Distribution robust scheduling method, device and equipment based on Gaussian mixture distribution

Abstract

The invention relates to the technical field of power dispatching, in particular to a distribution robust dispatching method, device and equipment based on Gaussian mixture distribution. The method comprises the following steps: constructing an initial Gaussian mixture distribution model; according to a pre-obtained output prediction error set, parameter estimation is carried out on the initial Gaussian mixture distribution model, a target Gaussian mixture distribution model is obtained, and the output prediction error set comprises output prediction errors of the renewable energy in each unit time period within a preset historical duration; constructing a distribution uncertainty set according to the target Gaussian mixture distribution model; constructing a distribution robust optimization framework based on the distribution uncertainty set, and constructing a first economic dispatching problem with the lowest operation cost as a target under the distribution robust optimization framework; solving the first economic dispatching problem to obtain a dispatching scheme; on the basis, accurate representation of output prediction error distribution of renewable energy sources is realized, and the economical efficiency of a unit combination in the operation process is ensured.

Description

Technical Field

[0001] The present disclosure relates to the technical field of power dispatching, and particularly to a distributionally robust dispatching method, device, and equipment based on Gaussian mixture distribution. Background Art

[0002] In a power system based on renewable energy, the unpredictability of renewable energy leads to the uncertainty of the power dispatching model, posing great challenges to the dispatching and planning of the power system.

[0003] Stochastic programming is a classical method for dealing with uncertainty in power dispatching models, but the inevitable errors in its probability distribution approximation and scenario sampling processes may lead to the unreliability of the unit commitment problem. Based on this, robust optimization is introduced to support the unit commitment model with network constraints, but only focusing on the worst-case scenario can ensure the reliability of the unit commitment but cannot balance the economy. The decision-making robustness of distributionally robust optimization is higher than that of stochastic programming, and its economy is better than that of robust optimization. It is achieved by considering all scenarios or probability distributions defined in the uncertainty set or ambiguity set.

[0004] However, the historical data relied on by distributionally robust optimization is difficult to characterize the accurate empirical distribution, which is likely to cause decision-making bias. Summary of the Invention

[0005] To solve the above technical problems, the present disclosure provides a distributionally robust dispatching method, device, and equipment based on Gaussian mixture distribution.

[0006] In the first aspect, the present disclosure provides a distributionally robust dispatching method based on Gaussian mixture distribution, including:

[0007] Construct an initial Gaussian mixture distribution model; perform parameter estimation on the initial Gaussian mixture distribution model according to the pre-obtained set of output prediction errors to obtain a target Gaussian mixture distribution model, where the set of output prediction errors includes the output prediction errors of each unit time period of renewable energy within a preset historical duration; construct a distribution uncertainty set according to the target Gaussian mixture distribution model; construct a distributionally robust optimization framework based on the distribution uncertainty set, and construct a first economic dispatching problem with the lowest operating cost as the objective under the distributionally robust optimization framework; solve the first economic dispatching problem to obtain a dispatching plan.

[0008] In the second aspect, the present disclosure provides a distributionally robust dispatching device based on Gaussian mixture distribution, including:

[0009] A first construction module for constructing an initial Gaussian mixture distribution model; an estimation module for parameter estimation of the initial Gaussian mixture distribution model according to a pre-obtained set of output prediction errors to obtain a target Gaussian mixture distribution model, where the set of output prediction errors includes the output prediction errors of each unit time period of renewable energy within a preset historical duration; a second construction module for constructing a distribution uncertainty set according to the target Gaussian mixture distribution model; a third construction module for constructing a distributionally robust optimization framework based on the distribution uncertainty set and constructing a first economic dispatch problem with the lowest operating cost as the objective under the distributionally robust optimization framework; and a solving module for solving the first economic dispatch problem to obtain a dispatch plan.

[0010] In a third aspect, the present disclosure provides a computer device, including:

[0011] A memory and a processor, which are communicatively connected to each other. The memory stores computer instructions, and the processor executes the computer instructions to execute the distributionally robust scheduling method based on Gaussian mixture distribution described in the first aspect and any of its embodiments.

[0012] In a fourth aspect, the present disclosure provides a computer-readable storage medium, on which computer instructions are stored, and the computer instructions are used to cause a computer to execute the distributionally robust scheduling method based on Gaussian mixture distribution described in the first aspect and any of its embodiments.

[0013] In a fifth aspect, the present disclosure provides a computer program product, including a computer program, and when the computer program is executed by a processor, the steps of the distributionally robust scheduling method based on Gaussian mixture distribution described in the first aspect and any of its embodiments are implemented.

[0014] The technical solutions provided in the embodiments of the present disclosure have the following advantages compared with the prior art:

[0015] The distributionally robust scheduling method based on Gaussian mixture distribution provided by the embodiments of the present disclosure constructs an initial Gaussian mixture distribution model; according to the pre-obtained set of output prediction errors, parameter estimation is performed on the initial Gaussian mixture distribution model to obtain a target Gaussian mixture distribution model, and the set of output prediction errors includes the output prediction errors of each unit time period of renewable energy within a preset historical duration; a distribution uncertainty set is constructed according to the target Gaussian mixture distribution model; a distributionally robust optimization framework is constructed based on the distribution uncertainty set, and a first economic scheduling problem with the lowest operating cost as the objective is constructed under the distributionally robust optimization framework; the first economic scheduling problem is solved to obtain a scheduling plan; the above solution first realizes the accurate characterization of the output prediction error distribution of renewable energy by utilizing the ability of the initial Gaussian mixture distribution model to characterize multiple continuous distributions, and solves the problem that the distributionally robust optimization cannot accurately characterize the output prediction error distribution; the economy of unit commitment during the operation process is ensured by constructing the first economic scheduling problem; finally, by adopting the column and constraint generation algorithm for parallel solution, the rapid solution of the target scheduling problem is realized, and the solution efficiency is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The accompanying drawings herein are incorporated into the specification and form a part of the specification, showing embodiments consistent with the present disclosure and used together with the specification to explain the principles of the present disclosure.

