Scene set reduction method for planning operation of active power distribution network
By modeling the power system planning and operation problems into two-stage random optimization form and performing scenario reduction in the problem space, the problem of inability to effectively approximate the original optimality in the existing technology is solved, and more accurate scenario reduction and smaller optimality gap are achieved.
Patent Information
- Application Number
- CN202411601687.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-11
- Publication Date
- 2025-04-01
AI Technical Summary
The existing scenario reduction technology cannot effectively ensure a good approximation of the original optimality, especially when the uncertainty information in the planning and operation of the active distribution network is incomplete.
A problem-driven scenario reduction method is proposed. By modeling the two-stage random optimization problem into a two-stage random optimization form, and performing scene reduction in the problem space, using a mixed integer linear programming form to select a representative scene set to ensure the smallest optimality gap.
More accurate scenario reduction is achieved, the optimality gap is smaller, and the uncertainty risks in the power system can be managed more effectively.
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Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of scenario set reduction, and in particular to a scenario set reduction method for active distribution network planning and operation. Background Art
[0002] The widespread access of renewable energy and new loads to power systems has led to increased variability and uncertainty in operations. Therefore, effective decisions for power system operations must take these uncertainties into account in order to effectively manage risks. In the case of complete uncertainty information (e.g., known probability distributions), distributionally robust optimization, chance-constrained optimization, and robust optimization have been shown to be effective methods. In the case of incomplete uncertainty information (e.g., only discrete scenarios obtained from historical observations or predictions are known), it is common practice to use scenario-based stochastic optimization, in which a limited set of scenarios is used to approximate the probability uncertainty distribution. However, scenario-based techniques often struggle with the "curse of dimensionality", which becomes more pronounced as the types and number of uncertainties increase. To reduce this complexity, scenario reduction can be used to identify a smaller set of representative scenarios that replaces the original set of scenarios for decision making while maintaining an acceptably robust optimal solution. However, existing scenario reduction techniques usually aim to achieve a statistical approximation of the reduced scenario set to the original set of scenarios and usually treat scenario reduction and scenario-based planning operations as two independent and decoupled processes, which cannot guarantee a good approximation of the original optimality. Summary of the invention
[0003] The purpose of the present invention is to solve the above-mentioned deficiencies in the prior art, thereby providing a scenario set reduction method for active distribution network planning and operation.
[0004] A problem-driven active distribution network planning operation scenario reduction method includes the following steps:
[0005] Step 1: Model the power system planning and operation problem in the two-stage stochastic optimization form based on scenario sets as a two-stage stochastic optimization problem;
[0006] Step 2: Project the distribution space to the problem space;
[0007] Step 3: Perform scenario reduction on the two-stage stochastic optimization problem in the problem space.
[0008] The two-stage stochastic optimization problem is expressed as:
[0009]
[0010] where F(z,ξ) is the objective function of the two-stage stochastic optimization problem; the original N scene set is represented by ξ={ξ1,ξ2,...,ξN}, f(z) is the objective function of the first stage, and the decision variable is z∈Z, represents a bounded feasible set; the second stage problem is to solve the uncertainty ξ i G(y i ,ξ i |z), where is the decision variable, z is the parameter, g(y i ,ξ i ) is the objective function of the second stage; scenario ξ i The weight is γ i ≥0, satisfied
[0011] The optimal solution of formula (1) is Denotes F(z,ξ i ):=f(z)+G(y i ,ξ i ),in Then there is The two-stage stochastic optimization problem is required to satisfy the relatively complete remediation assumption, that is, for any z∈Z and ξ∈ξ, the two-stage stochastic optimization problem has a solution.
[0012] Project the distribution space to the problem space, specifically:
[0013] Solve the problem F for each specific scenario ij , construct the matrix in, Realize the conversion of the original scene set in the distribution space to the problem space.
[0014] The scenario reduction of the two-stage stochastic optimization problem in the problem space is as follows:
[0015] In the problem space, the process of scene division and representative scene selection in the scene reduction problem is expressed as the following mixed integer linear optimization (MILP) problem, and the branch and bound method is applied to solve it to achieve scene reduction in the problem space;
[0016]
[0017] The total distance describing the scene division is the objective function, K is the optimal number of clusters, and the binary variable u j Representation scene j Whether it is selected as the representative scene of a cluster, binary variable v ij Decide on the scene i Is it included in the scene? j In the cluster represented by ij ≤u j Ensurei can only be assigned to the cluster with the specified representative, and v jj =u j Forced i must be assigned to its own cluster if it is to represent a scene, each scene ξ j can only be assigned to one cluster, forming exactly K clusters, and the obtained u j Indicates the optimal representative scene set ζ = {ζ1, ζ2, ..., ζ K}.
[0018] The present invention incorporates the scenario-based planning operation problem structure into the scenario reduction process and proposes a new problem-driven scenario reduction framework.
[0019] The present invention transforms the original scenario set from the distribution space into the problem space by analyzing the decision applicability between scenarios. Subsequently, a problem-driven distance metric is proposed to describe the similarity between scenarios, and the scenario reduction process is formulated as a mixed integer linear programming form to obtain a representative scenario set while minimizing the optimality gap.
