource scheduling, soft constraints).

[0035] This invention uses 15-minute intervals as a time period and employs the Lyapunov optimization method to transform the multi-time-period optimization problem into a series of sub-problems with 15-minute intervals for solution. As analyzed above, the time coupling constraints within the virtual power plant mainly consist of neighborhood time coupling constraints and wide-area time coupling constraints. Therefore, for neighborhood time coupling constraints... Rewritten as arrive The cumulative form, divided by the period T on both sides, gives: (8) Wide-area time coupling constraints It is known that maintaining the consistent energy storage state at the beginning and end of the energy storage system throughout the entire scheduling cycle facilitates continued scheduling in the next cycle, thereby improving the flexibility of energy storage resource scheduling. Therefore, preliminary results of time coupling relaxation can be obtained: (9) The above equation can be seen as the energy storage charging and discharging power maintaining a certain balance within a scheduling cycle, thus reflecting that the energy storage's state of charge is within a certain range. Equation (9) is a preliminary relaxation of the time coupling constraint, but the solution to the problem is still complex and difficult to handle. Therefore, a virtual queue reflecting the cumulative amount of energy storage state of charge is established: (10) By introducing the concept of a virtual queue, the relaxation condition in equation (9) is described as the net flow of the virtual queue being zero within a specific time period. Thus, both the wide-area coupling constraint and the neighborhood coupling constraint in the VPP internal optimization are transformed into a virtual queue. To address the stability issues, Lyapunov functions were constructed: (11) From the properties of Lyapunov functions, we know that when When the size of the virtual queue is large, the congestion level is high and the stability is poor; conversely, when the size of the virtual queue is small, the congestion level is low and the stability is good. To better measure the stability characteristics and evolution trend of the virtual queue, the Lyapunov drift function is further calculated. Used to represent the difference in congestion level of the virtual queue at adjacent times: (12) From the properties of the drift function, we know that for a virtual queue to tend to be stable, It should be as small as possible. To simultaneously consider the stability of the virtual queue and the objective function of the virtual power plant's internal optimization, a drift plus penalty (DPP) function is used to transform the multi-period centralized optimization problem into multiple single-period centralized optimization problems. That is, the optimization problem is transformed into: (13) when This can be seen as a trade-off between the stability of the virtual queue and the operating cost of the VPP. Equation (13) has an upper bound, which can be expressed as: (14) For the change in state of charge, it can be seen from equation (14) that the upper bound is... Since the value is constant, the above problem can be viewed as minimizing... Therefore, equation (14) can be transformed back into: (15) Thus, to address the wide-area and neighborhood time coupling constraints caused by the state of charge of energy storage, this invention employs a time decoupling strategy for relaxation decoupling. Before time decoupling, the optimization model needs to consider variables and constraints from multiple time periods simultaneously, resulting in high computational complexity. After decoupling, the time coupling constraints are transformed into the stability problem of the virtual queue, decomposing the multi-time-period optimization problem into multiple relatively independent single-time-period sub-problems. The solution of each sub-problem does not rely on prior information; optimization can be achieved solely based on the variable information of the current time period, thereby effectively reducing the overall solution difficulty. Although the reduced information interaction may lead to a loss of global information, in real-time dynamic systems such as virtual power plants, solution efficiency and the real-time nature of feasible solutions are usually more important than global optimality. Empirical evidence shows that this loss of optimality is generally acceptable and has a limited impact on system performance.

[0036] In step 3, the VPP scheduling problem is decoupled in time based on Lyapunov optimization theory, transforming the multi-period problem into a single-period concentrated optimization problem. Although this method reduces the problem size and computational complexity, the real-time optimization and dynamic updating of the feasible region required for intraday scheduling still pose a computational efficiency bottleneck after decoupling. Therefore, an improved particle swarm optimization method based on hybrid strategies, the Alternating Direction Multiplier Method (ADMM-HSIPSO), is proposed to simultaneously improve solution accuracy and speed. The optimization problem processing steps are as follows: 1) Distributed solution model for virtual power plants based on ADMM (1) Introducing slack variables To transform inequality constraints into equality constraints, slack variables are introduced. The process of transforming inequality constraints into equality constraints is as follows: (16) In the formula: It is a set of operating constraints for each unit and all of them are processed into In form, The introduced slack variable represents the first... The difference between the inequality constraints. In this way, all constraints are transformed into equality constraints, making them easier for ADMM to process.

[0037] (2) Constructing the augmented Lagrange function By incorporating the constraints of the optimization problem into the objective function through their respective dual multipliers, the original problem is transformed into an unconstrained optimization problem. Simultaneously, to accelerate convergence and ensure gradual constraint satisfaction, a quadratic penalty term is added, resulting in the augmented Lagrangian function: (17) In the formula: Equality constraints The dual multipliers; For the first Dual multipliers of inequality constraints. All are available express, This is the penalty coefficient.

[0038] (3) Decomposition of the optimization problem based on ADMM The first subproblem is optimizing continuous variables. , and slack variables and dual variables and Treating it as a constant, the first subproblem can be written as: (18) The second subproblem is slack variables. Update, at this point the original variable and dual variables and Treating auxiliary variables as constants, optimize them. The second subproblem can be written as: (19) Due to the original variable and dual variables and If we consider it as a constant, then the optimization objective can be further transformed into: (20) For each It can be optimized independently. By writing it as a single-variable optimization problem and expanding and simplifying the quadratic terms, we can obtain: (twenty one) For the above formula Take the partial derivatives and set them to 0, considering... Therefore, in the end The update expression is: Solving for: (twenty two) The dual variable is updated as follows: (twenty three) (twenty four) 2) Solving ADMM subproblems based on HSIPSO Virtual power plant intraday optimization and feasible region analysis are highly dynamic, requiring continuous updates to adapt to time-varying demands and constraints. Commercial solvers, due to their static assumptions, struggle to match dynamic environments, and their "black box" nature limits process control and debugging. In contrast, heuristic algorithms offer greater flexibility and can be customized to adapt to dynamic problems. The Particle Swarm Optimization (PSO) algorithm is widely used due to its simple structure, easily adjustable parameters, and strong adaptability. Therefore, this invention employs a hybrid strategy to improve PSO for solving sub-problems within the ADMM framework. The improvement strategy is as follows: (1) Population initialization using Sobol sequences This invention uses a Sobol sequence for initialization, leveraging its uniform distribution to more effectively cover the search space. The Sobol sequence is generated using a base-2 inversion algorithm, with a different matrix for each dimension, ensuring the generation of non-repeating and uniform points. The generation process of the nth point can be represented as: (25) It is the value of the previous point in the k-th dimension; The nth point in the k-th dimension of the direction number matrix Bit; This is an XOR operation. Using Sobol initialization results in a more uniform population distribution, leading to better coverage of the search space and improved algorithm performance.

