A distribution network piecewise linearization combined chance-constrained optimization scheduling method based on sample data, computer-readable storage medium and program product

Abstract

A sample data-based piecewise linearized joint chance-constrained optimization scheduling method for distribution networks, a computer-readable storage medium, and a program product are described. The method includes: establishing a joint chance-constrained scheduling model that considers node voltage uncertainty and power injection imbalance risk, using a preset voltage over-limit probability as a boundary condition to ensure controllable system operation risks; utilizing sample data and a Gaussian mixture model to accurately fit the distribution characteristics of uncertain variables and convert chance constraints into linear constraints; and employing a posterior iterative algorithm to dynamically adjust the joint default probability threshold to balance the model's conservatism and economy. This method can address the uncertainty issues associated with renewable energy integration into distribution networks, generate a power allocation plan that prioritizes both safety and economy, effectively reduce the risks of node voltage over-limit and line congestion, and achieve safe and economical operation of distribution networks.

Description

Technical Field

[0001] The present invention relates to a renewable energy power generation distribution network dispatching technology, and in particular to a distribution network piecewise linearization combined chance-constrained optimization dispatching method based on sample data. Background Art

[0002] Currently, an increasing number of renewable energy sources, such as distributed photovoltaic and wind power, are being connected to distribution networks. If deterministic optimization scheduling methods are used, the uncertainty inherent in renewable energy sources can lead to safety issues such as voltage overshoot and line congestion. To ensure safe and economical operation of distribution networks amidst the increasing penetration of renewable energy, it is necessary to fully account for the impact of uncertainty in the optimization scheduling process.

[0003] Common optimization methods that consider uncertainty include scenario-based stochastic optimization, robust optimization, and chance-constrained programming. Stochastic optimization generates a large number of scenarios or selects typical scenarios to represent uncertainty, then allocates weight to the objective function according to the probabilities of different scenarios. However, this approach suffers from low computational efficiency and an assumed uncertainty distribution that is inconsistent with reality. Robust optimization does not require assumptions about the sample distribution. Instead, it constructs an uncertainty set using sample data and requires that constraints be satisfied within this uncertainty set. While this approach ensures robustness and does not require an uncertainty distribution function, it is overly conservative and lacks economic efficiency.

[0004] Chance constraints are an intuitive modeling approach for accounting for uncertainty risk. They allow for small constraint violations, allowing system operators to effectively balance robustness and optimality based on their preferences. However, because chance constraints are implicit expressions, they require transformation before they can be solved. The main approaches for handling chance constraints include scenario-based methods, sampling average approximation methods, and analytical formula-based methods. Scenario-based methods require a large number of data samples to satisfy the constraint conditions, resulting in low computational efficiency and a decreasing cost-effectiveness of the optimized scheduling results as the number of samples increases. The sampling average approximation method introduces binary variables to approximate the probability of constraint violations for each sample. This approach is less conservative than scenario-based methods, but still requires a large number of samples and the introduction of binary variables, transforming the model into a mixed integer programming problem. This leads to low computational efficiency when the model has many conditions. Analytical formula-based methods assume that the distribution function of the known uncertainty variables is a standard Gaussian distribution or other common distribution. Chance constraints are solved by solving the cumulative probability distribution function to obtain the corresponding quantile of the allowable risk value. However, in reality, the distribution function of the uncertainty variables does not exactly conform to a specific distribution function, making this approach less practical.