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the present disclosure or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0018] Figure 1 It is a schematic flowchart of the distributionally robust scheduling method based on Gaussian mixture distribution provided by the embodiments of the present disclosure;

[0019] Figure 2 It is a schematic flowchart of determining the target Gaussian mixture distribution model provided by the embodiments of the present disclosure;

[0020] Figure 3 It is a schematic flowchart of solving the first economic scheduling problem provided by the embodiments of the present disclosure;

[0021] Figure 4 It is a device connection diagram of the distributionally robust scheduling method based on Gaussian mixture distribution provided by the embodiments of the present disclosure;

[0022] Figure 5 It is a computer device connection diagram provided by the embodiments of the present disclosure. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0023] To better understand the above objects, features, and advantages of the present disclosure, the solutions of the present disclosure will be further described below. It should be noted that, without conflict, the embodiments of the present disclosure and the features in the embodiments may be combined with each other.

[0024] In the following description, many specific details are set forth to facilitate a thorough understanding of the present disclosure. However, the present disclosure may be implemented in other ways different from those described herein. Obviously, the embodiments in the specification are only a part of the embodiments of the present disclosure, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope of protection of the present invention.

[0025] It should be noted that, in this text, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variation thereof is intended to cover a non-exclusive inclusion, such that a process, method, article or device comprising a series of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article or device. Without further limitation, an element defined by the phrase "comprising a..." does not exclude the existence of additional identical elements in the process, method, article or device comprising the element.

[0026] According to an embodiment of the present invention, an embodiment of a distributionally robust scheduling method based on Gaussian mixture distribution is provided. It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. And, although the logical order is shown in the flowchart, in some cases, the steps shown or described herein may be executed in a different order.

[0027] In this embodiment, a distributionally robust scheduling method based on Gaussian mixture distribution is provided, which can be used in a distributionally robust scheduling device based on Gaussian mixture distribution. Figure 1 is a flowchart of a distributionally robust scheduling method based on Gaussian mixture distribution according to an embodiment of the present invention, as Figure 1 shown, the process includes the following steps:

[0028] S101, construct an initial Gaussian mixture distribution model.

[0029] Specifically, considering the complexity of the prediction error of renewable energy output, the embodiments of the present disclosure construct an initial Gaussian mixture distribution model. By utilizing the ability of the initial Gaussian mixture distribution model to characterize multiple continuous distributions, the advantages of distributionally robust optimization are fully exploited to accurately characterize the distribution of the prediction error of renewable energy output.

[0030] Exemplarily, the initial Gaussian mixture distribution model constructed by S101 is as follows:

[0031]

[0032] where x i is a vector formed by the prediction errors of the output of n renewable energy power stations of the same type in the i-th unit time period, K is the total number of Gaussian components in the Gaussian mixture model, k is the k-th Gaussian component, and π k is the weight of the k-th Gaussian distribution, represents a multi-dimensional normal distribution with a mean of μ k and a covariance matrix of Σ k , and p(x i ) is the probability that the processing prediction error corresponding to the renewable energy power station conforms to distribution. It should be noted that due to the influence of geographical distribution, there is a correlation between the prediction errors of each renewable energy power station, so the diagonal elements of the covariance matrix are not zero.

[0033] S102. According to the pre-obtained set of output prediction errors, parameter estimation is performed on the initial Gaussian mixture distribution model to obtain a target Gaussian mixture distribution model.

[0034] Among them, the set of output prediction errors includes the output prediction errors of renewable energy in each unit time period within a preset historical duration. For example, the set of output prediction errors is D x =[x1, x2,... x N , where N is the total number of unit time periods included in the preset historical duration, and x N is a vector formed by the prediction errors of the output of n renewable energy power stations of the same type in the i-th unit time period. The output prediction error is the difference between the actual output value and the predicted output value. Since the renewable energy prediction technology takes into account the time correlation, it can be assumed that the sample data in the set of output prediction errors are independent and identically distributed. Renewable energy power stations include, but are not limited to, wind power stations, solar power stations, etc.

[0035] Specifically, first, according to the set of output prediction errors, parameter estimation is performed on the initial Gaussian mixture distribution model using a parameter estimation method to obtain target parameters; then, the target parameters are input into the initial Gaussian mixture distribution model to obtain a target Gaussian mixture distribution model. Parameter estimation methods include, but are not limited to, maximum likelihood estimation, moment estimation, and least squares estimation, etc.

[0036] In some alternative embodiments, as Figure 2 shown, S102 specifically includes the following steps:

[0037] S1021, normalize the output prediction error set to obtain the normalized output prediction error set.

[0038] Exemplarily, set the output prediction error set as D x = [x1, x2,... x N . Normalize the output prediction error set in the following manner:

[0039]

[0040] B = D x - μh

[0041] where μ is the empirical mean, B is the normalized output prediction error set, and h is a vector of all 1s.