[0039] (2) Adaptive inertia weight Standard PSO uses fixed inertia weights, which may lead to low efficiency. To fully leverage the advantages of PSO, this invention employs an adaptive weighting strategy, dynamically adjusting the inertia weights during iteration to optimize the balance between global search and local optimization, thereby accelerating the convergence process.

[0040] (26) In the formula, and These are the pre-defined minimum and maximum inertia coefficients, typically taken as 0.4 and 0.9, respectively. The average fitness of all particles at the next iteration and The minimum fitness of all particles at the next iteration is: (27) (28) As can be seen from the above formula, the particle is always compared with the average fitness during the iteration process, thereby flexibly adjusting the weight value and accelerating convergence.

[0041] (3) Asymmetric learning factor The asymmetric learning factor enhances the adaptability of PSO by dynamically adjusting its dependence on individual optimal solutions and the global optimal solution. This allows the algorithm to adjust its search strategy at different stages, thereby improving the balance between global and local search and enhancing the algorithm's convergence speed, accuracy, and stability. The asymmetric learning factor update expression is as follows: (29) In the formula, This is the initial value of the individual learning factor; This represents the final value of the individual learning factor. This is the initial value for the social learning factor; This represents the final value of the social learning factor. This represents the total number of iterations. Generally... and Therefore, during the iteration process, by gradually decreasing the individual learning factor and gradually increasing the social learning factor, premature convergence in the early stage can be avoided. At the same time, when approaching the optimal solution, the dependence on the global optimal solution is enhanced, thus accelerating the fine search.

[0042] (4) Adaptive Cauchy mutation strategy This invention proposes an adaptive Cauchy mutation strategy, which enhances the algorithm's ability to escape local optima by perturbing the current optimal solution. The specific improvements are as follows.

[0043] Local optimal solution identification: The determination method is as follows: If the fitness value of an individual in the population does not change by more than 10% of its original value in six consecutive iterations, then that individual is considered to have fallen into a local optimum. Then, the same method is used to determine the fitness of the remaining individuals, and the proportion of individuals fallen into a local optimum is counted. If this proportion exceeds a preset threshold, the algorithm is determined to have fallen into a local optimum; otherwise, the algorithm is considered not to have fallen into a local optimum. The relevant mathematical expressions are as follows: (30) (31) (32) In the formula: and The first The particle in the first The fitness value of the next iteration and the flag value indicating whether it has fallen into a local optimum; For all particles in The proportion of iterations that get trapped in local optima; For the algorithm in The threshold for determining whether the next iteration has fallen into a local optimum; For the algorithm in A flag indicating whether the next iteration has fallen into a local optimum.

[0044] Cauchy mutation: After the discrimination algorithm gets stuck in a local optimum, Cauchy mutation is performed on the current optimal solution. The mathematical expression is: (33) In the formula: for The new value of the optimal solution in the next iteration after Cauchy perturbation; It follows a standard Cauchy distribution. The algorithm obtains... Afterwards, comparison and The fitness value, if Superior Then replace the current optimal solution with Otherwise, do not replace.

[0045] (5) Local adaptive step size gradient descent In particle swarm optimization (PSO), the update step size may be too large when a particle is close to the optimal solution, affecting fine-grained search. To address this, this invention introduces a local search strategy (adaptive step-size gradient descent), which guides the particle to make precise adjustments using the gradient information of its current position after a global search. A smaller step size is used when the gradient is large to avoid over-adjustment; a larger step size is used when the gradient is small to accelerate convergence. The gradient calculation and position update formulas are as follows.

[0046] (34) (35) In the formula: The disturbance amount is usually set to a minimum value. No. The gradient value is obtained in each dimension. This is the step size factor, which controls the magnitude of each update.

[0047] In step 4, by analyzing the dispatch characteristics of the distribution network, the problem of representing the feasible region of multi-time period VPP is transformed into the problem of calculating the feasible region of each dispatch period: Within the rolling cycle, the dispatch demand of the distribution network varies across time periods. To improve the practicality of VPP feasible region characterization, time periods with potential dispatch demand should be identified and classified first. Then, the feasible regions of virtual power plants (VPPs) during these time periods should be specifically characterized to assist the distribution network in developing more targeted dispatch strategies. The dispatch instructions issued by the distribution network within a day are... Includes the start time of the scheduling instructions. Duration and scheduling power . and The constraints are as follows: (36) In the formula: The minimum value at the initial time; , , All values ​​are integers with the same unit. A rolling cycle has a 4-hour time window, with each 15-minute interval constituting a 16-interval. Therefore, within one rolling cycle... The upper limit is 16, and the lower limit is 1. For example, starting from 1:15 (there are 96 time slots in a day, and 1:15-1:30 is the 5th time slot), for 3 consecutive time slots (45 minutes), the virtual power plant is increased. MW output. (Using the 4 hours from 00:00 to 04:00 as an example for explanation) This indicates that the distribution network has a scheduling need at some point within the next 4 hours. For example... , This indicates that the distribution network has a dispatching need during the time period of 00:00-00:15. There are a total of 16 such duration types. Similarly, if... This means that there is a scheduling need within two consecutive time periods, for example... , This indicates that the distribution network has a dispatching need during the time period from 00:00 to 00:30. There are a total of 15 such time period types. And so on, we can see... and There are a total of 136 possible combinations. Therefore, for each time period type, it is necessary to calculate the feasible domain of the virtual power plant within that time period. The range of values, and based on the dataset The information is reported to the distribution network in the form of [the report]. , , It is a set consisting of the start time, duration, and schedulable power.

[0048] Furthermore, in step 6, the rotating reserve capacity is used to characterize the feasible region of the VPP after completing the original scheduling plan within each scheduling period. By analyzing the impact mechanism of wind and solar fluctuations on reserve capacity, a mathematical model of the VPP feasible region is constructed, and the ADMM-HSIPSO algorithm is used to solve the model. 6.1 Characterization of the Limiting Feasibility Region and Analysis of Dispatch Potential of Virtual Power Plant Virtual power plants cope with wind and solar fluctuations through spinning reserve capacity, and their total capacity represents the system's maximum capacity to withstand wind and solar fluctuations after the original dispatch plan has been completed. When calculating the feasible region, the total spinning reserve capacity is first determined through testing, and then the prediction error compensation capacity required by national standards is deducted. The remaining part is the actual usable feasible region capacity.