[0005] As more and more renewable energy resources, such as distributed photovoltaic and distributed wind power, are connected to distribution networks, traditional deterministic optimization scheduling methods are unable to handle the uncertainty of renewable energy, leading to safety issues such as voltage overshoot and line congestion in distribution network operations. Against the backdrop of increasing renewable energy penetration, it is necessary to fully consider the impact of uncertainty in distribution network optimization and scheduling. Currently, there is a lack of efficient methods for solving distribution network uncertainty optimization scheduling problems without assuming that the uncertainty satisfies a specific distribution function. Furthermore, stochastic optimization assumes a known uncertainty distribution function and generates a large number of scenarios or selects representative scenarios to represent the uncertainty, assigning weights to the objective function according to the probability of each scenario. This approach suffers from low computational efficiency and unrealistic assumptions about the uncertainty distribution. Furthermore, robust optimization does not require a sample distribution, but instead constructs an uncertainty set using sample data and requires that constraints be satisfied within this uncertainty set. While this approach ensures robustness and does not require an uncertainty distribution function, it is overly conservative and lacks economic efficiency. Furthermore, chance-constrained programming is a method that effectively balances robustness and optimality, but it lacks efficient solutions that do not assume that the uncertainty variables conform to a specific distribution function.

[0006] It should be noted that the information disclosed in the above background technology section is only used to understand the background of this application, and therefore may include information that does not constitute prior art known to ordinary technicians in this field. Summary of the Invention

[0007] The main purpose of the present invention is to overcome the defects existing in the above-mentioned background technology and provide a distribution network piecewise linearization joint chance constrained optimization scheduling method based on sample data.

[0008] To achieve the above object, the present invention adopts the following technical solutions:

[0009] A distribution network piecewise linearization combined with chance-constrained optimization scheduling method based on sample data includes the following steps:

[0010] S1. Establish a joint opportunity constraint dispatch model for the distribution network: Based on the uncertainty of distribution network node voltage and the risk of power injection imbalance, a joint opportunity constraint model is constructed, with the preset node voltage exceeding limit probability as the boundary condition to ensure that the system operation risk is controllable;

[0011] S2. Piecewise linearization of joint chance constraints: Using sample data to fit the distribution characteristics of uncertain variables, the Gaussian mixture model is used to accurately fit the joint probability distribution of uncertain variables. The piecewise linearization technique is then used to transform the nonlinear joint chance constraints into linear constraints that can be solved analytically.

[0012] S3. Joint default probability adjustment based on posterior iteration: Based on historical data and the initial dispatch solution, the joint default probability threshold is dynamically modified through the posterior iteration algorithm to balance the model's conservatism and economy. Combined with the linearization constraints and the adjusted default probability, the distribution network optimization dispatch model is solved to generate a power distribution plan that takes into account both safety and economy, reducing the risks of node voltage exceeding the limit and line congestion.

[0013] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the distribution network piecewise linearization combined with chance-constrained optimization scheduling method based on sample data.

[0014] A computer program product includes a computer program, which, when executed by a processor, implements the distribution network piecewise linearization combined with chance-constrained optimization scheduling method based on sample data.

[0015] The present invention has the following beneficial effects:

[0016] Against the backdrop of increasing penetration of renewable energy, the present invention provides an optimization scheduling method that can efficiently handle uncertainties in distribution networks. This method can accurately fit the distribution characteristics of uncertain variables through a Gaussian mixture model based on sample fitting, without assuming that these variables satisfy a specific distribution function. In addition, the method uses piecewise linearization technology to convert nonlinear chance constraints that were originally difficult to solve into linear constraints that are easy to handle, thereby improving computational efficiency. Through a joint default probability adjustment method based on posterior iteration, the present invention solves the conservatism problem existing in existing methods, so that the model has better economy while ensuring system safety. The method of the present invention not only improves the safe and economical operation of the distribution network, but also reduces the risk of node voltage over-limit and line congestion, realizes the efficient solution of the joint chance constraint optimization scheduling model, and meets the requirements of the distribution network for safety and reliability under uncertainty conditions.

[0017] Other beneficial effects of the embodiments of the present invention will be further described below. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Flowchart of the distribution network piecewise linearization combined with chance-constrained optimization scheduling method based on sample data implemented by the present invention. DETAILED DESCRIPTION

[0019] The following is a detailed description of the embodiments of the present invention. It should be emphasized that the following description is only exemplary and is not intended to limit the scope of the present invention and its application.