[0042] S1022, construct the log-likelihood function of the initial Gaussian mixture distribution model.

[0043] Exemplarily, the log-likelihood function of the initial Gaussian mixture distribution model is as follows:

[0044]

[0045] where θ is a set of parameters, the set of parameters θ includes the corresponding weight π in each Gaussian component k , mean μ k and covariance matrix Σ k , is the likelihood function.

[0046] S1023, introduce the prior distribution corresponding to each model parameter in the initial Gaussian mixture distribution model.

[0047] Exemplarily, the mean μ k follows a prior normal distribution the covariance matrix Σ k follows an inverse Wishart distribution the weight π k follows a symmetric Dirichlet distribution Dir(α), where μ0 is the mean, Σ0 is the covariance, Ψ is the precision matrix, ν is the degrees of freedom, and α are all hyperparameters of the Dirichlet distribution.

[0048] S1024, construct the posterior distribution based on the log-likelihood function and the prior distribution.

[0049] Exemplarily, the basic posterior distribution is as follows:

[0050]

[0051] Wherein, is the likelihood function after the posterior distribution, p(X|θ) is the log-likelihood function of the data, and p(θ) is the prior distribution of the parameters.

[0052] Substitute the log-likelihood function constructed in S202 and the prior distribution introduced in S203 into the basic posterior distribution, and the constructed posterior distribution obtained is as follows:

[0053]

[0054] S1025, input the output prediction error set into the posterior distribution, obtain the model parameters corresponding to the maximum of the posterior distribution, and determine the model parameters corresponding to the maximum posterior distribution as the target parameters.

[0055] Exemplarily, first, input each output prediction error vector x in the output prediction error set i into the constructed posterior distribution for the E-step calculation. Specifically, calculate the posterior probability that each output prediction error vector x i belongs to the k-th Gaussian component. The calculation method is as follows:

[0056]

[0057] Where γ ik is the posterior probability value that the prediction error vector x i belongs to the k-th Gaussian component.

[0058] Then, through Bayesian inference estimation, use the maximum a posteriori probability objective to update the model parameters, and optimize the model parameters in combination with the prior information.

[0059] The following optimization method is used to optimize the mean:

[0060]

[0061] The following optimization method is used to optimize the covariance matrix:

[0062]

[0063] The following optimization method is used to optimize the weights:

[0064]

[0065] Repeat S1025 continuously until the increment of the posterior probability of Bayesian inference is less than a set threshold epsilon. Then, determine the model parameters corresponding to the situation where the increment is less than the set threshold epsilon as the target parameters. The set threshold epsilon can be taken as 10 -3 。

[0066] S1026, input the target parameters into the initial Gaussian mixture distribution model to obtain the target Gaussian mixture distribution model.

[0067] In this embodiment, through Bayesian inference, the maximum a posteriori estimation is used to calculate the parameters in the Gaussian mixture model, enabling the Gaussian mixture model to perform more reasonable parameter estimation in the case of less data volume or prior knowledge.

[0068] S103, construct a distribution uncertainty set based on the target Gaussian mixture distribution model.

[0069] Specifically, when constructing the distribution uncertainty set, the distance between two distributions can be measured by methods such as total variation distance, probability distance, and earth mover's distance. After determining the corresponding distance threshold, construct the distribution uncertainty set according to the target Gaussian mixture distribution model and the determined distance threshold.

[0070] In some optional implementation manners, taking the Gaussian mixture distribution generated by the target Gaussian mixture distribution model as a benchmark, the distribution uncertainty set is composed of distributions with an earth mover's distance (Wassertein) less than a preset threshold from the Gaussian mixture distribution.

[0071] S104, construct a distributionally robust optimization framework based on the distribution uncertainty set, and construct a first economic dispatch problem with the lowest operating cost as the goal under the distributionally robust optimization framework.

[0072] Specifically, construct a distributionally robust optimization framework according to the distribution uncertainty set. Under the distributionally robust optimization framework, consider the no-load cost, start-stop cost, variable cost of the unit, load shedding and curtailment cost, and penalty factor of the slack variable, and construct a first economic dispatch problem with the lowest operating cost as the goal.

[0073] Exemplarily, the first economic dispatch problem includes an objective function and constraint conditions. Among them, the objective function is as follows:

[0074]

[0075] Among them, t is the time index, T is the time set, g is the unit index, is the unit set, x g,t is the operating status indication variable of unit g at time t, NL g is the unit no-load cost of unit g, u g,tIt is the startup status indication variable of unit g at time t, SU g It is the unit startup cost of unit g, v g,t It is the shutdown status indication variable of unit g at time t, SD g It is the unit shutdown cost of unit g, C g It is the cost function of unit g, p g,t It is the output of unit g at time t, d is the load index, It is the load set, It is the unit load shedding cost of load d at time t, It is the load shedding amount of load d at time t, w is the renewable energy index, It is the renewable energy set, It is the unit cost of curtailing renewable energy of renewable energy w, It is the curtailed renewable energy output of renewable energy w at time t, C Pen It is the slack variable penalty term, It is the power balance slack term of unit g at time t.

[0076] The constraints are as follows:

[0077] (1) Impose restrictions on the state transition equation of the unit:

[0078]

[0079] Among them, x g,t-1 is the operating state of unit g at time t - 1.