[0049] The adjustable equipment of the virtual power plant of this invention includes an energy storage system, a gas turbine, and load shedding. By setting a reasonable spinning reserve capacity, it can cope with situations where the power forecasts for wind and solar power generation are too high or too low. The spinning reserve is set as follows: (37) (38) Equations (37) and (38) represent the rotating reserve constraints set to address situations where wind and solar forecast data are too low or too high, respectively. , The corresponding prediction error coefficient can be set according to the guidelines in GB / T40607-2021. To address forecast errors during intraday optimized scheduling of VPP, a spinning reserve capacity is set, meaning the spinning reserve capacity must be greater than the capacity required to address wind and solar forecast errors.

[0050] To better characterize the fluctuations in wind and solar power output, using Characterizing the fluctuation of wind and solar power output, through analysis The range of values ​​for different scheduling periods is determined, and the range is gradually expanded within that range. The numerical values ​​are used to test the maximum wind and solar power fluctuations that the virtual power plant can withstand while fulfilling the original dispatch plan within each dispatch period, thereby determining the corresponding spinning reserve capacity and ultimately defining the feasible region of the virtual power plant. The first step is to test the values ​​for a single time period. We analyze the range of values ​​for . Equations (37) and (38) are transformed into the following forms: (39) (40) In the formula: and They are respectively The fluctuation range of wind and solar power output corresponding to upward and downward spin-up reserve within a given time period. As the aforementioned analysis shows, this fluctuation range reflects the degree to which the actual wind and solar power output deviates from the predicted values, and its magnitude directly determines the spin-up reserve capacity required by the virtual power plant. Therefore, exist The lower limit value within the time period is This means that the set capacity needs to be sufficient to cope with prediction errors. The upper limit value analysis within a single time period is as follows: Based on the original dispatch plan, the maximum value of the virtual power plant's spinning reserve capacity, i.e., its adjustable power (upward or downward adjustment), should be less than the limit value of the dispatchable power under ideal conditions. That is, ignoring the limitations of energy storage charging and discharging power and gas turbine ramping limitations, the maximum possible dispatchable power value of the virtual power plant within a time period is obtained, which is the limit feasible region of the virtual power plant. The limit of feasible region within a time period can be represented as: (41) (42) In the formula: , , , , This is the pre-scheduling plan for each unit of the VPP when there are no new scheduling instructions. , For VPP in The upper and lower boundaries of the time-limited feasible region, i.e., the virtual power plant in... The power that can be increased or decreased under ideal conditions during a given time period. Therefore, the following relationship exists: (43) (44) Therefore, within each time period and The range can be defined as follows: (45) (46) The above analysis determined the limit feasible region of the virtual power plant and the range of values ​​for wind and solar power fluctuations within a single time period. As shown in Section 5, the dispatch instructions issued by the distribution network within a day involve multiple consecutive time periods and require the virtual power plant to maintain stable power output throughout the entire duration. Therefore, when analyzing the limit feasible region within a duration, the maximum power range achievable throughout the entire duration is necessarily constrained by the feasible regions of each sub-time period within it. That is, the limit feasible region within the entire duration should depend on the minimum value among the limit feasible regions of all sub-time periods within that duration.

[0051] Taking two consecutive time periods as an example, the upper limit of the feasible region for the first time period. The upper limit of the feasible region for the second time period is Therefore, the upper limit of the limit feasible region of the virtual power plant over the entire duration should be the smaller of the two values, which is _____. If the output of the virtual power plant exceeds the limit capacity of any sub-time period, then the demand for continuous and stable power supply to the distribution network cannot be met during that continuous time period. Therefore, for the 136 scheduling time period types analyzed in Section 5, it is necessary to calculate the limit feasible region for each sub-time period within each time period type, and take the minimum value among them as the limit feasible region for that time period type. The limit feasible region corresponding to each scheduling time period type can be represented as: (47) In the formula: , For the first The scheduling start time and scheduling duration corresponding to each of the following situations; , For the first The upper and lower bounds of the limit feasible region corresponding to the duration of each scheduling event.

[0052] The above analysis shows that the limit feasible region for different scheduling durations determines the maximum wind and solar power output fluctuation that the virtual power plant can withstand within that duration. Based on this, the degree of wind and solar power output fluctuation within the duration can be further clarified. The range of values ​​for . Type of scheduling period within a duration The range of values ​​for is: (48) (49) and The first The analysis shows that, within the duration of each dispatch type, the range of wind and solar power output fluctuations corresponding to upward and downward spin-off reserves. The value range is not fixed, but changes dynamically with different scheduling period types. By calculating the value range of wind and solar power output fluctuations within each duration period, the feasible domain of the virtual power plant in different scheduling periods can be characterized.

[0053] 6.2 Calculation of the Feasible Region of a Virtual Power Plant 1) Basic Idea and Explanation of Two-Sided Characteristics The feasible region of a virtual power plant is two-sided: the upper limit represents the maximum additional capacity the virtual power plant can add beyond the original dispatch plan, and the lower limit can be derived similarly. Since the intraday dispatch demand of the distribution network typically involves only unidirectional adjustments—that is, within a certain time period, the distribution network can only request the virtual power plant to increase or decrease its output—the feasible region of a virtual power plant must be considered separately for both upward and downward adjustments when calculating its feasible region. and The ways in which values ​​are obtained are completely different.

[0054] 2) Detailed calculation steps of the feasible region To calculate the first The calculation steps are illustrated using the upper limit of the feasible region of the virtual power plant within the corresponding duration for a certain scheduling type as an example. The calculation method for the lower limit of the feasible region is similar: (1) Initialize the degree of wind and light fluctuation and Value The initial value is the prediction error compensation capacity. , Fixed as prediction error compensation capacity And it remains unchanged.

[0055] (2) Gradually increase over the duration The values ​​were examined on a time-by-time basis. First, gradually increase by a certain step size. The value; for each increase The feasibility of the calculated value needs to be verified for each sub-period throughout the entire duration. The specific verification method is as follows: The current and Substitute equations (39) and (40) into the equations and solve them simultaneously with the original scheduling plan mathematical model. First, solve for the first sub-period within the duration period: if there is no solution for the first sub-period, it means that the virtual power plant cannot withstand the current wind and solar fluctuations on the basis of completing the original scheduling plan. Stop the iteration and record the previous time when all sub-periods had solutions. The numerical value is used as the limit. If the first sub-time period has a solution, then all subsequent sub-time periods within the duration are solved sequentially. If all sub-time periods within the duration have solutions, it means that the current... The value is feasible throughout the entire duration and can be further increased. The numerical values ​​are then repeated over the entire duration. If no solution is found in any sub-time period within the duration, the iteration stops, and the previous iteration where all sub-time periods had solutions is recorded. The numerical value is used as the limit value.