[0020] Compared with the prior art, the present application can achieve more accurate scene reduction and obtain a smaller optimality gap. DETAILED DESCRIPTION
[0021] A problem-driven active distribution network planning and operation scenario reduction method is proposed, and the specific steps are as follows:
[0022] Step 1: For any power system planning and operation problem that can be modeled as a two-stage stochastic optimization form based on a scenario set, first construct its two-stage form as follows:
[0023]
[0024] where F(z,ξ) is the objective function of the two-stage stochastic optimization, including the cost of the first stage and the expected cost of the second stage. The original set of N scenarios is represented by ξ={ξ1,ξ2,...,ξ N}, f(z) is the objective function of the first stage, and the decision variable is z∈Z. Here, represents a bounded feasible set. The second stage problem is to solve the problem of uncertainty ξ i G(y i ,ξ i |z), where is the decision variable, z is the parameter. g(y i ,ξ i ) is the objective function of the second stage. i The probability is γ i ≥0, satisfied We express the optimal solution of (1) as In addition, we denote F(z,ξ i ):=f(z)+G(y i ,ξ i ),in We have We reasonably require that two-stage stochastic optimization satisfy the assumption of relative complete remediation, i.e., for any z∈Z and ξ∈ξ, two-stage stochastic optimization has a solution. This assumption is common in stochastic optimization and ensures that there are sufficient resources to deal with potential risks, even if they are costly.
[0025] In order to cope with the computational complexity challenge when N is large, scene reduction is used to significantly reduce the computational complexity while keeping the problem optimality approximation accuracy at an acceptable level. In the scene reduction process, the original scene set ξ is divided into K (K<<N) clusters and simplified to a representative scene set ζ={ζ1,ζ2,...,ζ K Each scene cluster C k By representative scene k The corresponding weight is satisfy
[0026] Step 2: Project the distribution space into the problem space
[0027] Solve the problem F for each specific scenario ij , construct the matrix in, The original scene set in the distribution space is transformed into the problem space.
[0028] Step 3: Solve the scenario reduction problem in the problem space
[0029] In the problem space, the process of scene division and representative scene selection in the two-stage stochastic optimization problem is expressed as the following MILP formula and solved:
[0030]
[0031] The total distance describing the scene division is the objective function, and K is the optimal number of clusters. j Representation scene j Whether it is selected as the representative scene of a cluster, and the binary variable v ij Decide on the scene i Is it included in the scene? j Represented cluster. Constraint v ij ≤u j Ensure i can only be assigned to the cluster with the specified representative, while v jj=u j Forced i must be assigned to its own cluster if it is representative of a scene. j can only be assigned to one cluster, forming exactly K clusters. The weight of each cluster is calculated as Get u j The optimal representative scene set ζ is indicated.
[0032] Solving this problem can achieve scenario reduction in the problem space.
Claims
1. A problem-driven active distribution network planning and operation scenario reduction method, characterized by: The following steps are involved: Step 1: Model the power system planning and operation problem in the two-stage stochastic optimization form based on scenario sets as a two-stage stochastic optimization problem; Step 2: Project the distribution space to the problem space; Step 3: Perform scenario reduction on the two-stage stochastic optimization problem in the problem space.
2. According to claim 1, a problem-driven active distribution network planning and operation scenario reduction method is characterized by: The two-stage stochastic optimization problem is expressed as: where F(z,ξ) is the objective function of the two-stage stochastic optimization problem; the original N scene set is represented by ξ={ξ1,ξ2,...,ξ N }, f(z) is the objective function of the first stage, and the decision variable is z∈Z, represents a bounded feasible set; The second stage problem is that under uncertainty ξ i G(y i ,ξ i |z), where y i ∈Y(z,ξ i ), is the decision variable, z is the parameter, g(y i ,ξ i ) is the objective function of the second stage; scenario ξ i The weight is γ i ≥0, satisfied The optimal solution of formula (1) is Denote F(z,ξ i ):=f(z)+G(y i ,ξ i ),in Then there is The two-stage stochastic optimization problem is required to satisfy the relatively complete remediation assumption, that is, for any z∈Z and ξ∈ξ, the two-stage stochastic optimization problem has a solution.
3. According to claim 1, a problem-driven active distribution network planning and operation scenario reduction method is characterized by: Project the distribution space to the problem space, specifically: Solve the problem F for each specific scenario ij , construct the matrix in, Realize the conversion of the original scene set in the distribution space to the problem space.
4. According to claim 1, a problem-driven active distribution network planning and operation scenario reduction method is characterized by: The scenario reduction of the two-stage stochastic optimization problem in the problem space is as follows: In the problem space, the process of scene division and representative scene selection in the scene reduction problem is expressed as the following mixed integer linear optimization (MILP) problem, and the branch and bound method is applied to solve it to achieve scene reduction in the problem space; The total distance describing the scene division is the objective function, K is the optimal number of clusters, and the binary variable u j Representation scene j Whether it is selected as the representative scene of a cluster, binary variable v ij Decide on the scene i Is it included in the scene? j In the cluster represented by ij ≤u j Ensure i can only be assigned to the cluster with the specified representative, and v jj =u j Forced i must be assigned to its own cluster if it is to represent a scene, each scene ξ j can only be assigned to one cluster, forming exactly K clusters, and the obtained u j Indicates the optimal representative scene set ζ = {ζ1, ζ2, ..., ζ K }.