[0080] (2) Impose restrictions on the minimum on - time of the unit:

[0081]

[0082] Among them, τ is an intermediate variable, defined by max{1, t - MU g +1}, MU g is the minimum on - time, u g，τ is the on - state indication of unit g at time τ.

[0083] (3) Impose restrictions on the minimum off - time of the unit:

[0084]

[0085] Among them, MD g is the minimum off - time of unit g, v g，τ is the off - state indication variable of unit g at time τ.

[0086] (4) Impose restrictions on the unit time production power of the unit:

[0087]

[0088] wherein, is the minimum output of unit g, is the maximum output of unit g, and x g is the operating status indication variable of unit g.

[0089] (5) Impose restrictions on the power ramp-up and ramp-down of the unit per unit time:

[0090]

[0091] wherein, is the maximum power ramp-down per unit time of unit g, and p g，t-1 is the active power output of g at time t-1, is the maximum power ramp-up per unit time of unit g.

[0092] (6) Impose restrictions on the load shedding amount:

[0093]

[0094] wherein, is the system load.

[0095] (7) Impose restrictions on the curtailment of renewable energy power generation:

[0096]

[0097] wherein, W w,t is the predicted value of the output of renewable energy w at time t, and ξ w,t is the output deviation value of renewable energy w at time t.

[0098] (8) Impose restrictions on the flow of transmission lines:

[0099]

[0100] wherein, F l is the maximum power of branch l, is the PTDF factor of unit g on branch l, is the PTDF factor of renewable energy w on branch l, is the PTDF factor of load d on branch l, and D d，t is the load power, is the set of branches.

[0101] (9) Power balance condition:

[0102]

[0103] When constructing the first economic dispatch problem in this embodiment, slack variables are attached to generators, such as in the flow limit and power balance conditions of transmission lines. Through slack variables, this solution hedges the boundary requirements of unit power, which can ensure the feasibility of problems with load shedding and renewable energy output curtailment. Thus, it overcomes the problem in the traditional cutting plane algorithm that feasibility cuts need to be added to ensure feasibility. In the distributionally robust optimization problem, this feasible cut is determined from an infinite-dimensional recourse problem. Using slack variables to avoid returning the feasibility cut can prevent the situation where a feasible cut cannot be returned when the objective value is infinite during the solution of the recourse problem. Therefore, based on the first economic dispatch problem, slack variables should be penalized by a large penalty factor in the objective function to ensure that non-zero slack variables are not allowed in the final solution. At the same time, compared with the conventional distributionally robust solution, this method can improve the solution speed.

[0104] S105. Solve the first economic dispatch problem to obtain a dispatch plan.

[0105] Specifically, as Figure 3 shown, S105 includes the following steps:

[0106] S1051. Convert the first economic dispatch problem into a second economic dispatch problem in a distributionally robust form.

[0107] S1051 includes the following steps:

[0108] Step a1. Decompose the variables in the first economic dispatch problem into first decision variables and second decision variables according to the response speed of the variables, and declare the variable abbreviations of the first decision variables and the variable abbreviations of the second decision variables.

[0109] Specifically, before converting the first economic dispatch problem into the second economic dispatch problem, first divide the variables in the first economic dispatch problem into first decision variables and second decision variables according to the response speed of the variables. The first decision variables are slow decision variables, and the second decision variables are fast decision variables. The first decision variables and the second decision variables are a general term for a type of variables. After obtaining the first decision variables and the second decision variables, declare the variable abbreviations of the first decision variables and the variable abbreviations of the second decision variables.

[0110] Exemplarily, the variable abbreviations of the first decision variables are as follows:

[0111]

[0112] Among them, is the start-stop and status variables that need to be determined in advance for the first type of units;

[0113] The variable abbreviations of the second decision variables are as follows:

[0114]

[0115] Among them, is the real-time regulator start-stop and state variables of the second type of unit in intraday scheduling.

[0116] Step a2, combining the variable abbreviations of the first decision variable and the second decision variable, transforms the first economic dispatch problem into a second economic dispatch problem in a distributionally robust form.

[0117] Specifically, considering the intraday observed uncertainty variables and their distributions, assuming that the distributions and values of the uncertainty variables are unknown, then, combining the variable abbreviations of the first decision variable and the second decision variable, the first economic dispatch problem can be transformed into a second economic dispatch problem in a distributionally robust form.

[0118] Exemplarily, the second economic dispatch problem is as follows:

[0119]

[0120] Among them, is the feasible region of the decision variable x, is the objective coefficient of the decision variable x, is the probability distribution belonging to the set, is the expectation operator with respect to the distribution, is the defined optimal value function, F is the coefficient matrix of the decision variable x, and f is the right-hand side term of the decision variable x.

[0121]

[0122] Among them, is the feasible region of the decision variable y, is the feasible region of the decision variable z, is the objective coefficient of the decision variable y, is the objective coefficient of the decision variable z, G, H, A, B, C, U, V are the coefficient matrices of the constraint conditions respectively, and g, h, d, w are the right-hand side terms of the constraint conditions respectively.

[0123] S1052, combining the distribution uncertainty set, transforms the second economic dispatch problem into an objective dispatch problem.

[0124] Exemplarily, taking the distribution generated by the target Gaussian mixture distribution model determined by S102 as the central empirical distribution, a series of distributions that are distant from the central empirical distribution are measured by the Wasserstein probability distance, and this series of distributions is used as the probability distribution in.