[0056] 3) Final calculation formula for the feasible region of the virtual power plant The above process determines the maximum wind and solar power fluctuations that the virtual power plant can withstand while fulfilling the original dispatch instructions within each duration period, thus obtaining the total spinning reserve capacity for that duration period. Subtracting the spinning reserve capacity used to address forecast errors yields the feasible region of the virtual power plant within that duration period. The upper and lower limits of the virtual power plant's feasible domain within the duration corresponding to each scheduling type can be expressed as: (50) (51) In the formula: , For the first The upper and lower limits of the feasible region for each dispatch scenario. Therefore, the dispatchable power that the distribution network can issue during this duration. The scope is: (52) The above method only needs to calculate the feasible region for 136 time period types, and then obtain the dataset of feasible regions within the rolling week. This allows for effective daily interaction between the virtual power plant and the distribution network, and the data is reported to the distribution network. When solving for the feasible region of the virtual power plant over a continuous period, it is still necessary to test the degree of wind and solar power fluctuations on a time-by-time basis. Therefore, its computational framework can be built upon the time decoupling strategy described in Chapter 3. Furthermore, since the feasible region for each time period type is actually solved based on the original scheduling plan of the virtual power plant, the characterized feasible region has high reliability and can effectively meet the power supply reliability requirements of the distribution network in practical application scenarios.

[0057] To meet the timeliness requirements of intraday interaction between the virtual power plant (VPP) and the distribution network, this invention analyzes the original dispatch plan only within a continuous time period when characterizing the VPP's feasible domain, quickly providing the feasible domain for each time period within the next 4 hours. However, it does not directly consider the potential impact of dispatch command execution on the original dispatch plan in subsequent time periods. According to the relevant requirements of the national standard GB / T44241-2024, the VPP needs to verify the feasibility of dispatch commands issued by the distribution network. Therefore, in practical engineering applications, after receiving a dispatch command, the VPP needs to further verify the feasibility of the command in subsequent time periods. If the verification finds that executing the command still satisfies the original dispatch plan, the VPP responds; otherwise, the VPP refuses to execute and promptly reports back to the distribution network.

[0058] Step 7 proposes a multi-VPP-distribution network collaborative optimization strategy based on the feasible region to achieve a coordinated unification of optimal power allocation in distribution network scheduling and VPP privacy protection: When multiple virtual power plants (VPPs) operate collaboratively within a distribution network, significant differences exist in their feasible regions, internal models, and operating costs. Therefore, it is necessary to coordinate their responses to distribution network commands and optimize overall dispatch costs without exposing the mathematical models of each VPP. To address this, this invention proposes a two-layer collaborative optimization framework based on the feasible region of each VPP: the upper layer allocates dispatch power from the distribution network, while the lower layer verifies power feasibility and feeds back dispatch costs to the distribution network from each VPP.

[0059] During intraday scheduling, if the distribution network has additional scheduling needs within a specific time period, the scheduling will be based on the feasible domain dataset reported by each VPP. Power allocation is performed. To protect the internal privacy of each VPP, the distribution network cannot directly access the internal model of each VPP. Therefore, in the upper-level optimization, the distribution network aims to meet the total dispatch power demand and minimize the dispatch cost by allocating corresponding dispatch power to each virtual power plant. In the lower-level optimization, each VPP verifies the allocated dispatch power in subsequent time periods. If it is responsive, it replies with a feasibility flag to the distribution network. and the VPP scheduling cost corresponding to the instruction. It participates in the economic dispatch of the distribution network; if it cannot respond, it replies to the distribution network. The distribution network iteratively adjusts power allocation based on feedback from each VPP until the optimal allocation of scheduling costs is achieved while satisfying the total dispatch power requirements. This strategy is similar to "black box" optimization, where VPPs do not need to expose their internal models, thus protecting their internal privacy. Furthermore, the verification of dispatch power and the calculation of dispatch costs are independent among each VPP, allowing for parallel computation and improved efficiency.

[0060] 1) Mathematical model for collaborative optimization of multiple virtual power plants and distribution networks (1) Upper-level optimization model To achieve economical operation of the distribution network, the objective function is to optimize the cost of distribution network dispatching instructions, as follows: (53) In the formula: The operating cost of issuing new dispatch instructions to the distribution network during a specific period of the day; For the first The cost of the power allocated to each VPP; For the first The feasibility of the power allocated to a VPP in the remaining scheduling plan is determined by a value of 1. If the value is 1, it means that executing the current power can guarantee the completion of the original scheduling plan in the subsequent time period. If the value is 0, it means that after the virtual power plant executes the scheduled power in the current time period, the subsequent scheduling plan cannot be completed. The penalty term is generated when the distribution network allocates dispatch power according to the feasible domain reported by each VPP, but the VPP cannot meet the requirements; This is the power difference; , These refer to the start and duration periods of dispatching the daily demand of the distribution network. The penalty coefficient is set at 100 times the time-of-use electricity price. It is the difference between the power demand of the distribution network and the sum of the outputs of each VPP.

[0061] Since each virtual power plant has reported its feasible region to the distribution network, each VPP already includes its internal constraints when characterizing its own feasible region. Therefore, there is no need to consider the internal constraints of the VPP here; only power balance and the feasible region range constraints of the VPP need to be considered.

[0062] (54) In the formula: For distribution network Power required for scheduling during a given time period; , For the first The range of upper and lower feasible regions corresponding to each VPP time period.

[0063] (2) Lower-level optimization model In the lower-level optimization, each virtual power plant only needs to verify the feasibility and calculate the cost of the dispatched power allocated to the distribution network during the remaining dispatch period, and then feed the results back to the distribution network. This process is similar to the black box effect, thus offering better privacy. The mathematical model that needs to be changed is the load variation.

[0064] (55) In the formula: For the first Each VPP corresponds to a new load within a given time period. For the first Each VPP corresponds to the original load within a given time period.

[0065] (3) Model Solving In the upper-level optimization, the distribution network only needs to allocate dispatch power to each VPP without calculating its execution cost. Therefore, the HSIPSO algorithm is used to solve the upper-level problem, where each particle represents the power allocated to each VPP. In the lower-level optimization, each VPP needs to verify the feasibility of the upper-level power allocation and calculate the execution cost. Unlike the dynamic characteristics of VPP rolling optimization scheduling and feasible region analysis, the scheduling period and power are already determined by the upper level. The mathematical model of the optimization problem is completely static during the solution process and does not need to respond to real-time data changes. This characteristic allows commercial solvers to directly call pre-compiled optimization models, avoiding the time overhead of repeatedly reconstructing matrices in dynamic problems. Therefore, in the lower-level optimization, the feasibility verification of VPP dispatch power and the calculation of dispatch costs can be completed by the commercial solver CPLEX.