[0020] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of such features. In the description of the embodiments of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0021] See Figure 1 The embodiment of the present invention provides a distribution network piecewise linearization joint chance-constrained optimization scheduling method based on sample data, comprising the following steps:

[0022] Step S1, establishing a joint opportunity constraint dispatch model for the distribution network: Based on the uncertainty of distribution network node voltage and the risk of power injection imbalance, a joint opportunity constraint model is constructed, with the preset node voltage over-limit probability as the boundary condition to ensure that the system operation risk is controllable.

[0023] In a preferred embodiment, step S1 specifically includes: constructing an optimization model with the goal of minimizing the operating cost of the distribution network, which includes the cost of purchasing electricity from the wholesale market and the cost of distributed generators (DGs); modeling the generation cost of DGs as a quadratic function to reflect the increase in marginal generation cost when the generation power increases; determining the optimization variables, namely, the amount of energy purchased from the wholesale market, the most economical generation power of the aggregator (AGG) and DGs under the premise of system safety; introducing the node voltage amplitude and phase angle, as well as the nodes adjacent to the node, to represent the power flow constraints of the distribution network line; by defining a matrix, the linear relationship between the node power injection amount and the node voltage amplitude and phase angle is expressed in matrix form; considering the uncertainty of renewable energy output and load, the node absorbs unbalanced power by relaxing the node, and expresses the voltage uncertainty in linear form; using joint opportunity constraints to constrain the node voltage to ensure that the overall system risk meets the preset voltage limit probability.

[0024] In a preferred embodiment, in step S1, the optimization of the dispatch model specifically includes: determining the wholesale market electricity price and the amount of electricity purchased from the wholesale market; determining the active power and reactive power output constraints of distributed generators; determining the charging and discharging power and dispatching fees of the aggregator (AGG); determining the active and reactive loads of the distribution network nodes; determining the day-ahead predicted output of distributed photovoltaic and wind turbines; and expressing the linear relationship between the power injection amount of all nodes except the reference node in the linearized distribution network flow model and the node voltage amplitude and phase angle in matrix form by defining a matrix.

[0025] Step S2, piecewise linearization of joint chance constraints: using sample data to fit the distribution characteristics of uncertain variables, accurately fitting the joint probability distribution of uncertain variables through the Gaussian mixture model, and using piecewise linearization technology to transform the nonlinear joint chance constraints into a linear constraint form that can be solved analytically.

[0026] In a preferred embodiment, in step S2, the process of fitting uncertainty variables using a Gaussian mixture model specifically includes: defining a normalized representation of the constraint conditions to uniformly represent the constraints of node power uncertainty; decomposing the constraint conditions into a single chance constraint with risk probability as a variable; calculating the overall joint violation probability of all possible constraint violation event combinations; using a Gaussian mixture model to fit the joint probability distribution function of historical data of node power uncertainty; determining the weight, mean and variance of each sub-distribution in the Gaussian mixture model; obtaining the Gaussian mixture model parameters under the normalized constraint conditions through affine transformation; and converting the chance constraint into the form of a cumulative density function to facilitate linearization processing.

[0027] In a preferred embodiment, in step S2, the process of linearizing the chance constraint using the piecewise linearization technique specifically includes: piecewise linearizing the cumulative density function of the standard Gaussian function; determining the segment parameters of each segment and the total number of segments; converting the cumulative density function into a form suitable for a specific problem through a translation transformation; introducing auxiliary variables to convert the linear sum form of the cumulative density function of the Gaussian mixture model into a linear form; and converting the nonlinear chance constraint into a linear constraint form that can be solved analytically through the piecewise linearization technique to facilitate processing in the optimization model.

[0028] Step S3, joint default probability adjustment based on posterior iteration: Based on historical data and the initial scheduling solution, the joint default probability threshold is dynamically modified through the posterior iteration algorithm to balance the conservatism and economy of the model. In combination with the linearization constraints and the adjusted default probability, the distribution network optimization scheduling model is solved to generate a power distribution plan that takes into account both safety and economy, thereby reducing the risks of node voltage exceeding the limit and line congestion.