[0125]

[0126] Among them, α k , β, and γ are dual variables, is the variable x in the initial Gaussian mixture model i , p is a set object, Ω is the support set, and P k is the conditional probability distribution.

[0127] Exemplarily, by introducing the infinite-dimensional duality theory and the strong duality principle, and combining the probability distributions in the distribution uncertainty set, the second economic dispatch problem is first transformed into:

[0128]

[0129] Among them, μ T is the transpose of μ, and θ is a set of coefficients.

[0130] Furthermore, the above formula is transformed into:

[0131]

[0132] Among them, ε k represents the introduced auxiliary variable, and ‖ε k ‖ * represents the dual norm operator. By adopting the equivalent way of the 1-norm and the infinity-norm equality, the above expression is transformed into:

[0133]

[0134] Fx ≥ f

[0135] ‖ε k ‖ * ≤ γ

[0136]

[0137] Among them:

[0138]

[0139] Among them, π1, π2, π3, and π4 are the dual variables of each constraint.

[0140] To eliminate the max-min expression in α k , perform a dual transformation on the problem to obtain:

[0141]

[0142] Directly transform the above-mentioned expression in the unified form into the following target dispatch problem:

[0143]

[0144] S1053. Solve the target scheduling problem through a column and constraint generation algorithm with parallel solution to obtain a scheduling plan.

[0145] Exemplarily, the process of solving the target scheduling problem through a column and constraint generation algorithm with parallel solution is as follows:

[0146] First, perform initialization settings. For example, determine the convergence tolerance ε, set the upper bound UB = ∞, set the lower bound LB = -∞, and set the iteration count c = 1.

[0147] Then, decompose the target scheduling problem generated in S1052 into at least one master problem and at least one sub - problem corresponding to each master problem. The master problem can be understood as an optimization problem for slow decision variables, and the sub - problem can be understood as an optimization problem for fast decision variables under different distributions included in the distribution uncertainty set.

[0148] Exemplarily, the master problem is as follows:

[0149]

[0150] Fx≥f

[0151] ‖ε k ‖ * ≤γ

[0152]

[0153] where z l，k is the decision variable z in the k - th scenario of the l - th iteration, y l，k is the decision variable y in the k - th scenario of the l - th iteration, and ξ l，k is the decision variable ξ in the k - th scenario of the l - th iteration.

[0154] Solve the above master problem to obtain the optimal solution of the master problem and the objective value corresponding to the optimal solution. The optimal solution can be understood as the values of each slow variable that minimize the operating cost, and the objective value is the value obtained by substituting the slow variables into the master problem. For example, in this embodiment, let (x c , α k，c , β c , γ c , ε k，c ) be the optimal solution of the master problem in the c - th iteration, and let be the objective value corresponding to the optimal solution.

[0155] After solving the master problem, update the lower bound LB to Then, solve multiple sub - problems corresponding to the master problem in parallel. Exemplarily, the k - th sub - problem is as follows:

[0156]

[0157] Solve the k-th sub-problem to obtain the optimal solution and objective value corresponding to the k-th sub-problem. For example, in the c-th iteration, the optimal solution of the k-th sub-problem is (ξ c，k , π c，k ), and the objective value of the k-th sub-problem is After solving the sub-problems, update the upper bound UB to

[0158] After the end of the c-th iteration process, judge whether the convergence condition is reached according to the updated upper bound and lower bound. For example, when (UB - LB) / LB ≥ ε, form a scheduling plan according to the optimal solutions of the master problem and the sub-problems, and terminate the program. Otherwise, update ξ to ξ c,k , let c = c + 1, and return to perform a new round of iteration, that is, solve the master problem and the sub-problems again until the convergence condition is reached and a scheduling plan is obtained. The above process solves the target scheduling problem through a parallel column and constraint generation algorithm, decomposes the distribution robustness of the multivariate data Gaussian mixture distribution so that the central node only calculates the master problem, and multiple distributed nodes only calculate the sub-problems. In this way, the central node only needs to wait for the master problem with the longest calculation time to obtain all the distribution information to update the slow decision variables corresponding to the master problem, greatly reducing the solution time and improving the solution efficiency.

[0159] The distributionally robust scheduling method based on Gaussian mixture distribution provided by the embodiments of the present disclosure constructs an initial Gaussian mixture distribution model; estimates the parameters of the initial Gaussian mixture distribution model according to a pre-obtained set of output power prediction errors to obtain a target Gaussian mixture distribution model, where the set of output power prediction errors includes the output power prediction errors of each unit time period of renewable energy within a preset historical duration; constructs a distribution uncertainty set according to the target Gaussian mixture distribution model; constructs a distributionally robust optimization framework based on the distribution uncertainty set, and constructs a first economic scheduling problem with the lowest operating cost as the objective under the distributionally robust optimization framework; solves the first economic scheduling problem to obtain a scheduling plan; the above solution first realizes the accurate characterization of the output power prediction error distribution of renewable energy by using the ability of the initial Gaussian mixture distribution model to characterize multiple continuous distributions, and solves the problem that distributionally robust optimization cannot accurately characterize the output power prediction error distribution; ensures the economy of unit commitment during operation by constructing the first economic scheduling problem; finally, realizes the rapid solution of the target scheduling problem by adopting a parallel column and constraint generation algorithm, improving the solution efficiency.