[0066] Example 3: Taking a VPP in a certain area as an example, the effectiveness of the virtual power plant distributed optimization algorithm and feasible region characterization method proposed in this invention is verified using a distribution network test system containing 3 VPPs, such as... Figure 14As shown, the following analysis is conducted. Taking VPP1 data as an example, 1) the impact of the time decoupling strategy of this invention on improving computational efficiency and solution accuracy is analyzed; 2) the performance of the ADMM algorithm based on the hybrid strategy to improve particle swarm optimization in this invention is analyzed using a test function; 3) the feasible region calculation results of this algorithm during a certain scheduling period are analyzed; 4) the proposed method is compared and analyzed with the feasible region characterized by the traditional probabilistic scenario generation method to verify the advantages of the proposed method in terms of efficiency and reliability in characterizing the feasible region; 5) the collaborative optimization operation effect of multiple VPPs under the coordination of the distribution network is analyzed, with the background of multiple virtual power plants jointly responding to the distribution network scheduling demand.

[0067] The specific parameters of each VPP in the simulation example are shown in Table 2.

[0068] Table 2 Operating parameters of each VPP

[0069] 1) Analysis of the effectiveness and feasibility of time decoupling (1) Validation of the effectiveness of time decoupling in a virtual power plant To verify the effectiveness of time decoupling, using the day-ahead dispatch plan data of a virtual power plant as an example, the optimization period was tested from time period 41 to 48 (i.e., 10:00 AM to 12:00 PM). The ADMM-HSIPSO algorithm was used for optimization without new dispatch instructions from the distribution network or without performing feasible region analysis of the virtual power plant, demonstrating the necessity of time decoupling and the computational efficiency after decoupling. The scenario is as follows.

[0070] Scenario 1: No time decoupling is performed.

[0071] Scenario 2: Perform time decoupling processing.

[0072] The number of objective functions and constraints before and after time decoupling is shown in Table 3.

[0073] Table 3 Comparison of optimization problems before and after time decoupling.

[0074] As shown in Table 3, before time decoupling, the optimization problem required simultaneous consideration of constraints and variables across eight time periods, resulting in high computational complexity. This was verified through multiple tests.

[0075] (2) Feasibility verification of time decoupling in virtual power plant To verify the feasibility of time decoupling in a virtual power plant and to evaluate the impact of different time decoupling strategies on optimality loss, this study uses the day-ahead scheduling plan of a virtual power plant as an example to calculate the daily operating cost and quantitatively analyze the optimality loss caused by time decoupling. The following scenario is set up. Scenario 3: Time decoupling is achieved by using independent optimization for each time period, meaning that the optimization decisions for each time period are independent of each other and the cumulative effect of states across time periods is not considered.

[0076] Scenario 4: Using Lyapunov optimization for time decoupling.

[0077] Scenario 5: Solving the global optimization problem directly without time decoupling. The iteration count was set to 600 times for each scenario, and the cost of operating a virtual power plant for one day was calculated and analyzed. All scenarios were calculated five times, and the average result was taken.

[0078] 2) Performance Analysis of ADMM-HSIPSO Algorithm To verify the effectiveness of the ADMM-HSIPSO algorithm, six classic test functions, including single-peak and multi-peak tests, were used for its evaluation. It was also compared with commonly used intelligent algorithms. The parameter settings for each algorithm are shown in Table 4. The maximum number of iterations for all algorithms was set to 300, the population size was set to 30, and each algorithm was run independently 30 times. The average value was used as the evaluation metric.

[0079] Table 4 Algorithm Parameter Settings

[0080] 3) Analysis of the feasible region of the virtual power plant Think , Taking the period from 0:15 to 1:15 as an example, the VPP can increase its power output by a maximum of 2.4MW and decrease it by a maximum of 1.2MW based on the original dispatch plan. This is because wind power resources are relatively abundant during this period, providing a large dispatch margin, allowing the VPP to increase its output within a certain range. However, in the scenario of reducing power, due to internal constraints such as energy storage capacity and equipment output limits, the adjustable margin is relatively small, thus preventing further power reduction. The proposed feasible region characterization method takes 89 seconds, effectively meeting the timeliness requirements for interaction between the VPP and the distribution network.

[0081] 4) Comparative Analysis of Feasible Domain Characterization Methods for Virtual Power Plants This is compared to the feasible region characterized by common probability density-based statistical methods. Again, using VPP1 data as an example, 1000 wind and solar power output scenarios are randomly generated using the Monte Carlo method to simulate the uncertainty of wind and solar power output. The probability density function of the percentage of positive / negative prediction errors for wind and solar power in the intraday ultra-short term is obtained using the Gaussian kernel density estimation method.

[0082] For each wind and solar power output scenario, the maximum additional output that the virtual power plant can withstand while meeting the original dispatch plan is calculated to determine the feasible region for that time period. To further characterize the impact of wind and solar power output uncertainty on the feasible region, the Feasibility Satisfaction Probability (FSP) for different wind and solar power output scenarios is calculated based on probability distribution. Specifically, let there be a total of For each of the following power generation scenarios, the maximum feasible power output that the virtual power plant can provide in that scenario is calculated. For a specific feasible output level Statistical satisfaction Number of scenes Then the probability that the feasible region satisfies the following definition is: (4-21) This probability reflects that, under conditions of uncertainty in wind and solar power output, the VPP can meet a specific feasible output. The possibilities are analyzed to provide probabilistic support for scheduling decisions. Taking the 2nd and 17th time periods (i.e., 0:15 to 4:15, lasting 4 hours) as examples, the feasible region of VPP is analyzed in the time period corresponding to the instruction start time period of 14 hours and lasting for 1 hour.

[0083] 5) Analysis of the results of collaborative optimization of multiple virtual power plants and distribution networks To verify the effectiveness of the intraday power allocation strategy with two-layer optimization, it is assumed that the VPPs are rolling over the second time period, and the distribution network has a dispatching requirement. The dispatching instruction is [2,3,4] or [2,3,-3], which means that during the period from 0:15 to 1:00, the sum of the output of each VPP needs to continuously increase by 4MW or decrease by 3MW.

