+

CN114421483A - An analytical probabilistic power flow calculation method, device and storage medium - Google Patents

An analytical probabilistic power flow calculation method, device and storage medium Download PDF

Info

Publication number
CN114421483A
CN114421483A CN202210126978.7A CN202210126978A CN114421483A CN 114421483 A CN114421483 A CN 114421483A CN 202210126978 A CN202210126978 A CN 202210126978A CN 114421483 A CN114421483 A CN 114421483A
Authority
CN
China
Prior art keywords
power
node
power system
nodes
power flow
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202210126978.7A
Other languages
Chinese (zh)
Inventor
杨银国
陆秋瑜
伍双喜
朱誉
林英明
于珍
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Guangdong Power Grid Co Ltd
Electric Power Dispatch Control Center of Guangdong Power Grid Co Ltd
Original Assignee
Guangdong Power Grid Co Ltd
Electric Power Dispatch Control Center of Guangdong Power Grid Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Guangdong Power Grid Co Ltd, Electric Power Dispatch Control Center of Guangdong Power Grid Co Ltd filed Critical Guangdong Power Grid Co Ltd
Priority to CN202210126978.7A priority Critical patent/CN114421483A/en
Publication of CN114421483A publication Critical patent/CN114421483A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for AC mains or AC distribution networks
    • H02J3/04—Circuit arrangements for AC mains or AC distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
    • G06Q50/06—Energy or water supply

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Business, Economics & Management (AREA)
  • Health & Medical Sciences (AREA)
  • Economics (AREA)
  • General Physics & Mathematics (AREA)
  • Public Health (AREA)
  • General Business, Economics & Management (AREA)
  • Marketing (AREA)
  • Primary Health Care (AREA)
  • Strategic Management (AREA)
  • Tourism & Hospitality (AREA)
  • General Health & Medical Sciences (AREA)
  • Human Resources & Organizations (AREA)
  • Water Supply & Treatment (AREA)
  • Power Engineering (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • Supply And Distribution Of Alternating Current (AREA)

Abstract

The invention discloses an analytic probability load flow calculation method, an analytic probability load flow calculation device and a storage medium. According to the method, after the mapping relation between the injection power of the node and the operation state of the power system is determined through the linear power flow model, the operation state of the power system is corrected by adopting a first-order polynomial fitting correction method, so that the corrected operation state of the power system is closer to the real operation state, the linear power flow model is updated according to the mapping relation between the injection power of the node and the corrected operation state of the power system, and the analytic probability power flow calculation is carried out by utilizing the updated linear power flow model, so that the probability power flow calculation precision is effectively improved.

Description

一种解析式概率潮流计算方法、装置及存储介质An analytical probabilistic power flow calculation method, device and storage medium

技术领域technical field

本发明涉及电力系统运行分析技术领域，尤其涉及一种解析式概率潮流计算方法、装置及存储介质。The invention relates to the technical field of power system operation analysis, in particular to an analytical probabilistic power flow calculation method, device and storage medium.

背景技术Background technique

大规模风电并网将会给电力系统带来不可忽视的随机性。在电力系统运行中，这种注入功率的随机性的影响之一是造成线路传输功率出现波动，甚至出现线路过载。为了量化评估这种由风电随机性引起的线路潮流越限风险，采用概率潮流(ProbabilisticLoad Flow，PLF)计算方法来分析风电并网后电力系统的运行情况。常用的概率潮流计算方法有蒙特卡洛仿真法(Monte Carlo Simulation Method，MCSM)。蒙特卡洛仿真法的最大缺点在于需要大规模采样数据，耗时较长。为了快速准确地进行概率潮流计算，尤其是计算多条线路功率的联合概率分布，迫切要求发展解析式概率潮流计算方法。但现有的解析式概率潮流计算方法往往仅利用线性潮流模型实现节点注入功率到电力系统运行状态的映射，在计算精度上有所欠缺，如何有效提高概率潮流计算精度，成为当前的研究热点。The integration of large-scale wind power into the grid will bring randomness that cannot be ignored to the power system. In the operation of the power system, one of the effects of the randomness of the injected power is to cause fluctuations in the transmission power of the line, or even overloading of the line. In order to quantitatively evaluate the line power flow over-limit risk caused by the randomness of wind power, the Probabilistic Load Flow (PLF) calculation method is used to analyze the operation of the power system after wind power is connected to the grid. The commonly used probabilistic power flow calculation method is Monte Carlo Simulation Method (MCSM). The biggest disadvantage of the Monte Carlo simulation method is that it requires large-scale sampling of data, which takes a long time. In order to perform probabilistic power flow calculation quickly and accurately, especially to calculate the joint probability distribution of power of multiple lines, it is urgent to develop analytical probabilistic power flow calculation methods. However, the existing analytical probabilistic power flow calculation methods often only use the linear power flow model to realize the mapping of the node injected power to the operating state of the power system, which is lacking in calculation accuracy. How to effectively improve the probabilistic power flow calculation accuracy has become a current research focus.

发明内容SUMMARY OF THE INVENTION

为了克服现有技术的缺陷，本发明提供一种解析式概率潮流计算方法、装置及存储介质，能够有效提高概率潮流计算精度。In order to overcome the defects of the prior art, the present invention provides an analytical method, device and storage medium for probabilistic power flow calculation, which can effectively improve the probabilistic power flow calculation accuracy.

为了解决上述技术问题，第一方面，本发明一实施例提供一种解析式概率潮流计算方法，包括：In order to solve the above technical problems, in a first aspect, an embodiment of the present invention provides an analytical method for calculating probabilistic power flow, including:

根据接入电力系统的节点的注入功率，构建高斯混合模型，并采用EM算法，根据所述节点的注入功率的历史数据得到所述高斯混合模型的参数集，基于所述参数集更新所述高斯混合模型；According to the injected power of the node connected to the power system, a Gaussian mixture model is constructed, and the EM algorithm is used to obtain the parameter set of the Gaussian mixture model according to the historical data of the injected power of the node, and the Gaussian mixture model is updated based on the parameter set. mixed model;

根据所述电力系统的电导、电纳信息和所述节点的注入功率，构建线性潮流模型，以通过所述线性潮流模型确定所述节点的注入功率与所述电力系统的运行状态之间的映射关系；According to the conductance and susceptance information of the power system and the injected power of the node, a linear power flow model is constructed to determine the mapping between the injected power of the node and the operating state of the power system through the linear power flow model relation;

采用一阶多项式拟合校正方法修正所述电力系统的运行状态，并根据所述节点的注入功率与修正后的电力系统的运行状态之间的映射关系，更新所述线性潮流模型；A first-order polynomial fitting correction method is used to correct the operating state of the power system, and the linear power flow model is updated according to the mapping relationship between the injected power of the node and the corrected operating state of the power system;

通过所述高斯混合模型和所述线性潮流模型，将所述节点的注入功率的概率分布映射到所述修正后的电力系统的运行状态的概率分布，得到所述电力系统的运行状态的概率潮流。Through the Gaussian mixture model and the linear power flow model, the probability distribution of the injected power of the node is mapped to the probability distribution of the corrected operating state of the power system to obtain the probability power flow of the operating state of the power system .

进一步地，所述高斯混合模型为：Further, the Gaussian mixture model is:

Figure BDA0003500462650000021
Figure BDA0003500462650000021

其中，ωj为第j个高斯分量的权重系数，ωj>0，

Figure BDA0003500462650000022
J为高斯分量的总数；
Figure BDA0003500462650000023
Nj(·)为第j个高斯分量，X为所述节点的注入功率，μj、σj分别为第j个高斯分量的均值向量和协方差矩阵，W为所述节点的注入功率的维度，det(.)为矩阵行列式，T表示矩阵的转置。Among them, ω j is the weight coefficient of the jth Gaussian component, ω j >0,
Figure BDA0003500462650000022
J is the total number of Gaussian components;
Figure BDA0003500462650000023
N j ( ) is the j-th Gaussian component, X is the injection power of the node, μ j and σ j are the mean vector and covariance matrix of the j-th Gaussian component, respectively, and W is the injection power of the node. Dimension, det(.) is the matrix determinant, and T is the transpose of the matrix.