[0029] In a preferred embodiment, step S3 specifically includes: initializing the iterative process, setting the number of iterations, the default probability allowed by the system, the historical data set, the initial value of the joint default probability and the convergence parameter; substituting the initial value of the joint default probability into the optimization scheduling model to solve the current scheduling decision; using the historical data set to evaluate the default probability corresponding to the current scheduling decision to determine whether there is a default; estimating the joint violation probability and calculating the overall joint violation probability of all possible constraint violation event combinations; dynamically adjusting the joint default probability threshold based on the evaluation results to balance the conservatism and economy of the model; checking the iteration termination condition, if the maximum value of the default probability is less than the allowed default probability or the maximum value of the joint default probability is less than the convergence parameter, then terminate the iteration; otherwise, update the joint default probability and continue the iterative solution.

[0030] The proposed method for piecewise linearized joint chance-constrained optimal scheduling of distribution networks based on sample data accurately fits the distribution characteristics of uncertain variables by utilizing a Gaussian mixture model technique based on sample fitting. It also transforms chance constraints into linear constraints that are easier to solve using piecewise linearization techniques. Furthermore, a posterior-based joint probability density adjustment algorithm significantly improves the conservatism inherent in the model. This method achieves efficient solution of the joint chance-constrained optimal scheduling model, ensuring safe and economical operation of the distribution network.

[0031] The following further describes specific embodiments of the present invention and algorithm examples.

[0032] A piecewise linearization joint opportunity constrained optimization scheduling method for distribution network based on sample data. Figure 1 Among them, the accurate fitting of the distribution characteristics of uncertain variables is achieved through a Gaussian mixture model based on sample fitting; the opportunity constraints based on the Gaussian mixture model are converted into solvable linear constraints using the piecewise linearization method; and the conservative problem of the existing methods based on Boolean inequalities is solved through the joint default probability adjustment method based on posterior iteration.

[0033] The specific steps include:

[0034] (1) Establishing a distribution network opportunity-constrained optimization scheduling model

[0035] The optimization objective of the distribution network's optimal dispatch model is to minimize the network's operating costs while satisfying the network's safe operation constraints. The operating costs of a distribution network include the cost of purchasing electricity from the wholesale market and the generation costs of distributed generators (DGs). The DG cost function is a quadratic function; as the generated power increases, its marginal generation cost also increases. The optimization variables for the distribution network are to determine the most economical power generation from the wholesale market and the aggregator (AGG) and DGs, while ensuring system safety:

[0036] (1)

[0037] Where, represents the electricity price in the wholesale market; Represents the amount of electricity purchased from the wholesale market; represents the active power of distributed generators; and Indicates the charge and discharge power of AGG; Indicates the cost of scheduling AGG; 、 and represents the power generation cost coefficient of distributed generators; A collection of nodes representing a distribution network.

[0038] The active and reactive output constraints of DG are expressed as follows:

[0039] (2)

[0040] (3)

[0041] Where, and Indicates the upper and lower limits of active power output; and Indicates the upper and lower limits of reactive power output.

[0042] The constraints on the AGG active power are expressed as follows:

[0043] (4)

[0044] Where, and Represents the feasible region parameter of AGG.

[0045] The power flow constraints of the distribution lines are as follows:

[0046]

[0047]

[0048] Where, , ; represents the node voltage amplitude; represents the phase angle of the node voltage; Representatives and Nodes adjacent nodes; and Represent the active and reactive loads of the node respectively; Equations (7) and (8) represent the active power balance constraints of the node connected to AGG; and They represent the distributed photovoltaic and wind turbine outputs predicted on the previous day respectively.