[0084] In another embodiment of the present invention, a virtual power plant distributed optimization and feasible region analysis system is provided, which can be used to implement the above-mentioned virtual power plant distributed optimization and feasible region analysis method. Specifically, the system includes: The model building module is used to build an interactive physical model of the virtual power plant and the distribution network; The problem transformation module is used to relax and decouple the wide-area and neighborhood time coupling constraints caused by the state of charge of the energy storage system based on the interactive physical model and Lyapunov optimization theory, transforming the multi-period optimization problem of the virtual power plant into a single-period optimization sub-problem. The solution module is used to solve single-time-period optimization subproblems by adopting the particle swarm optimization algorithm HSIPSO based on a hybrid strategy and integrating it into the ADMM distributed optimization framework to form the ADMM-HSIPSO algorithm. The feasible region calculation module is used to transform the feasible region representation problem of virtual power plants in multiple time periods into the calculation problem of feasible regions in each scheduling period based on the analysis of distribution network scheduling characteristics. Within each scheduling period, the feasible region of the virtual power plant after completing the original scheduling plan is represented by the spinning reserve capacity. A mathematical model of the feasible region of the virtual power plant is constructed and solved using the ADMM-HSIPSO algorithm. This achieves the coordination and unification of optimal allocation of distribution network scheduling power among virtual power plants and privacy protection within virtual power plants.

[0085] The module division in this embodiment of the invention is illustrative and represents only one logical functional division. In actual implementation, other division methods may be used. Furthermore, the functional modules in the various embodiments of the invention can be integrated into a single processor, exist as separate physical entities, or be integrated into a single module. The integrated modules described above can be implemented in hardware or as software functional modules.

[0086] In another embodiment of the present invention, a computer device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions from the computer storage medium to achieve a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used in the operation of a virtual power plant distributed optimization and feasible domain analysis method.

[0087] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory), which is a memory device in a computer device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the computer device and extended storage media supported by the computer device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the virtual power plant distributed optimization and feasible domain analysis method in the above embodiments.

[0088] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0089] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0090] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0091] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A method for distributed optimization and feasible region analysis of a virtual power plant, characterized in that, include: Establish an interactive physical model between the virtual power plant and the distribution network; Based on the interactive physical model, the Lyapunov optimization theory is used to relax and decouple the wide-area and neighborhood time coupling constraints caused by the state of charge of the energy storage system, transforming the multi-period optimization problem of the virtual power plant into a single-period optimization subproblem. For single-time-period optimization subproblems, the particle swarm optimization algorithm HSIPSO based on a hybrid strategy is adopted and integrated into the ADMM distributed optimization framework to form the ADMM-HSIPSO algorithm for distributed solution of single-time-period optimization subproblems. Based on the analysis of distribution network dispatch characteristics, the problem of representing the feasible region of virtual power plants in multiple time periods is transformed into the problem of calculating the feasible region of each dispatch period. Within each scheduling period, the spinning reserve capacity is used to characterize the feasible region of the virtual power plant after completing the original scheduling plan. A mathematical model of the feasible region of the virtual power plant is constructed and solved using the ADMM-HSIPSO algorithm. To achieve optimal allocation of power dispatching in the distribution network among virtual power plants and coordinated protection of privacy within the virtual power plants.

2. The method for distributed optimization and feasible region analysis of a virtual power plant according to claim 1, characterized in that, The establishment of the interactive physical model between the virtual power plant and the distribution network includes: The physical model of the interaction between the virtual power plant and the distribution network is as follows: Objective function: （1） （2） In the formula: VPP day-ahead operating costs; Number of time periods within a day; , , , , , , They are respectively from the day before Operating costs for wind power, photovoltaic power, energy storage batteries, gas turbines, demand response, off-load penalty, and surplus power to the grid; , , , , , These are the wind power operating cost coefficient, photovoltaic operating cost coefficient, energy storage battery operating cost coefficient, demand response compensation cost coefficient, load shedding penalty coefficient (100 times the time-of-use price), and surplus electricity grid connection price. , This is the operating cost coefficient for gas turbines; , , , , , , They are respectively Wind power output, photovoltaic power output, energy storage battery output, gas turbine output, load reduction output, off-load power, and surplus power fed into the grid during specific time periods; The duration of a time period; Constraints: Virtual power plant power balance constraints （3） In the formula: These are new dispatch instructions to be issued by the distribution network within a certain period of time in the future. For the loads already determined by the distribution network dispatch instructions; Energy storage battery operating constraints （4） In the formula: , For energy storage batteries Discharge power and charging power during the time period; , This represents the charge / discharge state of the energy storage battery, and is a 0-1 variable. , This represents the maximum charging and discharging power of the energy storage battery. , For the charging and discharging efficiency of energy storage batteries; This refers to the rated capacity of the energy storage battery. For energy storage batteries State of charge at the end of the time period; , These represent the minimum and maximum permissible states of charge of the energy storage battery, respectively. , These represent the initial and final states of charge of the energy storage battery during a day; Gas turbine operating constraints （5） In the formula: It is a 0-1 variable, representing the start-up and shutdown status of the gas turbine; , These are the minimum and maximum power outputs of the gas turbine, respectively. , These represent the downward and upward ramp rates of the gas turbine, respectively. Reduced load operating constraints （6） In the formula: for During certain periods, the maximum output power of the load can be reduced; Electricity sales constraints （7） In the formula: These represent the upper limit of the power that a virtual power plant can sell to the grid.