进一步地，所述线性潮流模型为：Further, the linear power flow model is:

Figure BDA0003500462650000024
Figure BDA0003500462650000024

其中，θ、V分别为所述节点的电压相角和电压幅值，P、Q分别为所述节点的注入功率中的有功功率和无功功率，下标R表示Vθ节点构成的集合，K表示PV节点和Vθ节点构成的集合，S表示PV节点和PQ节点构成的集合，

Figure BDA0003500462650000025
表示PQ节点构成的集合，Vθ节点表示电压幅值和电压相位给定，有功功率和无功功率是待求量的节点，PV节点表示有功功率和电压幅值给定，无功功率和电压相位是待求量的节点，PQ节点表示有功功率和无功功率给定，电压幅值和电压相位是待求量的节点；Λ、C均为由所述电力系统的电导、电纳信息构成的参数矩阵，
Figure BDA0003500462650000031
G、B分别为电导矩阵和电纳矩阵，上标'表示忽略所有接地支路的电纳矩阵，N为PV节点和PQ节点的个数之和，M为PQ节点的个数。Among them, θ and V are the voltage phase angle and voltage amplitude of the node, respectively, P and Q are the active power and reactive power in the injected power of the node, respectively, the subscript R represents the set composed of Vθ nodes, and K represents the set composed of PV nodes and Vθ nodes, S represents the set composed of PV nodes and PQ nodes,
Figure BDA0003500462650000025
Represents the set of PQ nodes, Vθ node represents the given voltage amplitude and voltage phase, active power and reactive power are the nodes to be calculated, PV node represents the active power and voltage amplitude given, reactive power and voltage phase is the node of the quantity to be calculated, the PQ node represents the given active power and reactive power, and the voltage amplitude and voltage phase are the nodes of the quantity to be calculated; Λ and C are both composed of the conductance and susceptance information of the power system parameter matrix,
Figure BDA0003500462650000031
G and B are the conductance matrix and the susceptance matrix, respectively, the superscript ' indicates the susceptance matrix ignoring all grounding branches, N is the sum of the number of PV nodes and PQ nodes, and M is the number of PQ nodes.

进一步地，所述节点的注入功率与所述电力系统的运行状态之间的映射关系，为：Further, the mapping relationship between the injected power of the node and the operating state of the power system is:

Figure BDA0003500462650000032
Figure BDA0003500462650000032

其中，Y为所述电力系统的运行状态，X为所述节点的注入功率，

Figure BDA0003500462650000033
β和γ均为预设参数，T表示矩阵的转置。Among them, Y is the operating state of the power system, X is the injected power of the node,
Figure BDA0003500462650000033
Both β and γ are preset parameters, and T represents the transpose of the matrix.

进一步地，所述采用一阶多项式拟合校正方法修正所述电力系统的运行状态，具体为：Further, the first-order polynomial fitting correction method is used to correct the operating state of the power system, specifically:

随机生成多组功率数据作为多组所述节点的注入功率，采用交流潮流计算方法得到多组电力系统的实际运行状态，以及通过所述线性潮流模型得到多组电力系统的理论运行状态；Randomly generating multiple sets of power data as the injected power of multiple sets of the nodes, using the AC power flow calculation method to obtain the actual operating states of the multiple sets of power systems, and obtaining the theoretical operating states of the multiple sets of power systems through the linear power flow model;

将多组所述电力系统的实际运行状态和多组所述电力系统的理论运行状态代入预先定义的一阶多项式方程，得到所述一阶多项式方程的系数，并基于所述系数更新所述一阶多项式方程；Substitute multiple sets of the actual operating states of the power system and multiple sets of the theoretical operating states of the power system into a pre-defined first-order polynomial equation, obtain coefficients of the first-order polynomial equation, and update the first-order polynomial equation based on the coefficients. order polynomial equation;

在通过所述线性潮流模型得到所述电力系统的运行状态后，将所述电力系统的运行状态代入所述一阶多项式方程，得到所述修正后的电力系统的运行状态。After the operating state of the power system is obtained through the linear power flow model, the operating state of the power system is substituted into the first-order polynomial equation to obtain the corrected operating state of the power system.

进一步地，所述一阶多项式方程为：Further, the first-order polynomial equation is:

Y(AC)＝ρY+ζ；Y (AC) =ρY+ζ;

其中，Y(AC)为所述电力系统的实际运行状态，Y为所述电力系统的理论运行状态，ρ和

Figure BDA0003500462650000041
均为所述系数。where Y (AC) is the actual operating state of the power system, Y is the theoretical operating state of the power system, ρ and
Figure BDA0003500462650000041
are the coefficients.

进一步地，所述修正后的电力系统的运行状态为：Further, the modified operating state of the power system is:

Figure BDA0003500462650000042
Figure BDA0003500462650000042

其中，X为所述节点的注入功率，Λ、C均为由所述电力系统的电导、电纳信息构成的参数矩阵，

Figure BDA0003500462650000043
β和γ均为预设参数，T表示矩阵的转置，N为PV节点和PQ节点的个数之和，M为PQ节点的个数，PV节点表示有功功率和电压幅值给定，无功功率和电压相位是待求量的节点，PQ节点表示有功功率和无功功率给定，电压幅值和电压相位是待求量的节点。Among them, X is the injected power of the node, Λ and C are parameter matrices composed of the conductance and susceptance information of the power system,
Figure BDA0003500462650000043
β and γ are preset parameters, T represents the transpose of the matrix, N is the sum of the number of PV nodes and PQ nodes, M is the number of PQ nodes, PV node represents the given active power and voltage amplitude, no The active power and voltage phase are the nodes to be calculated, the PQ node represents the given active power and reactive power, and the voltage amplitude and voltage phase are the nodes to be calculated.

进一步地，所述参数集包括各个高斯分量的权重系数、均值向量和协方差矩阵。Further, the parameter set includes the weight coefficient, mean vector and covariance matrix of each Gaussian component.

第二方面，本发明一实施例提供一种解析式概率潮流计算装置，包括：In a second aspect, an embodiment of the present invention provides an analytical probabilistic power flow calculation device, including:

高斯混合模型构建模块，用于根据接入电力系统的节点的注入功率，构建高斯混合模型，并采用EM算法，根据所述节点的注入功率的历史数据得到所述高斯混合模型的参数集，基于所述参数集更新所述高斯混合模型；The Gaussian mixture model building module is used to construct a Gaussian mixture model according to the injected power of the node connected to the power system, and the EM algorithm is used to obtain the parameter set of the Gaussian mixture model according to the historical data of the injected power of the node, based on the parameter set updates the Gaussian mixture model;

线性潮流模型构建模块，用于根据所述电力系统的电导、电纳信息和所述节点的注入功率，构建线性潮流模型，以通过所述线性潮流模型确定所述节点的注入功率与所述电力系统的运行状态之间的映射关系；A linear power flow model building module, configured to construct a linear power flow model according to the conductance and susceptance information of the power system and the injected power of the node, so as to determine the injected power of the node and the electric power through the linear power flow model The mapping relationship between the operating states of the system;

运行状态修正模块，用于采用一阶多项式拟合校正方法修正所述电力系统的运行状态，并根据所述节点的注入功率与修正后的电力系统的运行状态之间的映射关系，更新所述线性潮流模型；an operating state correction module, configured to use a first-order polynomial fitting correction method to correct the operating state of the power system, and update the operating state of the power system according to the mapping relationship between the injected power of the node and the corrected operating state of the power system Linear power flow model;

概率潮流计算模块，用于通过所述高斯混合模型和所述线性潮流模型，将所述节点的注入功率的概率分布映射到所述修正后的电力系统的运行状态的概率分布，得到所述电力系统的运行状态的概率潮流。A probability power flow calculation module, configured to map the probability distribution of the injected power of the node to the probability distribution of the modified operating state of the power system through the Gaussian mixture model and the linear power flow model, and obtain the power The probabilistic power flow of the operating state of the system.