[0160] In this embodiment, a distributionally robust scheduling device based on Gaussian mixture distribution is further provided. This device is used to implement the above-mentioned embodiments and preferred implementation manners, and those that have been described will not be repeated here. As used hereinafter, the term "module" can be a combination of software and / or hardware that realizes a predetermined function. Although the devices described in the following embodiments are preferably implemented in software, implementation in hardware, or a combination of software and hardware is also possible and contemplated.

[0161] This embodiment provides a distributionally robust scheduling device based on Gaussian mixture distribution, as Figure 4 shown, including:

[0162] A first construction module 401, configured to construct an initial Gaussian mixture distribution model;

[0163] An estimation module 402, configured to perform parameter estimation on the initial Gaussian mixture distribution model according to a pre-acquired set of output prediction errors, and obtain a target Gaussian mixture distribution model. The set of output prediction errors includes the output prediction errors of each unit time period of renewable energy within a preset historical duration;

[0164] A second construction module 403, configured to construct a distribution uncertainty set according to the target Gaussian mixture distribution model;

[0165] A third construction module 404, configured to construct a distributionally robust optimization framework based on the distribution uncertainty set, and construct a first economic scheduling problem with the lowest operating cost as the goal under the distributionally robust optimization framework;

[0166] A solving module 405, configured to solve the first economic scheduling problem to obtain a scheduling plan.

[0167] In some alternative implementation manners, the estimation module 402 includes:

[0168] A normalization sub-module, configured to perform normalization processing on the set of output prediction errors to obtain a normalized set of output prediction errors; a first construction sub-module, configured to construct a log-likelihood function of the initial Gaussian mixture distribution model; an introduction sub-module, configured to introduce a prior distribution corresponding to each model parameter in the initial Gaussian mixture distribution model; a second construction sub-module, configured to construct a posterior distribution according to the log-likelihood function and the prior distribution; a first determination sub-module, configured to input the normalized set of output prediction errors into the posterior distribution to obtain the model parameters corresponding to the maximum posterior distribution, and determine the model parameters corresponding to the maximum posterior distribution as the target parameters; a second determination sub-module, configured to input the target parameters into the initial Gaussian mixture distribution model to obtain a target Gaussian mixture distribution model.

[0169] In some alternative implementation manners, the second construction module 403 includes:

[0170] The third construction sub-module is used to form a distribution uncertainty set consisting of distributions with an earth mover's distance from the Gaussian mixture distribution generated by the target Gaussian mixture distribution model less than a preset threshold.

[0171] In some alternative embodiments, the first economic dispatch problem constructed by the third construction module 404 includes an objective function and constraint conditions. The objective function is as follows:

[0172]

[0173] where t is the time index, T is the set of times, g is the unit index, is the set of units, x g,t is the operating status indicator variable of unit g at time t, NL g is the unit no-load cost of unit g, u g,t is the startup status indicator variable of unit g at time t, SU g is the unit startup cost of unit g, v g,t is the shutdown status indicator variable of unit g at time t, SD g is the unit shutdown cost of unit g, C g is the cost function of unit g, p g,t is the output of unit g at time t, d is the load index, is the set of loads, is the unit load shedding cost of load d at time t, is the load shedding amount of load d at time t, w is the renewable energy index, is the set of renewable energies, is the unit renewable energy curtailment cost of renewable energy w, is the curtailed renewable energy output of renewable energy w at time t, C Pen is the slack variable penalty term, is the power balance slack term of unit g at time t;

[0174] The constraint conditions are as follows:

[0175] Restrictions are imposed on the state transition equation of the unit:

[0176]

[0177] where x g,t-1 is the operating status of unit g at time t - 1;

[0178] Restrictions are imposed on the minimum on-time of the unit:

[0179]

[0180] Among them, τ is an intermediate variable, defined by max{1, t - MU g + 1}, where MU g is the minimum startup time, and u g , τ is the startup indication status of unit g at time τ;

[0181] Place a limit on the minimum shutdown time of the unit:

[0182]

[0183] Among them, MD g is the minimum shutdown time of unit g, and v g，τ is the shutdown status indication variable of unit g at time τ;

[0184] Place a limit on the production power per unit time of the unit:

[0185]

[0186] Among them, is the minimum output of unit g, is the maximum output of unit g, and x g is the operation status indication variable of unit g;

[0187] Place a limit on the power ramp-up and ramp-down per unit time of the unit:

[0188]

[0189] Among them, is the maximum ramp-down power per unit time of unit g, p g，t-1 is the active power output of g at time t - 1, is the maximum ramp-up power per unit time of unit g;

[0190] Place a limit on the load shedding amount:

[0191]

[0192] Among them, is the system load;

[0193] Place a limit on the curtailment of renewable energy generation:

[0194]

[0195] Among them, W w,t is the predicted value of the output of renewable energy w at time t, and ξ w,t is the output deviation value of renewable energy w at time t;

[0196] Flow limit of transmission line:

[0197]

[0198] Among them, F l is the maximum power of branch l, is the PTDF factor of unit g on branch l, is the PTDF factor of renewable energy w on branch l, is the PTDF factor of load d on branch l, D d，t is the load power, is the branch set;

[0199] Power balance condition:

[0200]

[0201] In some alternative embodiments, the solving module 405 includes:

[0202] A first conversion sub-module for converting the first economic dispatch problem into a second economic dispatch problem in a distributionally robust form; a second conversion sub-module for combining a distributionally uncertain set to convert the second economic dispatch problem into an objective dispatch problem; a solving sub-module for solving the objective dispatch problem through a column-and-constraint generation algorithm with parallel solving to obtain a dispatch plan.