3. The method for distributed optimization and feasible region analysis of a virtual power plant according to claim 1, characterized in that, The interactive physical model, using Lyapunov optimization theory, relaxes and decouples the wide-area and neighborhood time coupling constraints caused by the state of charge of the energy storage system, transforming the multi-period optimization problem of the virtual power plant into a single-period optimization sub-problem, including: The Lyapunov optimization method is used to transform the multi-time-period optimization problem into a subproblem within a single time period for solution; for neighborhood time-coupled constraints... Rewritten as arrive The cumulative form, divided by the period T on both sides, gives: （8） Wide-area time coupling constraints It is known that, throughout the entire scheduling cycle, the energy storage status of the first and last stages of the energy storage system should remain consistent: （9） Equation (9) is a preliminary relaxation of the time coupling constraint, establishing a virtual queue reflecting the accumulated state of charge of the energy storage: （10） By introducing the concept of a virtual queue, the relaxation condition in equation (9) is described as the net flow of the virtual queue being zero within a set time; both the wide-area coupling constraint and the neighborhood coupling constraint in the VPP internal optimization are transformed into virtual queues. To address the stability issues, Lyapunov functions were constructed: （11） when When the virtual queue is large, the congestion level is high and the stability is poor; conversely, when the virtual queue is small, the congestion level is low and the stability is good. Used to represent the difference in congestion level of the virtual queue at adjacent times: （12） The drift penalty function DPP is used to transform the multi-period centralized optimization problem into multiple single-period centralized optimization problems, that is, to transform the optimization problem into: （13） when This can be seen as a trade-off between the stability of the virtual queue and the operating cost of the VPP; Equation (13) has an upper bound, expressed as: （14） For the change in state of charge, it can be seen from equation (14) that the upper bound is... Since the value is constant, the above problem can be considered as minimizing... Therefore, equation (14) is transformed back into: （15）。 4. The method for distributed optimization and feasible region analysis of a virtual power plant according to claim 1, characterized in that, For the single-time-period optimization subproblem, the improved particle swarm optimization algorithm HSIPSO based on a hybrid strategy is adopted and integrated into the ADMM distributed optimization framework to form the ADMM-HSIPSO algorithm. This algorithm is used for the distributed solution of the single-time-period optimization subproblem, including: The optimization process is as follows: 1) Distributed solution model for virtual power plants based on ADMM (1) Introducing slack variables Transform inequality constraints into equality constraints: （16） In the formula: It is a set of operating constraints for each unit and all of them are processed into In form, The introduced slack variable represents the first... The difference between the inequality constraints; (2) Constructing the augmented Lagrange function By incorporating the constraints of the optimization problem into the objective function through their respective dual multipliers, the original problem is transformed into an unconstrained optimization problem. Adding a quadratic penalty term, the augmented Lagrangian function becomes: （17） In the formula: Equality constraints The dual multipliers; For the first Dual multipliers of inequality constraints; All express, This is the penalty coefficient; (3) Decomposition of the optimization problem based on ADMM The first subproblem is optimizing continuous variables. , and slack variables and dual variables and Treating it as a constant, the first subproblem is written as: （18） The second subproblem is slack variables. Update, at this point the original variable and dual variables and Treating auxiliary variables as constants, optimize them. The second subproblem is written as: （19） Original variable and dual variables and Treating it as a constant, the optimization objective is further transformed into: （20） For each Independent optimization, written as a single-variable optimization problem, and expanded and simplified by the quadratic terms, yields: （21） For the above formula Take the partial derivatives and set them to 0. ,final The update expression is: Solving for: （22） The dual variable is updated as follows: （23） （24） 2) Solving ADMM subproblems based on HSIPSO (1) Population initialization using Sobol sequences The Sobol sequence is generated using a base-2 inversion algorithm, with a different matrix for each dimension, ensuring that the generated points are non-repeating and uniform. The generation process of the nth point is represented as follows: （25） It is the value of the previous point in the k-th dimension; The nth point in the k-th dimension of the direction number matrix Bit; For XOR operation; (2) Adaptive inertia weight An adaptive weighting strategy is adopted to dynamically adjust the inertia weight during the iteration process, optimize the balance between global search and local optimization, and accelerate the convergence process. （26） In the formula, and These are the pre-defined minimum and maximum inertia coefficients; The average fitness of all particles at the next iteration and The minimum fitness of all particles at the next iteration is: （27） （28） (3) Asymmetric learning factor The expression for updating the asymmetric learning factor is as follows: （29） In the formula, This is the initial value of the individual learning factor; This represents the final value of the individual learning factor. This is the initial value for the social learning factor; This represents the final value of the social learning factor. This represents the total number of iterations. (4) Adaptive Cauchy mutation strategy Local optimal solution identification: The determination method is as follows: If the fitness value of an individual in the population does not change by more than 10% of its original value in 6 consecutive iterations, then that individual is considered to have fallen into a local optimum. Then, the same method is used to determine the fitness of the remaining individuals, and the proportion of individuals fallen into a local optimum is counted. If this proportion exceeds a preset threshold, the algorithm is determined to have fallen into a local optimum; otherwise, the algorithm is considered not to have fallen into a local optimum. The mathematical expression is as follows: （30） （31） （32） In the formula: and The first The particle in the first The fitness value of the next iteration and the flag value indicating whether it has fallen into a local optimum; For all particles in The proportion of iterations that get trapped in local optima; For the algorithm in The threshold for determining whether the next iteration has fallen into a local optimum; For the algorithm in A flag indicating whether the next iteration has fallen into a local optimum; After the discrimination algorithm gets stuck in a local optimum, Cauchy mutation is performed on the current optimal solution. The mathematical expression is: （33） In the formula: for The new value of the optimal solution in the next iteration after Cauchy perturbation; It is a standard Cauchy distribution; the algorithm obtains Afterwards, comparison and The fitness value, if Superior Then replace the current optimal solution with Otherwise, do not replace.

5. The method for distributed optimization and feasible region analysis of a virtual power plant according to claim 1, characterized in that, The analysis based on distribution network dispatch characteristics transforms the problem of representing the feasible region of a virtual power plant across multiple time periods into a problem of calculating the feasible region for each dispatch period, including: The dispatch instructions issued by the distribution network within the day are Includes the start time of the scheduling instructions. Duration and scheduling power ; and The constraints are as follows: （36） In the formula: The minimum value at the initial time; , , All values ​​are integers with the same unit; the time window of a rolling cycle is 4 hours, with each 15-minute interval comprising 16 intervals. Within one rolling cycle, The upper limit is 16, and the lower limit is 1; when hour, There are a total of 16 types of this time period. hour, There are 15 possible time periods. For each time period, the feasible domain of the virtual power plant within that time period is calculated. The range of values, and based on the dataset The information is reported to the distribution network in the form of [the following]; among which , , It is a set consisting of the start time, duration, and schedulable power.