第三方面，本发明一实施例提供一种计算机可读存储介质，所述计算机可读存储介质包括存储的计算机程序；其中，在所述计算机程序运行时控制所述计算机可读存储介质所在设备执行如上所述的解析式概率潮流计算方法。In a third aspect, an embodiment of the present invention provides a computer-readable storage medium, where the computer-readable storage medium includes a stored computer program; wherein, when the computer program runs, a device where the computer-readable storage medium is located is controlled Perform the analytical probabilistic power flow calculation method described above.

本发明的实施例，具有如下有益效果：The embodiment of the present invention has the following beneficial effects:

通过根据接入电力系统的节点的注入功率，构建高斯混合模型，并采用EM算法，根据节点的注入功率的历史数据得到高斯混合模型的参数集，基于参数集更新高斯混合模型，根据电力系统的电导、电纳信息和节点的注入功率，构建线性潮流模型，以通过线性潮流模型确定节点的注入功率与电力系统的运行状态之间的映射关系，采用一阶多项式拟合校正方法修正电力系统的运行状态，并根据节点的注入功率与修正后的电力系统的运行状态之间的映射关系，更新线性潮流模型，通过高斯混合模型和线性潮流模型，将节点的注入功率的概率分布映射到修正后的电力系统的运行状态的概率分布，得到电力系统的运行状态的概率潮流，完成计算概率潮流。相比于现有技术，本发明的实施例在通过线性潮流模型确定节点的注入功率与电力系统的运行状态之间的映射关系后，采用一阶多项式拟合校正方法修正电力系统的运行状态，使修正后的电力系统的运行状态更加接近真实的运行状态，根据节点的注入功率与修正后的电力系统的运行状态之间的映射关系，更新线性潮流模型，利用更新后的线性潮流模型进行解析式概率潮流计算，从而有效提高概率潮流计算精度。By constructing a Gaussian mixture model according to the injected power of the node connected to the power system, and using the EM algorithm, the parameter set of the Gaussian mixture model is obtained according to the historical data of the injected power of the node, and the Gaussian mixture model is updated based on the parameter set. Conductance, susceptance information and the injected power of the node, build a linear power flow model to determine the mapping relationship between the injected power of the node and the operating state of the power system through the linear power flow model, and use the first-order polynomial fitting correction method to correct the power system. According to the mapping relationship between the injected power of the node and the revised operating state of the power system, the linear power flow model is updated, and the probability distribution of the injected power of the node is mapped to the corrected power flow through the Gaussian mixture model and the linear power flow model. The probability distribution of the operating state of the power system is obtained, the probability power flow of the operating state of the power system is obtained, and the calculation of the probability power flow is completed. Compared with the prior art, in the embodiment of the present invention, after determining the mapping relationship between the injected power of the node and the operating state of the power system through a linear power flow model, the first-order polynomial fitting correction method is used to correct the operating state of the power system, Make the operating state of the revised power system closer to the real operating state, update the linear power flow model according to the mapping relationship between the injected power of the node and the operating state of the revised power system, and use the updated linear power flow model for analysis Probabilistic power flow calculation can effectively improve the accuracy of probability power flow calculation.

附图说明Description of drawings

图1为本发明第一实施例中的一种解析式概率潮流计算方法的流程示意图；1 is a schematic flowchart of an analytical method for calculating probabilistic power flow in the first embodiment of the present invention;

图2为本发明第二实施例中的一种解析式概率潮流计算装置的结构示意图。FIG. 2 is a schematic structural diagram of an analytical probabilistic power flow calculation device in a second embodiment of the present invention.

具体实施方式Detailed ways

下面将结合本发明中的附图，对本发明中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

需要说明的是，文中的步骤编号，仅为了方便具体实施例的解释，不作为限定步骤执行先后顺序的作用。本实施例提供的方法可以由相关的终端设备执行，且下文均以处理器作为执行主体为例进行说明。It should be noted that the step numbers in the text are only for the convenience of the explanation of the specific embodiment, and do not serve as a function of limiting the order of execution of the steps. The method provided in this embodiment may be executed by a related terminal device, and the following description will be made by taking a processor as an execution subject as an example.

如图1所示，第一实施例提供一种解析式概率潮流计算方法，包括步骤S1～S4：As shown in FIG. 1 , the first embodiment provides an analytical probabilistic power flow calculation method, including steps S1 to S4:

S1、根据接入电力系统的节点的注入功率，构建高斯混合模型，并采用EM算法，根据节点的注入功率的历史数据得到高斯混合模型的参数集，基于参数集更新高斯混合模型；S1. Construct a Gaussian mixture model according to the injected power of the node connected to the power system, and use the EM algorithm to obtain a parameter set of the Gaussian mixture model according to the historical data of the injected power of the node, and update the Gaussian mixture model based on the parameter set;

S2、根据电力系统的电导、电纳信息和节点的注入功率，构建线性潮流模型，以通过线性潮流模型确定节点的注入功率与电力系统的运行状态之间的映射关系；S2. According to the conductance and susceptance information of the power system and the injected power of the node, a linear power flow model is constructed to determine the mapping relationship between the injected power of the node and the operating state of the power system through the linear power flow model;

S3、采用一阶多项式拟合校正方法修正电力系统的运行状态，并根据节点的注入功率与修正后的电力系统的运行状态之间的映射关系，更新线性潮流模型；S3, using the first-order polynomial fitting correction method to correct the operating state of the power system, and updating the linear power flow model according to the mapping relationship between the injected power of the node and the corrected operating state of the power system;

S4、通过高斯混合模型和线性潮流模型，将节点的注入功率的概率分布映射到修正后的电力系统的运行状态的概率分布，得到电力系统的运行状态的概率潮流。S4. Through the Gaussian mixture model and the linear power flow model, the probability distribution of the injected power of the node is mapped to the probability distribution of the corrected operating state of the power system, and the probability power flow of the operating state of the power system is obtained.

本实施例在通过线性潮流模型确定节点的注入功率与电力系统的运行状态之间的映射关系后，采用一阶多项式拟合校正方法修正电力系统的运行状态，使修正后的电力系统的运行状态更加接近真实的运行状态，根据节点的注入功率与修正后的电力系统的运行状态之间的映射关系，更新线性潮流模型，利用更新后的线性潮流模型进行解析式概率潮流计算，从而有效提高概率潮流计算精度。In this embodiment, after the linear power flow model is used to determine the mapping relationship between the injected power of the node and the operating state of the power system, the first-order polynomial fitting correction method is used to correct the operating state of the power system, so that the corrected operating state of the power system is It is closer to the real operating state. According to the mapping relationship between the injected power of the node and the revised operating state of the power system, the linear power flow model is updated, and the updated linear power flow model is used for analytical probabilistic power flow calculation, thereby effectively improving the probability of Power flow calculation accuracy.