[0049] By defining the matrix and , the linear relationship between the power injection amount of all nodes except the reference node in the above linearized distribution network power flow model and the node voltage amplitude and phase angle can be expressed in matrix form:

[0050]

[0051] Where, 、 、 and denote the injected active power, injected reactive power, node phase angle and node voltage amplitude except the relaxed nodes respectively; and yes and The matrix after removing the first row and the first column; and yes and The vector consisting of the first element in the first column of excluding ; and represents the phase angle and voltage magnitude of the relaxed node.

[0052] Considering the uncertainty of renewable energy output and load predicted in the day ahead, it will lead to imbalance of node power injection. These unbalanced powers will be absorbed and balanced by slack nodes (nodes connected to the main grid). is reversible. According to equations (13) and (15), by By performing the inversion, the voltage uncertainty associated with the unbalanced power can be expressed in the following linear form:

[0053]

[0054] Where, represents the vector of unbalanced power components of nodes except the relaxed nodes; Represents the uncertainty of the node voltage; Represents the linear mapping matrix from unbalanced power to node voltage change; Represents the inverse matrix.

[0055] Considering the uncertainty of node voltage caused by the uncertainty of node injection power, in order to ensure that the overall system risk meets the requirements, the node voltage is constrained by using joint chance constraints:

[0056]

[0057] Where, and Respectively represent the upper and lower limits of the node voltage; It represents the joint risk probability of system node voltage exceeding the limit.

[0058] (2) Joint Chance Constrained Linearization

[0059] First, by defining and To unify and normalize the constraints in the formula:

[0060]

[0061] According to the inclusion-exclusion principle, (19) can be equivalently decomposed into a single opportunity constraint with risk probability as the variable:

[0062]

[0063] Where, Representation Constraints the risk probability; represents the overall joint violation probability after summing over all possible constraint violation event combinations.

[0064] The joint probability distribution function of the historical data of node power uncertainty can be fitted by a Gaussian mixture model:

[0065]

[0066] Where, It is the Gaussian mixture model m The weight of the sub-distribution; is the probability density function of the Gaussian distribution; represents the mean; Represents variance.

[0067] The parameters of the Gaussian mixture model can be obtained by using formula (16) Performing an affine transformation yields:

[0068]

[0069] Formula (20) can be equivalently transformed into the form of cumulative density function:

[0070]

[0071] According to the Gaussian mixture model, formula (21) can be expressed as the linear sum of the cumulative density functions of multiple Gaussian functions:

[0072]

[0073] Where, is the cumulative density function of the Gaussian function.

[0074] The cumulative density function of the standard Gaussian function can be linearized and approximated by piecewise linearization technology:

[0075]

[0076] Where, and Represents the segment parameters of the nth segment; Indicates the total number of segments.

[0077] Can be achieved through Performing translation transformation yields:

[0078]

[0079] By introducing auxiliary variables , formula (24) can be transformed into the following linear form:

[0080]

[0081] (3) Joint default probability adjustment based on posterior iteration

[0082] The following joint default probability adjustment algorithm based on posterior iteration is used to determine the value of formula (21): Value:

[0083] 1) Iteration initialization: Initialize the number of iterations c Equal to 0; set the default probability allowed by the system ;Historical dataset ; Joint default probability Initial value of ; Convergence parameter .

[0084] 2) Model solution: Set as To solve the current optimization scheduling model to get the current scheduling decision .

[0085] 3) Scheduling decision evaluation: Use historical data sets to evaluate the default probability corresponding to the current decision Conduct an assessment:

[0086]

[0087] Where, is If the vector If there is any value greater than 0, then ,on the contrary .

[0088] 4) Estimation of Joint Violation Probability: The joint violation probability is estimated by the following formula:

[0089]

[0090] 5) Update the joint violation probability: If Greater than mean Overrated, so Set as To further constrain the risk, otherwise Update.

[0091] 6) Iteration termination condition test: If The maximum value is less than or The maximum value is less than , terminate the iteration; otherwise, return to step 2 to continue the iteration.