6. The method for distributed optimization and feasible region analysis of a virtual power plant according to claim 1, characterized in that, Within each scheduling period, the feasible region of the virtual power plant after completing the original scheduling plan is characterized by rotating reserve capacity. A mathematical model of the feasible region of the virtual power plant is constructed and solved using the ADMM-HSIPSO algorithm, including: The rotation standby settings are as follows: （37） （38） Equations (37) and (38) represent the rotating reserve constraints set to address situations where wind and solar forecast data are too low or too high, respectively. , The corresponding prediction error coefficients are... To address forecast errors during intraday optimized scheduling of VPPs, a spinning reserve capacity is set, meaning the spinning reserve capacity must be greater than the capacity required to handle wind and solar forecast errors; utilizing Characterizing the fluctuation of wind and solar power output, through analysis The range of values ​​for different scheduling periods is determined, and the range is gradually expanded within that range. The values ​​are used to test the maximum wind and solar power fluctuations that the virtual power plant can withstand while fulfilling the original dispatch plan during each dispatch period, and to determine the corresponding spinning reserve capacity. This is first done for a single time period. We analyze the range of values ​​for ; we transform equations (37) and (38) into the following forms: （39） （40） In the formula: and They are respectively The degree of fluctuation in wind and solar power output corresponding to upward and downward rotation of reserve within a certain period; The upper limit value analysis within a single time period is as follows: Based on the original dispatch plan, the maximum value of the virtual power plant's spinning reserve capacity (i.e., adjustable power) should be less than the limit value of the dispatchable power under ideal conditions. This means ignoring the limitations of energy storage charging and discharging power and gas turbine ramping limitations, thus deriving the maximum possible dispatchable power value of the virtual power plant within a given time period, which is the limit of the virtual power plant's feasible region. The limit of feasible region within a time period can be represented as: （41） （42） In the formula: , , , , This is the pre-scheduling plan for each unit of the VPP when there are no new scheduling instructions; , For VPP in The upper and lower boundaries of the time-limited feasible region, i.e., the virtual power plant in... The power that can be increased or decreased under ideal conditions during a given time period; the following relationship exists: （43） （44） Within each time period and The scope is defined as follows: （45） （46） No. The limit feasible region corresponding to each scheduling time period type is represented as follows: （47） In the formula: , For the first The scheduling start time and scheduling duration corresponding to each of the following situations; , For the first The upper and lower bounds of the limit feasible region corresponding to the duration of each scheduling event; No. Type of scheduling period within a duration The range of values ​​for is: （48） （49） and The first The range of wind and solar power output fluctuations corresponding to upward and downward rotational reserve during the duration of each dispatch type; Virtual power plant feasible domain calculation Detailed calculation steps of the feasible region 1) Initialize the degree of wind and light fluctuation and Value The initial value is the prediction error compensation capacity. , Fixed as prediction error compensation capacity And remain unchanged; 2) Gradually increase over the duration. The values ​​were examined on a time-by-time basis. First, gradually increase by a certain step size. The value; for each increase The feasibility of the calculated value needs to be verified for each sub-period throughout the entire duration. The specific verification method is as follows: The current and Substitute equations (39) and (40) into the equations and solve them simultaneously with the original scheduling plan mathematical model. First, solve for the first sub-period within the duration period: if there is no solution for the first sub-period, it means that the virtual power plant cannot withstand the current wind and solar fluctuations on the basis of completing the original scheduling plan. Stop the iteration and record the previous time when all sub-periods had solutions. The numerical value is used as the limit; if the first sub-time period has a solution, then all subsequent sub-time periods within the duration are solved sequentially. If all sub-time periods within the duration have solutions, it means that the current... The value is feasible throughout the entire duration and can be further increased. The numerical values ​​are then repeated over the entire duration; if no solution is found in any sub-time period within the duration, the iteration stops, and the previous iteration where all sub-time periods had solutions is recorded. Numerical values ​​are used as limit values; 3) Final calculation formula for the feasible region of the virtual power plant No. The upper and lower limits of the virtual power plant's feasible domain within the duration corresponding to each scheduling type can be expressed as: （50） （51） In the formula: , For the first The upper and lower limits of the feasible region for each dispatch scenario; the dispatch power that the distribution network can issue during this duration. The scope is: （52）。 7. A method for distributed optimization and feasible region analysis of a virtual power plant according to claim 6, characterized in that, The coordination and unification of achieving optimal allocation of power dispatching in the distribution network among virtual power plants and privacy protection within virtual power plants includes: Mathematical Model for Collaborative Optimization of Multiple Virtual Power Plants and Distribution Networks (1) Upper-level optimization model To achieve economical operation of the distribution network, the objective function is to optimize the cost of distribution network dispatching instructions, as follows: （53） In the formula: The operating cost of issuing new dispatch instructions to the distribution network during a specific period of the day; For the first The cost of the power allocated to each VPP; For the first The feasibility of the power allocated to each VPP in the remaining scheduling plan: if it is 1, it means that executing the current power can also guarantee the completion of the original scheduling plan in the subsequent time period; if it is 0, it means that after the virtual power plant executes the scheduling power in the time period, the subsequent scheduling plan cannot be completed. The penalty term is generated when the distribution network allocates dispatch power according to the feasible domain reported by each VPP, but the VPP cannot meet the requirements; This is the power difference; , These refer to the start and duration periods of dispatching the daily demand of the distribution network. The penalty coefficient is set at 100 times the time-of-use electricity price. It is the difference between the power demand of the distribution network and the sum of the outputs of each VPP; （54） In the formula: For distribution network Power required for scheduling during a given time period; , For the first The range of upper and lower feasible regions corresponding to each VPP time period; (2) Lower-level optimization model （55） In the formula: For the first New load on each VPP during the corresponding time period For the first The original load within the time period corresponding to each VPP; (3) Model Solving The HSIPSO algorithm is used to solve the upper-level problem, in which each particle represents the power allocated to each VPP. In the lower-level optimization, the feasibility verification of VPP scheduling power and the calculation of scheduling costs can be completed using the commercial solver CPLEX.

8. A distributed optimization and feasible region analysis system for a virtual power plant, characterized in that, include: The model building module is used to build an interactive physical model of the virtual power plant and the distribution network; The problem transformation module is used to relax and decouple the wide-area and neighborhood time coupling constraints caused by the state of charge of the energy storage system based on the interactive physical model and Lyapunov optimization theory, transforming the multi-period optimization problem of the virtual power plant into a single-period optimization sub-problem. The solution module is used to solve single-time-period optimization subproblems by adopting the particle swarm optimization algorithm HSIPSO based on a hybrid strategy and integrating it into the ADMM distributed optimization framework to form the ADMM-HSIPSO algorithm. The feasible region calculation module is used to transform the problem of representing the feasible region of a virtual power plant in multiple time periods into the problem of calculating the feasible region of each time period based on the analysis of the dispatch characteristics of the distribution network. Within each scheduling period, the spinning reserve capacity is used to characterize the feasible region of the virtual power plant after completing the original scheduling plan. A mathematical model of the feasible region of the virtual power plant is constructed and solved using the ADMM-HSIPSO algorithm. To achieve optimal allocation of power dispatching in the distribution network among virtual power plants and coordinated protection of privacy within the virtual power plants.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the virtual power plant distributed optimization and feasible domain analysis method as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the distributed optimization and feasible domain analysis method for a virtual power plant as described in any one of claims 1 to 7.

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