在优选的实施例当中，高斯混合模型为：In a preferred embodiment, the Gaussian mixture model is:

Figure BDA0003500462650000061
Figure BDA0003500462650000061

其中，ωj为第j个高斯分量的权重系数，ωj>0，

Figure BDA0003500462650000062
J为高斯分量的总数；
Figure BDA0003500462650000071
Nj(·)为第j个高斯分量，X为节点的注入功率，μj、σj分别为第j个高斯分量的均值向量和协方差矩阵，W为节点的注入功率的维度，det(.)为矩阵行列式，T表示矩阵的转置。Among them, ω j is the weight coefficient of the jth Gaussian component, ω j >0,
Figure BDA0003500462650000062
J is the total number of Gaussian components;
Figure BDA0003500462650000071
N j ( ) is the jth Gaussian component, X is the injected power of the node, μ j and σ j are the mean vector and covariance matrix of the jth Gaussian component, W is the dimension of the injected power of the node, det( .) is the matrix determinant, and T represents the transpose of the matrix.

在本实施例的一优选实施方式中，参数集包括各个高斯分量的权重系数、均值向量和协方差矩阵。In a preferred implementation of this embodiment, the parameter set includes the weight coefficient, mean vector and covariance matrix of each Gaussian component.

作为示例性地，高斯混合模型(Gaussian mixture model，GMM)用于描述一个随机向量X的联合概率分布，它被定义为多个高斯分布函数的凸组合，记符号Ω＝{ωj,μj,σj；j＝1,2,…J}为GMM的可调参数集。As an example, a Gaussian mixture model (GMM) is used to describe the joint probability distribution of a random vector X, which is defined as a convex combination of multiple Gaussian distribution functions, denoted by the notation Ω={ω j , μ j ,σ j ; j=1,2,...J} is the adjustable parameter set of GMM.

GMM的数学表达式如式(1)所示：The mathematical expression of GMM is shown in formula (1):

Figure BDA0003500462650000072
Figure BDA0003500462650000072

式(1)中，ωj为第j个高斯分量的权重系数，ωj>0，

Figure BDA0003500462650000073
J为高斯分量的总数；
Figure BDA0003500462650000074
Nj(·)为第j个高斯分量，X为节点的注入功率，μj、σj分别为第j个高斯分量的均值向量和协方差矩阵，W为节点的注入功率的维度，det(.)为矩阵行列式，T表示矩阵的转置。In formula (1), ω j is the weight coefficient of the jth Gaussian component, ω j >0,
Figure BDA0003500462650000073
J is the total number of Gaussian components;
Figure BDA0003500462650000074
N j ( ) is the jth Gaussian component, X is the injected power of the node, μ j and σ j are the mean vector and covariance matrix of the jth Gaussian component, W is the dimension of the injected power of the node, det( .) is the matrix determinant, and T represents the transpose of the matrix.

在本实施例的一优选实施方式中，参数集包括各个高斯分量的权重系数、均值向量和协方差矩阵。In a preferred implementation of this embodiment, the parameter set includes the weight coefficient, mean vector and covariance matrix of each Gaussian component.

可以理解的是，确定GMM的参数集Ω是一个典型的参数估计问题。如果随机变量X为公式(1)所示的GMM所表征，并且随机变量Y是满足Y＝AX+C的X的线性变换，那么Y的分布也是一个GMM，该GMM的每个分量是均值为Aμj+C，协方差矩阵为A∑jAT的高斯分布，权重系数为ωj。It can be understood that determining the parameter set Ω of GMM is a typical parameter estimation problem. If the random variable X is represented by the GMM shown in formula (1), and the random variable Y is a linear transformation of X satisfying Y=AX+C, then the distribution of Y is also a GMM, and each component of the GMM is the mean Aμ j +C, the covariance matrix is the Gaussian distribution of A∑ j A T , and the weight coefficient is ω j .

基于X的历史数据，可以采用极大似然估计技术获得GMM的参数集。典型的算法包括期望最大化算法(Expectation Maximization，EM)。EM算法通过E步骤和M步骤的迭代计算，最终实现对GMM参数的估计。Based on the historical data of X, the maximum likelihood estimation technique can be used to obtain the parameter set of the GMM. Typical algorithms include Expectation Maximization (EM). The EM algorithm finally realizes the estimation of GMM parameters through the iterative calculation of E-step and M-step.

作为示例性地，针对GMM中第j个高斯分量的第k次迭代计算过程如式(2)～(5)：As an example, the calculation process of the k-th iteration for the j-th Gaussian component in the GMM is as formulas (2) to (5):

Figure BDA0003500462650000081
Figure BDA0003500462650000081

Figure BDA0003500462650000082
Figure BDA0003500462650000082

Figure BDA0003500462650000083
Figure BDA0003500462650000083

Figure BDA0003500462650000084
Figure BDA0003500462650000084

其中，

Figure BDA0003500462650000085
是第n条历史数据。in,
Figure BDA0003500462650000085
is the nth historical data.

在优选的实施例当中，线性潮流模型为：In a preferred embodiment, the linear power flow model is:

Figure BDA0003500462650000086
Figure BDA0003500462650000086

其中，θ、V分别为节点的电压相角和电压幅值，P、Q分别为节点的注入功率中的有功功率和无功功率，下标R表示Vθ节点构成的集合，K表示PV节点和Vθ节点构成的集合，S表示PV节点和PQ节点构成的集合，

Figure BDA0003500462650000087
表示PQ节点构成的集合，Vθ节点表示电压幅值和电压相位给定，有功功率和无功功率是待求量的节点，PV节点表示有功功率和电压幅值给定，无功功率和电压相位是待求量的节点，PQ节点表示有功功率和无功功率给定，电压幅值和电压相位是待求量的节点；Λ、C均为由电力系统的电导、电纳信息构成的参数矩阵，
Figure BDA0003500462650000088
G、B分别为电导矩阵和电纳矩阵，上标'表示忽略所有接地支路的电纳矩阵，N为PV节点和PQ节点的个数之和，M为PQ节点的个数。Among them, θ and V are the voltage phase angle and voltage amplitude of the node, respectively, P and Q are the active power and reactive power in the injected power of the node, respectively, the subscript R represents the set formed by the Vθ node, K represents the PV node and The set composed of Vθ nodes, S represents the set composed of PV nodes and PQ nodes,
Figure BDA0003500462650000087
Represents the set of PQ nodes, Vθ node represents the given voltage amplitude and voltage phase, active power and reactive power are the nodes to be calculated, PV node represents the active power and voltage amplitude given, reactive power and voltage phase is the node of the quantity to be calculated, the PQ node represents the given active power and reactive power, the voltage amplitude and voltage phase are the nodes of the quantity to be calculated; Λ and C are the parameter matrix composed of the conductance and susceptance information of the power system ,
Figure BDA0003500462650000088
G and B are the conductance matrix and the susceptance matrix, respectively, the superscript ' indicates the susceptance matrix ignoring all grounding branches, N is the sum of the number of PV nodes and PQ nodes, and M is the number of PQ nodes.