[0092] An embodiment of the present invention further provides a storage medium for storing a computer program, which at least performs the above method when executed.

[0093] An embodiment of the present invention further provides a control device, comprising a processor and a storage medium for storing a computer program; wherein the processor is configured to execute at least the method described above when executing the computer program.

[0094] An embodiment of the present invention further provides a processor, which executes a computer program and at least performs the method described above.

[0095] The storage medium can be implemented by any type of non-volatile storage device, or a combination thereof. Among them, the non-volatile memory can be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), a magnetic random access memory (FRAM), a flash memory, a magnetic surface memory, an optical disc, or a compact disc read-only memory (CD-ROM); the magnetic surface memory can be a magnetic disk memory or a magnetic tape memory. The storage medium described in the embodiments of the present invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0096] In the several embodiments provided by the present invention, it should be understood that the disclosed systems and methods can be implemented in other ways. The device embodiments described above are merely schematic. For example, the division of the units is merely a logical function division. In actual implementation, there may be other division methods, such as: multiple units or components can be combined, or can be integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the components shown or discussed can be through some interfaces, and the indirect coupling or communication connection of the devices or units can be electrical, mechanical or other forms.

[0097] The units described above as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units; some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0098] In addition, all functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may be separately used as a unit, or two or more units may be integrated into one unit; the above-mentioned integrated units may be implemented in the form of hardware or in the form of hardware plus software functional units.

[0099] Those skilled in the art will appreciate that all or part of the steps of the above-mentioned method embodiments may be implemented by hardware associated with program instructions, and the aforementioned program may be stored in a computer-readable storage medium. When the program is executed, the program executes the steps of the above-mentioned method embodiments. The aforementioned storage medium includes various media that can store program codes, such as mobile storage devices, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical disks.

[0100] Alternatively, if the above-mentioned integrated unit of the present invention is implemented in the form of a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiment of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the methods described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as mobile storage devices, ROM, RAM, magnetic disks or optical disks.

[0101] The methods disclosed in the several method embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method embodiments.

[0102] The features disclosed in several product embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new product embodiments.

[0103] The features disclosed in several method or device embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method embodiments or device embodiments.

[0104] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. Those skilled in the art will recognize that, without departing from the scope of the present invention, several equivalent substitutions or obvious variations can be made, and the performance or use of the same should be considered to fall within the scope of protection of the present invention.

Claims

1. A distribution network piecewise linearization joint opportunity constrained optimization scheduling method based on sample data, characterized in that: The following steps are involved: S1. Establish a joint opportunity-constrained dispatch model for the distribution network: Based on the uncertainty of distribution network node voltage and the risk of power injection imbalance, a joint opportunity-constrained model for the distribution network is constructed, with the preset node voltage exceeding limit probability as the boundary condition to ensure that the system operation risk is controllable; S2. Piecewise linearization of joint chance constraints: Using sample data to fit the distribution characteristics of uncertain variables, the Gaussian mixture model is used to accurately fit the joint probability distribution of uncertain variables. The piecewise linearization technique is then used to transform the nonlinear joint chance constraints into linear constraints that can be solved analytically. S3. Joint default probability adjustment based on posterior iteration: Based on historical data and the initial dispatch solution, the joint default probability threshold is dynamically revised through a posterior iteration algorithm to balance model conservatism and economy. Combined with the linearized constraints and the revised joint default probability threshold, the distribution network joint opportunity-constrained dispatch model is solved to generate a power allocation plan that balances safety and economy, reducing the risks of node voltage exceeding the limit and line congestion. Step S3 specifically includes: Initialize the iterative process, set the number of iterations, the default probability of a single constraint allowed by the system, the historical data set, the initial value of the joint default probability, and the convergence parameters; By substituting the initial value of the joint default probability into the distribution network joint opportunity constrained dispatch model, the current dispatch decision is obtained; Use historical data sets to evaluate the default probability corresponding to the current scheduling decision to determine whether there is a default; Estimate the joint default probability, and calculate the overall joint default probability for all possible constraint violation event combinations; Dynamically adjust the joint default probability threshold based on the assessment results to balance the model's conservatism and economy; Check the iteration termination condition. If the maximum default probability of a single constraint is less than the allowed default probability or the maximum joint default probability is less than the convergence parameter, terminate the iteration; otherwise, update the joint default probability and continue the iterative solution.