[0203] In some alternative embodiments, the first conversion sub-module includes:

[0204] A decomposition unit for decomposing the variables in the first economic dispatch problem into first decision variables and second decision variables according to the response speed of the variables, and declaring the variable abbreviations of the first decision variables and the variable abbreviations of the second decision variables; a conversion unit for combining the variable abbreviations of the first decision variables and the variable abbreviations of the second decision variables to convert the first economic dispatch problem into a second economic dispatch problem in a distributionally robust form.

[0205] The further function descriptions of the above-mentioned various modules and units are the same as those in the corresponding above embodiments, and will not be elaborated here.

[0206] The distributionally robust scheduling device based on Gaussian mixture distribution in this embodiment is presented in the form of functional units. Here, the unit refers to an ASIC (Application Specific Integrated Circuit) circuit, a processor and a memory that execute one or more software or fixed programs, and / or other devices that can provide the above functions.

[0207] The embodiment of the present invention also provides a computer device having the above Figure 4The distribution robust scheduling device based on Gaussian mixture distribution as shown.

[0208] Please refer to Figure 5 , Figure 5 which is a schematic structural diagram of a computer device provided by an alternative embodiment of the present invention. As Figure 5 shown, the computer device includes: one or more processors 10, a memory 20, and interfaces for connecting various components, including a high-speed interface and a low-speed interface. Each component communicates with each other using different buses and can be installed on a common motherboard or installed in other ways as needed. The processor can process instructions executed within the computer device, including instructions stored in the memory or on the memory to display graphical information of the GUI on an external input / output device (such as a display device coupled to the interface). In some alternative embodiments, if necessary, multiple processors and / or multiple buses can be used together with multiple memories. Similarly, multiple computer devices can be connected, and each device provides some necessary operations (such as an array of servers, a set of blade servers, or a multi-processor system). Figure 5 In

[0209]

[0210]

[0211]

[0212] The memory 20 stores instructions executable by at least one processor 10, so that the at least one processor 10 executes the method shown in the above embodiments.

[0212] The memory 20 may include volatile memory, such as random access memory; the memory may also include non-volatile memory, such as flash memory, a hard disk, or a solid state drive; the memory 20 may further include a combination of the above types of memory.

[0213] The computer device further includes a communication interface 30 for the computer device to communicate with other devices or a communication network.

[0214] Embodiments of the present invention also provide a computer-readable storage medium. The method according to the embodiments of the present invention can be implemented in hardware, firmware, or be implemented as computer code that can be recorded on a storage medium, or be implemented by a computer code originally stored in a remote storage medium or a non-transitory machine-readable storage medium and downloaded through a network and to be stored in a local storage medium, so that the method described herein can be stored in such software processing on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. Among them, the storage medium can be a magnetic disk, an optical disk, a read-only memory, a random access memory, a flash memory, a hard disk, or a solid state drive, etc.; further, the storage medium can also include a combination of the above types of memory. It can be understood that a computer, a processor, a microprocessor controller, or programmable hardware includes a storage component that can store or receive software or computer code, and when the software or computer code is accessed and executed by the computer, the processor, or the hardware, the method shown in the above embodiments is implemented.

[0215] In addition to the above computer device and computer-readable storage medium, embodiments of the present application may also be a computer program product, which includes computer program instructions that cause a processor to execute the steps of the sound source localization method provided in any embodiment of the present application when the computer program instructions are run by the processor.

[0216] The computer program product can be written in any combination of one or more programming languages to write program code for performing the operations of the embodiments of the present application. The programming languages include object-oriented programming languages, such as Java, C++, etc., and also include conventional procedural programming languages, such as the "C" language or similar programming languages. The program code can be executed entirely on the user computing device, partially on the user device, executed as an independent software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server.

[0217] The above are only specific embodiments of the present disclosure, enabling those skilled in the art to understand or implement the present disclosure. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present disclosure. Therefore, the present disclosure will not be limited to these embodiments described herein, but rather will be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A distributionally robust scheduling method based on Gaussian mixture distribution, characterized in that, Including: Construct an initial Gaussian mixture distribution model; According to the pre-obtained output prediction error set, perform parameter estimation on the initial Gaussian mixture distribution model to obtain a target Gaussian mixture distribution model, where the output prediction error set includes the output prediction errors of each unit time period of renewable energy within a preset historical duration; Construct a distribution uncertainty set according to the target Gaussian mixture distribution model; Construct a distributionally robust optimization framework based on the distribution uncertainty set, and construct a first economic dispatch problem with the lowest operating cost as the goal under the distributionally robust optimization framework; Solve the first economic dispatch problem to obtain a dispatch plan.

2. The method according to claim 1, wherein The step of performing parameter estimation on the initial Gaussian mixture distribution model according to the pre-obtained output prediction error set to obtain a target Gaussian mixture distribution model includes: Perform normalization processing on the output prediction error set to obtain a normalized output prediction error set; Construct the log-likelihood function of the initial Gaussian mixture distribution model; Introduce a prior distribution corresponding to each model parameter in the initial Gaussian mixture distribution model; Construct a posterior distribution according to the log-likelihood function and the prior distribution; Input the normalized output prediction error set into the posterior distribution to obtain the model parameters corresponding to the maximum posterior distribution, and determine the model parameters corresponding to the maximum posterior distribution as the target parameters; Input the target parameters into the initial Gaussian mixture distribution model to obtain the target Gaussian mixture distribution model.