作为示例性地，线性潮流模型为一种不依赖于运行点的电压相角解耦的线性潮流(Stateindependent Voltageangle Decoupled Linearized Power Flow，DLPF)模型，线性潮流模型的数学表达式如式(6)所示：As an example, the linear power flow model is a state-independent Voltageangle Decoupled Linearized Power Flow (DLPF) model that does not depend on the voltage phase angle of the operating point. The mathematical expression of the linear power flow model is as shown in Equation (6). Show:

Figure BDA0003500462650000089
Figure BDA0003500462650000089

式(6)中，θ、V分别为节点的电压相角和电压幅值，P、Q分别为节点的注入功率中的有功功率和无功功率，下标R表示Vθ节点构成的集合，K表示PV节点和Vθ节点构成的集合，S表示PV节点和PQ节点构成的集合，

Figure BDA0003500462650000091
表示PQ节点构成的集合，Vθ节点表示电压幅值和电压相位给定，有功功率和无功功率是待求量的节点，PV节点表示有功功率和电压幅值给定，无功功率和电压相位是待求量的节点，PQ节点表示有功功率和无功功率给定，电压幅值和电压相位是待求量的节点；Λ、C均为由电力系统的电导、电纳信息构成的参数矩阵，
Figure BDA0003500462650000092
G、B分别为电导矩阵和电纳矩阵，上标'表示忽略所有接地支路的电纳矩阵，N为PV节点和PQ节点的个数之和，M为PQ节点的个数。In formula (6), θ and V are the voltage phase angle and voltage amplitude of the node, respectively, P and Q are the active power and reactive power in the injected power of the node, respectively, the subscript R represents the set of nodes Vθ, and K represents the set composed of PV nodes and Vθ nodes, S represents the set composed of PV nodes and PQ nodes,
Figure BDA0003500462650000091
Represents the set of PQ nodes, Vθ node represents the given voltage amplitude and voltage phase, active power and reactive power are the nodes to be calculated, PV node represents the active power and voltage amplitude given, reactive power and voltage phase is the node of the quantity to be calculated, the PQ node represents the given active power and reactive power, the voltage amplitude and voltage phase are the nodes of the quantity to be calculated; Λ and C are the parameter matrix composed of the conductance and susceptance information of the power system ,
Figure BDA0003500462650000092
G and B are the conductance matrix and the susceptance matrix, respectively, the superscript ' indicates the susceptance matrix ignoring all grounding branches, N is the sum of the number of PV nodes and PQ nodes, and M is the number of PQ nodes.

在优选的实施例当中，节点的注入功率与电力系统的运行状态之间的映射关系，为：In a preferred embodiment, the mapping relationship between the injected power of the node and the operating state of the power system is:

Figure BDA0003500462650000093
Figure BDA0003500462650000093

其中，Y为电力系统的运行状态，X为节点的注入功率，

Figure BDA0003500462650000094
β和γ均为预设参数，T表示矩阵的转置。Among them, Y is the operating state of the power system, X is the injected power of the node,
Figure BDA0003500462650000094
Both β and γ are preset parameters, and T represents the transpose of the matrix.

作为示例性地，采用式(6)所示的线性潮流模型描述各节点的注入功率

Figure BDA0003500462650000095
与电力系统的运行状态
Figure BDA0003500462650000096
之间的映射关系。考虑到风力发电机注入功率的随机性，各节点注入的有功功率PS和无功功率QL分别满足式(8)、(9)：As an example, the linear power flow model shown in equation (6) is used to describe the injected power of each node
Figure BDA0003500462650000095
with the operating status of the power system
Figure BDA0003500462650000096
mapping relationship between them. Considering the randomness of the injected power of wind turbines, the active power P S and reactive power QL injected by each node satisfy equations (8) and (9) respectively:

Figure BDA0003500462650000097
Figure BDA0003500462650000097

Figure BDA0003500462650000098
Figure BDA0003500462650000098

其中，in,

Figure BDA0003500462650000101
Figure BDA0003500462650000101

Figure BDA0003500462650000102
Figure BDA0003500462650000102

Figure BDA0003500462650000103
Figure BDA0003500462650000103

Figure BDA0003500462650000104
Figure BDA0003500462650000104

β和γ均为已知量。β and γ are known quantities.

根据电力系统的电导、电纳信息，形成Λ和C矩阵，从而形成如式(6)所示的DLPF模型表达式。According to the conductance and susceptance information of the power system, the Λ and C matrices are formed, thereby forming the DLPF model expression as shown in equation (6).

根据DLPF模型表达式，构建Y与X如式(7)所示的线性变换关系。According to the DLPF model expression, the linear transformation relationship between Y and X as shown in Equation (7) is constructed.

在优选的实施例当中，所述采用一阶多项式拟合校正方法修正所述电力系统的运行状态，具体为：随机生成多组功率数据作为多组节点的注入功率，采用交流潮流计算方法得到多组电力系统的实际运行状态，以及通过线性潮流模型得到多组电力系统的理论运行状态；将多组电力系统的实际运行状态和多组电力系统的理论运行状态代入预先定义的一阶多项式方程，得到一阶多项式方程的系数，并基于系数更新一阶多项式方程；在通过线性潮流模型得到电力系统的运行状态后，将电力系统的运行状态代入一阶多项式方程，得到修正后的电力系统的运行状态。In a preferred embodiment, the first-order polynomial fitting correction method is used to correct the operating state of the power system, specifically: randomly generating multiple sets of power data as the injected power of multiple sets of nodes, and using an AC power flow calculation method to obtain multiple sets of power data. The actual operating state of the power system of the group of power systems, and the theoretical operating state of the power system of the multiple groups of power systems are obtained through the linear power flow model; The coefficients of the first-order polynomial equation are obtained, and the first-order polynomial equation is updated based on the coefficients; after obtaining the operating state of the power system through the linear power flow model, the operating state of the power system is substituted into the first-order polynomial equation to obtain the revised operation of the power system. state.

在本实施例的一优选实施方式中，一阶多项式方程为：In a preferred implementation of this embodiment, the first-order polynomial equation is:

Y(AC)＝ρY+ζ (10)；Y (AC) =ρY+ζ(10);

其中，Y(AC)为电力系统的实际运行状态，Y为电力系统的理论运行状态，ρ和

Figure BDA0003500462650000105
均为系数。Among them, Y (AC) is the actual operating state of the power system, Y is the theoretical operating state of the power system, ρ and
Figure BDA0003500462650000105
are all coefficients.

在本实施例的一优选实施方式中，修正后的电力系统的运行状态为：In a preferred implementation of this embodiment, the corrected operating state of the power system is:

Figure BDA0003500462650000106
Figure BDA0003500462650000106

其中，X为节点的注入功率，Λ、C均为由电力系统的电导、电纳信息构成的参数矩阵，

Figure BDA0003500462650000107
β和γ均为预设参数，T表示矩阵的转置，N为PV节点和PQ节点的个数之和，M为PQ节点的个数，PV节点表示有功功率和电压幅值给定，无功功率和电压相位是待求量的节点，PQ节点表示有功功率和无功功率给定，电压幅值和电压相位是待求量的节点。Among them, X is the injected power of the node, Λ and C are the parameter matrix composed of the conductance and susceptance information of the power system,
Figure BDA0003500462650000107
β and γ are preset parameters, T represents the transpose of the matrix, N is the sum of the number of PV nodes and PQ nodes, M is the number of PQ nodes, PV node represents the given active power and voltage amplitude, no The active power and voltage phase are the nodes to be calculated, the PQ node represents the given active power and reactive power, and the voltage amplitude and voltage phase are the nodes to be calculated.

作为示例性地，采用一阶多项式拟合校正方法，对DLPF模型得到的电力系统的运行状态进行修正，具体如下：As an example, the first-order polynomial fitting correction method is used to correct the operating state of the power system obtained by the DLPF model, as follows:

首先，随机生成H组节点的注入功率

Figure BDA0003500462650000111
其中H的取值可以是一个较小的数字，比如12。First, randomly generate the injected power of H group nodes
Figure BDA0003500462650000111
The value of H can be a small number, such as 12.