2. The distribution network piecewise linearization combined opportunity constrained optimization scheduling method based on sample data according to claim 1 is characterized in that: Step S1 specifically includes: Build an optimization model to minimize the distribution network operating cost, which includes the cost of electricity purchased from the wholesale market and the cost of distributed generator (DG) power generation; The generation cost of DG is modeled as a quadratic function to reflect the increase in marginal generation cost when the generation power increases; Determine the optimization variables, namely, the amount of electricity purchased from the wholesale market, the most economical power generation from aggregators (AGGs), and DGs, while ensuring system security; The node voltage amplitude and phase angle, as well as the nodes adjacent to the node, are introduced to represent the power flow constraints of the distribution network. By defining a matrix, the linear relationship between the node power injection amount and the node voltage amplitude and phase angle is expressed in matrix form; Considering the uncertainty of renewable energy output and load, the unbalanced power is absorbed by relaxing the nodes and the voltage uncertainty is expressed in a linear form; Joint chance constraints are used to constrain node voltages to ensure that the overall system risk meets the preset voltage limit probability.

3. The distribution network piecewise linearization combined with chance-constrained optimization scheduling method based on sample data according to claim 2 is characterized in that: In step S1, the optimization of the scheduling model specifically includes: Determine wholesale market electricity prices and the amount of electricity purchased from the wholesale market; Determine the active power and reactive power output constraints of distributed generators; Determine the charging and discharging power and dispatching fees of the aggregator (AGG); Determine the active and reactive loads at distribution network nodes; Determine the day-ahead forecast of distributed photovoltaic and wind turbine output; By defining a matrix, the linear relationship between the power injection amount of all nodes except the reference node in the linearized distribution network power flow model and the node voltage amplitude and phase angle is expressed in matrix form.

4. The distribution network piecewise linearization combined with chance-constrained optimization scheduling method based on sample data according to claim 1 is characterized in that: In step S2, the process of fitting the uncertainty variables using the Gaussian mixture model specifically includes: Define a normalized representation of constraints to uniformly represent the constraints of node power uncertainty; Decompose the constraints into a single chance constraint with risk probability as variable; Calculate the overall joint default probability for all possible constraint violation event combinations; Use Gaussian mixture model to fit the joint probability distribution function of historical data of node power uncertainty; Determine the weight, mean, and variance of each subdistribution in the Gaussian mixture model; Obtain the Gaussian mixture model parameters under normalized constraints through affine transformation; The chance constraint is converted into the form of cumulative density function to facilitate linearization.

5. The distribution network piecewise linearization combined with chance-constrained optimization scheduling method based on sample data according to claim 1 is characterized in that: In step S2, the process of linearizing the chance constraint using the piecewise linearization technique specifically includes: The cumulative density function of the standard Gaussian function is piecewise linearized and approximated; Determine the segment parameters of each segment and the total number of segments; The cumulative density function is converted into a form suitable for a specific problem through translation transformation; Auxiliary variables are introduced to transform the linear sum form of the cumulative density function of the Gaussian mixture model into a linear form; Through piecewise linearization technology, nonlinear chance constraints are transformed into linear constraints that can be solved analytically, so as to facilitate processing in the optimization model.

6. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the distribution network piecewise linearization joint chance-constrained optimization scheduling method based on sample data according to any one of claims 1 to 5 is implemented.

7. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the distribution network piecewise linearization joint chance-constrained optimization scheduling method based on sample data according to any one of claims 1 to 5 is implemented.

Images