3. The method according to claim 1, wherein The step of constructing a distribution uncertainty set according to the target Gaussian mixture distribution model includes: Taking the Gaussian mixture distribution generated by the target Gaussian mixture distribution model as a benchmark, the distribution uncertainty set is composed of distributions with a Wasserstein distance less than a preset threshold from the Gaussian mixture distribution.

4. The method according to claim 1, wherein The first economic dispatch problem includes an objective function and constraint conditions. The objective function is as follows: where \(t\) is the time index, \(T\) is the set of time, \(g\) is the unit index, is the set of units, \(x\) g,t is the operation status indicator variable of unit \(g\) at time \(t\), \(NL\) g is the no-load cost per unit of unit \(g\), \(u\) g,t is the startup status indicator variable of unit \(g\) at time \(t\), \(SU\) g is the startup cost per unit of unit \(g\), \(v\) g,t is the shutdown status indicator variable of unit \(g\) at time \(t\), \(SD\) g is the shutdown cost per unit of unit \(g\), \(C\) g is the cost function of unit \(g\), \(p\) g,t is the output of unit \(g\) at time \(t\), \(d\) is the load index, is the set of loads, is the cost per unit of load shedding of load \(d\) at time \(t\), is the amount of load shedding of load \(d\) at time \(t\), \(w\) is the renewable energy index, is the set of renewable energy, is the cost per unit of curtailment of renewable energy \(w\), is the curtailed output of renewable energy \(w\) at time \(t\), \(C\) Pen is the penalty term of the slack variable, is the power balance slack term of unit \(g\) at time \(t\); The constraint conditions are as follows: Impose restrictions on the state transition equation of the unit; where x g,t-1 is the operating state of unit g at time t-1; Impose restrictions on the minimum on-time of the unit; where τ is an intermediate variable defined by max{1, t - MU g + 1}, MU g is the minimum start-up time, and u g，τ is the start-up indication status of unit g at time τ; Impose restrictions on the minimum off-time of the unit; Among them, MD g is the minimum downtime of unit g, and v g，τ is the shutdown status indication variable of unit g at time τ; Impose restrictions on the unit time production power of the unit; Among them, is the minimum output of unit g, is the maximum output of unit g, and x g is the operating status indication variable of unit g; Impose restrictions on the unit time power ramp-up and ramp-down of the unit; Among them, is the maximum landslide descent power per unit time of unit g, p g，t-1 is the active power output at time t - 1, is the maximum climbing ascent power per unit time of unit g; Impose restrictions on the load shedding amount; Among them, is the system load; Impose restrictions on the abandoned renewable energy power generation; Among them, W w,t is the predicted output value of renewable energy w at time t, and ξ w,t is the output deviation value of renewable energy w at time t; Impose restrictions on the flow of the transmission line; Among them, F l is the maximum power of the branch, is the PTDF factor of unit g on branch l, is the PTDF factor of renewable energy w on branch l, is the PTDF factor of load d on branch l, D d，t is the load power, is the branch set; Power balance condition:

5. The method according to claim 1, wherein The step of solving the first economic dispatch problem to obtain a dispatch plan includes: Convert the first economic dispatch problem into a second economic dispatch problem in a distributionally robust form; Combined with the distribution uncertainty set, convert the second economic dispatch problem into a target dispatch problem; Solve the target dispatch problem through a column-and-constraint generation algorithm with parallel solution to obtain a dispatch plan.

6. The method according to claim 5, characterized in that, The step of converting the first economic dispatch problem into a second economic dispatch problem in a distributionally robust form includes: According to the response speed of the variables, decompose the variables in the first economic dispatch problem into first decision variables and second decision variables, and declare the variable abbreviations of the first decision variables and the variable abbreviations of the second decision variables; Combined with the variable abbreviations of the first decision variable and the variable abbreviations of the second decision variable, the first economic dispatch problem is transformed into a second economic dispatch problem in a distributionally robust form.

7. A distributionally robust scheduling device based on Gaussian mixture distribution, characterized in that, Including: A first construction module for constructing an initial Gaussian mixture distribution model; An estimation module for parameter estimating the initial Gaussian mixture distribution model according to a pre-obtained set of output prediction errors, where the set of output prediction errors includes the output prediction errors of each unit time period of renewable energy within a preset historical duration; A second construction module for constructing a distribution uncertainty set according to the target Gaussian mixture distribution model; A third construction module for constructing a distributionally robust optimization framework based on the distribution uncertainty set and constructing a first economic dispatch problem with the lowest operating cost as the objective under the distributionally robust optimization framework; A solution module for solving the first economic dispatch problem to obtain a dispatch plan.

8. A computer device, characterized in that, Including: A memory and a processor, which are communicatively connected to each other. The memory stores computer instructions, and the processor executes the computer instructions to execute the distributionally robust dispatch method based on Gaussian mixture distribution according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, Computer instructions are stored on the computer-readable storage medium, and the computer instructions are used to cause a computer to execute the distributionally robust dispatch method based on Gaussian mixture distribution according to any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, the steps of the distributionally robust dispatch method based on Gaussian mixture distribution according to any one of claims 1 to 6 are implemented.

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