然后，根据H组不同的节点的注入功率，利用交流潮流计算方法得到H组电力系统的实际运行状态：Then, according to the injected power of different nodes in group H, the actual operating state of the power system in group H is obtained by using the AC power flow calculation method:

Figure BDA0003500462650000112
Figure BDA0003500462650000112

并利用DLPF模型得到H组电力系统的理论运行状态Y：And use the DLPF model to obtain the theoretical operating state Y of the H group power system:

Figure BDA0003500462650000113
Figure BDA0003500462650000113

合理地假设Y(AC)和Y间满足仿射变换关系：It is reasonable to assume that the affine transformation relationship between Y (AC) and Y is satisfied:

Figure BDA0003500462650000114
Figure BDA0003500462650000114

最后，利用H组Y(AC)和Y的数据，通过一阶多项式拟合获得ρ和

Figure BDA0003500462650000115
Finally, using the data of H groups Y (AC) and Y, obtain ρ and
Figure BDA0003500462650000115

通过对DLPF模型得到的电力系统的运行状态Y进行修正，得到了和交流潮流计算结果Y(AC)几乎完全一致的电力系统的运行状态Yp即，以Y(AC)作为真实的运行状态，相比于DLPF模型得到的电力系统运行状态Y，修正后的Yp与Y(AC)几乎完全一致，从而有利于实现了高精度的线性潮流计算。By correcting the operating state Y of the power system obtained by the DLPF model, the operating state Y p of the power system that is almost identical to the AC power flow calculation result Y (AC) is obtained. That is, taking Y (AC) as the real operating state, Compared with the power system operating state Y obtained by the DLPF model, the corrected Y p is almost identical to Y (AC) , which is conducive to the realization of high-precision linear power flow calculation.

根据DLPF推导出节点的注入功率X和电力系统的运行状态Y间的表达式(7)，结合Y(AC)和Y间所满足的仿射变换关系式(14)，得到如式(15)所示的高精度的电力系统的运行状态的表达式：According to the DLPF, the expression (7) between the injected power X of the node and the operating state Y of the power system is deduced. Combined with the affine transformation relationship (14) satisfied between Y (AC) and Y, the formula (15) is obtained. The expression of the operating state of the power system with high precision is shown:

Figure BDA0003500462650000116
Figure BDA0003500462650000116

结合GMM的线性不变性，可以解析地将节点的注入功率X的概率分布映射到电力系统的运行状态Yp的概率分布。由于Yp与Y(AC)几乎完全一致，从而实现了高精度的解析式概率潮流计算。Combined with the linear invariance of GMM, the probability distribution of the injected power X of a node can be analytically mapped to the probability distribution of the operating state Y p of the power system. Since Y p and Y (AC) are almost identical, high-precision analytical probabilistic power flow calculation is achieved.

基于与第一实施例相同的发明构思，第二实施例提供如图2所示的一种解析式概率潮流计算装置，包括：高斯混合模型构建模块21，用于根据接入电力系统的节点的注入功率，构建高斯混合模型，并采用EM算法，根据所述节点的注入功率的历史数据得到所述高斯混合模型的参数集，基于所述参数集更新所述高斯混合模型；线性潮流模型构建模块22，用于根据所述电力系统的电导、电纳信息和所述节点的注入功率，构建线性潮流模型，以通过所述线性潮流模型确定所述节点的注入功率与所述电力系统的运行状态之间的映射关系；运行状态修正模块23，用于采用一阶多项式拟合校正方法修正所述电力系统的运行状态，并根据所述节点的注入功率与修正后的电力系统的运行状态之间的映射关系，更新所述线性潮流模型；概率潮流计算模块24，用于通过所述高斯混合模型和所述线性潮流模型，将所述节点的注入功率的概率分布映射到所述修正后的电力系统的运行状态的概率分布，得到所述电力系统的运行状态的概率潮流。Based on the same inventive concept as the first embodiment, the second embodiment provides an analytical probabilistic power flow calculation device as shown in FIG. 2 , including: a Gaussian mixture model building module 21 for Inject power, construct a Gaussian mixture model, and use the EM algorithm to obtain the parameter set of the Gaussian mixture model according to the historical data of the injected power of the node, and update the Gaussian mixture model based on the parameter set; Linear power flow model building module 22, for constructing a linear power flow model according to the conductance and susceptance information of the power system and the injected power of the node, so as to determine the injected power of the node and the operating state of the power system through the linear power flow model The mapping relationship between the operating state correction module 23 is used to correct the operating state of the power system by adopting a first-order polynomial fitting correction method, and according to the injected power of the node and the corrected operating state of the power system to update the linear power flow model; the probability power flow calculation module 24 is used to map the probability distribution of the injected power of the node to the modified power through the Gaussian mixture model and the linear power flow model The probability distribution of the operating state of the system is obtained to obtain the probability power flow of the operating state of the power system.

在优选的实施例当中，高斯混合模型为：In a preferred embodiment, the Gaussian mixture model is:

Figure BDA0003500462650000121
Figure BDA0003500462650000121

其中，ωj为第j个高斯分量的权重系数，ωj>0，

Figure BDA0003500462650000122
J为高斯分量的总数；
Figure BDA0003500462650000123
Nj(·)为第j个高斯分量，X为节点的注入功率，μj、σj分别为第j个高斯分量的均值向量和协方差矩阵，W为节点的注入功率的维度，det(.)为矩阵行列式，T表示矩阵的转置。Among them, ω j is the weight coefficient of the jth Gaussian component, ω j >0,
Figure BDA0003500462650000122
J is the total number of Gaussian components;
Figure BDA0003500462650000123
N j ( ) is the jth Gaussian component, X is the injected power of the node, μ j and σ j are the mean vector and covariance matrix of the jth Gaussian component, W is the dimension of the injected power of the node, det( .) is the matrix determinant, and T represents the transpose of the matrix.

在本实施例的一优选实施方式中，参数集包括各个高斯分量的权重系数、均值向量和协方差矩阵。In a preferred implementation of this embodiment, the parameter set includes the weight coefficient, mean vector and covariance matrix of each Gaussian component.

在优选的实施例当中，线性潮流模型为：In a preferred embodiment, the linear power flow model is:

Figure BDA0003500462650000124
Figure BDA0003500462650000124

其中，θ、V分别为节点的电压相角和电压幅值，P、Q分别为节点的注入功率中的有功功率和无功功率，下标R表示Vθ节点构成的集合，K表示PV节点和Vθ节点构成的集合，S表示PV节点和PQ节点构成的集合，

Figure BDA0003500462650000131
表示PQ节点构成的集合，Vθ节点表示电压幅值和电压相位给定，有功功率和无功功率是待求量的节点，PV节点表示有功功率和电压幅值给定，无功功率和电压相位是待求量的节点，PQ节点表示有功功率和无功功率给定，电压幅值和电压相位是待求量的节点；Λ、C均为由电力系统的电导、电纳信息构成的参数矩阵，
Figure BDA0003500462650000132
G、B分别为电导矩阵和电纳矩阵，上标'表示忽略所有接地支路的电纳矩阵，N为PV节点和PQ节点的个数之和，M为PQ节点的个数。Among them, θ and V are the voltage phase angle and voltage amplitude of the node, respectively, P and Q are the active power and reactive power in the injected power of the node, respectively, the subscript R represents the set formed by the Vθ node, K represents the PV node and The set composed of Vθ nodes, S represents the set composed of PV nodes and PQ nodes,
Figure BDA0003500462650000131
Represents the set of PQ nodes, Vθ node represents the given voltage amplitude and voltage phase, active power and reactive power are the nodes to be calculated, PV node represents the active power and voltage amplitude given, reactive power and voltage phase is the node of the quantity to be calculated, the PQ node represents the given active power and reactive power, the voltage amplitude and voltage phase are the nodes of the quantity to be calculated; Λ and C are the parameter matrix composed of the conductance and susceptance information of the power system ,
Figure BDA0003500462650000132
G and B are the conductance matrix and the susceptance matrix, respectively, the superscript ' indicates the susceptance matrix ignoring all grounding branches, N is the sum of the number of PV nodes and PQ nodes, and M is the number of PQ nodes.

在优选的实施例当中，节点的注入功率与电力系统的运行状态之间的映射关系，为：In a preferred embodiment, the mapping relationship between the injected power of the node and the operating state of the power system is:

Figure BDA0003500462650000133
Figure BDA0003500462650000133

其中，Y为电力系统的运行状态，X为节点的注入功率，

Figure BDA0003500462650000134
β和γ均为预设参数，T表示矩阵的转置。Among them, Y is the operating state of the power system, X is the injected power of the node,
Figure BDA0003500462650000134
Both β and γ are preset parameters, and T represents the transpose of the matrix.

在优选的实施例当中，所述采用一阶多项式拟合校正方法修正电力系统的运行状态，具体为：随机生成多组功率数据作为多组节点的注入功率，采用交流潮流计算方法得到多组电力系统的实际运行状态，以及通过线性潮流模型得到多组电力系统的理论运行状态；将多组电力系统的实际运行状态和多组电力系统的理论运行状态代入预先定义的一阶多项式方程，得到一阶多项式方程的系数，并基于系数更新一阶多项式方程；在通过线性潮流模型得到电力系统的运行状态后，将电力系统的运行状态代入一阶多项式方程，得到修正后的电力系统的运行状态。In a preferred embodiment, the first-order polynomial fitting correction method is used to correct the operating state of the power system, specifically: randomly generating multiple sets of power data as the injected power of multiple sets of nodes, and using an AC power flow calculation method to obtain multiple sets of power The actual operating state of the system, and the theoretical operating states of multiple groups of power systems obtained through the linear power flow model; the actual operating states of the multiple groups of power systems and the theoretical operating states of the multiple groups of power systems are substituted into the pre-defined first-order polynomial equations to obtain a The coefficients of the first-order polynomial equation are obtained, and the first-order polynomial equation is updated based on the coefficients; after obtaining the operating state of the power system through the linear power flow model, the operating state of the power system is substituted into the first-order polynomial equation to obtain the revised operating state of the power system.

在本实施例的一优选实施方式中，一阶多项式方程为：In a preferred implementation of this embodiment, the first-order polynomial equation is:

Y(AC)＝ρY+ζ (19)；Y (AC) =ρY+ζ(19);

在本实施例的一优选实施方式中，修正后的电力系统的运行状态为：In a preferred implementation of this embodiment, the corrected operating state of the power system is:

Figure BDA0003500462650000141
Figure BDA0003500462650000141

其中，X为节点的注入功率，Λ、C均为由电力系统的电导、电纳信息构成的参数矩阵，

Figure BDA0003500462650000142
β和γ均为预设参数，T表示矩阵的转置，N为PV节点和PQ节点的个数之和，M为PQ节点的个数，PV节点表示有功功率和电压幅值给定，无功功率和电压相位是待求量的节点，PQ节点表示有功功率和无功功率给定，电压幅值和电压相位是待求量的节点。Among them, X is the injected power of the node, Λ and C are the parameter matrix composed of the conductance and susceptance information of the power system,
Figure BDA0003500462650000142
β and γ are preset parameters, T represents the transpose of the matrix, N is the sum of the number of PV nodes and PQ nodes, M is the number of PQ nodes, PV node represents the given active power and voltage amplitude, no The active power and voltage phase are the nodes to be calculated, the PQ node represents the given active power and reactive power, and the voltage amplitude and voltage phase are the nodes to be calculated.

第三实施例提供一种计算机可读存储介质，计算机可读存储介质包括存储的计算机程序；其中，在计算机程序运行时控制计算机可读存储介质所在设备执行如第一实施例所述的解析式概率潮流计算方法，且能达到与之相同的有益效果。The third embodiment provides a computer-readable storage medium, where the computer-readable storage medium includes a stored computer program; wherein, when the computer program runs, the device where the computer-readable storage medium is located is controlled to execute the analytical expression described in the first embodiment Probabilistic power flow calculation method, and can achieve the same beneficial effect.

综上所述，实施本发明的实施例，具有如下有益效果：To sum up, implementing the embodiments of the present invention has the following beneficial effects:

通过根据接入电力系统的节点的注入功率，构建高斯混合模型，并采用EM算法，根据节点的注入功率的历史数据得到高斯混合模型的参数集，基于参数集更新高斯混合模型，根据电力系统的电导、电纳信息和节点的注入功率，构建线性潮流模型，以通过线性潮流模型确定节点的注入功率与电力系统的运行状态之间的映射关系，采用一阶多项式拟合校正方法修正电力系统的运行状态，并根据节点的注入功率与修正后的电力系统的运行状态之间的映射关系，更新线性潮流模型，通过高斯混合模型和线性潮流模型，将节点的注入功率的概率分布映射到修正后的电力系统的运行状态的概率分布，得到电力系统的运行状态的概率潮流，完成计算概率潮流。本发明的实施例在通过线性潮流模型确定节点的注入功率与电力系统的运行状态之间的映射关系后，采用一阶多项式拟合校正方法修正电力系统的运行状态，使修正后的电力系统的运行状态更加接近真实的运行状态，根据节点的注入功率与修正后的电力系统的运行状态之间的映射关系，更新线性潮流模型，利用更新后的线性潮流模型进行解析式概率潮流计算，从而有效提高概率潮流计算精度。By constructing a Gaussian mixture model according to the injected power of the node connected to the power system, and using the EM algorithm, the parameter set of the Gaussian mixture model is obtained according to the historical data of the injected power of the node, and the Gaussian mixture model is updated based on the parameter set. Conductance, susceptance information and the injected power of the node, build a linear power flow model to determine the mapping relationship between the injected power of the node and the operating state of the power system through the linear power flow model, and use the first-order polynomial fitting correction method to correct the power system. According to the mapping relationship between the injected power of the node and the revised operating state of the power system, the linear power flow model is updated, and the probability distribution of the injected power of the node is mapped to the corrected power flow through the Gaussian mixture model and the linear power flow model. The probability distribution of the operating state of the power system is obtained, the probability power flow of the operating state of the power system is obtained, and the calculation of the probability power flow is completed. In the embodiment of the present invention, after the mapping relationship between the injected power of the node and the operating state of the power system is determined through the linear power flow model, the first-order polynomial fitting correction method is used to correct the operating state of the power system, so that the corrected power system has a The operating state is closer to the real operating state. According to the mapping relationship between the injected power of the node and the revised operating state of the power system, the linear power flow model is updated, and the updated linear power flow model is used for analytical probabilistic power flow calculation, so as to effectively Improve the accuracy of probabilistic power flow calculation.

以上所述是本发明的优选实施方式，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以做出若干改进和润饰，这些改进和润饰也视为本发明的保护范围。The above are the preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, without departing from the principles of the present invention, several improvements and modifications can be made, and these improvements and modifications may also be regarded as It is the protection scope of the present invention.

本领域普通技术人员可以理解实现上述实施例中的全部或部分流程，是可以通过计算机程序来指令相关的硬件来完成，所述的程序可存储于一计算机可读取存储介质中，该程序在执行时，可包括如上述各实施例的流程。其中，所述的存储介质可为磁碟、光盘、只读存储记忆体(Read-Only Memory，ROM)或随机存储记忆体(Random Access Memory，RAM)等。Those of ordinary skill in the art can understand that the realization of all or part of the processes in the above embodiments can be accomplished by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium. During execution, the processes of the above-mentioned embodiments may be included. The storage medium may be a magnetic disk, an optical disk, a read-only memory (Read-Only Memory, ROM), or a random access memory (Random Access Memory, RAM) or the like.

Claims (10)

1. An analytic probability power flow calculation method is characterized by comprising the following steps:
according to the injection power of a node accessed to a power system, constructing a Gaussian mixture model, obtaining a parameter set of the Gaussian mixture model according to historical data of the injection power of the node by adopting an EM (effective electromagnetic range) algorithm, and updating the Gaussian mixture model based on the parameter set;
constructing a linear power flow model according to the conductance and susceptance information of the power system and the injection power of the node, and determining a mapping relation between the injection power of the node and the running state of the power system through the linear power flow model;
correcting the running state of the power system by adopting a first-order polynomial fitting correction method, and updating the linear power flow model according to the mapping relation between the injection power of the node and the corrected running state of the power system;
and mapping the probability distribution of the injection power of the node to the probability distribution of the operation state of the corrected power system through the Gaussian mixture model and the linear power flow model to obtain the probability power flow of the operation state of the power system.
2. The analytical probabilistic power flow calculation method of claim 1, wherein the gaussian mixture model is:
Figure FDA0003500462640000011
wherein, ω isjIs the weight coefficient of the jth Gaussian component, ωj＞0，
Figure FDA0003500462640000012
J is the total number of Gaussian components;
Figure FDA0003500462640000013
Nj(. h) is the jth Gaussian component, X is the injection power of the node, μj、σjRespectively, a mean vector and a covariance matrix of the jth gaussian component, W is the dimension of the injection power of the node, det (.) is a matrix determinant, and T represents a transpose of the matrix.
3. The analytical probabilistic power flow calculation method of claim 1, wherein the linear power flow model is:
Figure FDA0003500462640000021
wherein θ and V are the voltage phase angle and the voltage amplitude of the node, P, Q is the active power and the reactive power of the injected power of the node, the subscript R represents the set of nodes V θ, K represents the set of nodes PV and V θ, S represents the set of nodes PV and PQ,
Figure FDA0003500462640000022
representing a set formed by PQ nodes, wherein a V theta node represents a given voltage amplitude and a given voltage phase, active power and reactive power are nodes of a quantity to be solved, a PV node represents a given active power and voltage amplitude, a given reactive power and voltage phase are nodes of the quantity to be solved, a PQ node represents a given active power and reactive power, and a given voltage amplitude and voltage phase are nodes of the quantity to be solved; the lambda and the C are parameter matrixes formed by conductance and susceptance information of the power system,
Figure FDA0003500462640000023
G. b is a conductance matrix and a susceptance matrix respectively, the superscript' represents the susceptance matrix neglecting all grounding branches, N is the sum of the number of PV nodes and PQ nodes, and M is the number of PQ nodes.
4. The analytical probabilistic power flow calculation method of claim 3 wherein the mapping between the injected power of the node and the operating state of the power system is:
Figure FDA0003500462640000024
wherein Y is the operating state of the power system, X is the injected power of the node,
Figure FDA0003500462640000025
beta and gamma are preset parameters, and T represents the transposition of the matrix.
5. The analytical probabilistic power flow calculation method according to claim 1, wherein the correcting the operation state of the power system by using a first-order polynomial fitting correction method includes:
randomly generating a plurality of groups of power data as the injection power of a plurality of groups of nodes, obtaining the actual operation state of a plurality of groups of power systems by adopting an alternating current power flow calculation method, and obtaining the theoretical operation state of the plurality of groups of power systems through the linear power flow model;
substituting the actual operating states of the multiple groups of power systems and the theoretical operating states of the multiple groups of power systems into a predefined first-order polynomial equation to obtain coefficients of the first-order polynomial equation, and updating the first-order polynomial equation based on the coefficients;
and after the running state of the power system is obtained through the linear power flow model, substituting the running state of the power system into the first-order polynomial equation to obtain the corrected running state of the power system.
6. The analytical probabilistic power flow calculation method of claim 5, wherein the first order polynomial equation is:
Y(AC)＝ρY+ζ；
wherein, Y(AC)Is the actual operating state of the power system, Y is the theoretical operating state of the power system, ρ and
Figure FDA0003500462640000031
are all the coefficients.
7. The analytical probabilistic power flow calculation method according to claim 6, wherein the modified operating state of the power system is:
Figure FDA0003500462640000032
wherein X is the injection power of the node, and Λ and C are parameter matrixes formed by conductance and susceptance information of the power system,
Figure FDA0003500462640000033
beta and gamma are preset parameters, T represents the transpose of a matrix, N is the sum of the number of PV nodes and PQ nodes, M is the number of PQ nodes, PV nodes represent nodes with given active power and voltage amplitude, the given reactive power and voltage phase are the quantity to be solved, PQ nodes represent nodes with given active power and reactive power, and the given voltage amplitude and voltage phase are the quantity to be solved.
8. The analytical probabilistic power flow calculation method of claim 2, wherein the set of parameters includes a weight coefficient, a mean vector and a covariance matrix for each gaussian component.
9. An analytic probability power flow calculation device, comprising:
the Gaussian mixture model building module is used for building a Gaussian mixture model according to the injection power of a node accessed to the power system, obtaining a parameter set of the Gaussian mixture model according to the historical data of the injection power of the node by adopting an EM (effective electromagnetic field) algorithm, and updating the Gaussian mixture model based on the parameter set;
the linear power flow model building module is used for building a linear power flow model according to the conductance and susceptance information of the power system and the injection power of the node so as to determine the mapping relation between the injection power of the node and the running state of the power system through the linear power flow model;
the operation state correction module is used for correcting the operation state of the power system by adopting a first-order polynomial fitting correction method and updating the linear power flow model according to the mapping relation between the injection power of the node and the corrected operation state of the power system;
and the probability power flow calculation module is used for mapping the probability distribution of the injection power of the node to the probability distribution of the corrected operation state of the power system through the Gaussian mixture model and the linear power flow model so as to obtain the probability power flow of the operation state of the power system.
10. A computer-readable storage medium, characterized in that the computer-readable storage medium comprises a stored computer program; wherein, when the computer program runs, the computer readable storage medium is controlled to execute the analytic probability power flow calculation method according to any one of claims 1 to 8.
CN202210126978.7A 2022-02-10 2022-02-10 An analytical probabilistic power flow calculation method, device and storage medium Pending CN114421483A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210126978.7A CN114421483A (en) 2022-02-10 2022-02-10 An analytical probabilistic power flow calculation method, device and storage medium

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210126978.7A CN114421483A (en) 2022-02-10 2022-02-10 An analytical probabilistic power flow calculation method, device and storage medium

Publications (1)

Publication Number Publication Date
CN114421483A true CN114421483A (en) 2022-04-29

Family

ID=81279232

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210126978.7A Pending CN114421483A (en) 2022-02-10 2022-02-10 An analytical probabilistic power flow calculation method, device and storage medium

Country Status (1)

Country Link
CN (1) CN114421483A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117313304A (en) * 2023-05-16 2023-12-29 上海交通大学 Gaussian mixture model method for analyzing overall sensitivity of power flow of power distribution network

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105529714A (en) * 2016-02-17 2016-04-27 中国农业大学 A fast probabilistic power flow calculation method based on the combined characteristics of normal distribution
CN109347110A (en) * 2018-10-29 2019-02-15 河海大学 An adaptive linearization probabilistic power flow calculation method with a high proportion of wind power grid-connected
CN109376494A (en) * 2018-12-17 2019-02-22 华北电力大学 A method and system for probabilistic power flow determination based on power system
CN111463793A (en) * 2020-04-23 2020-07-28 国网上海市电力公司 Analytic probabilistic power flow calculation method and system

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105529714A (en) * 2016-02-17 2016-04-27 中国农业大学 A fast probabilistic power flow calculation method based on the combined characteristics of normal distribution
CN109347110A (en) * 2018-10-29 2019-02-15 河海大学 An adaptive linearization probabilistic power flow calculation method with a high proportion of wind power grid-connected
CN109376494A (en) * 2018-12-17 2019-02-22 华北电力大学 A method and system for probabilistic power flow determination based on power system
CN111463793A (en) * 2020-04-23 2020-07-28 国网上海市电力公司 Analytic probabilistic power flow calculation method and system

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117313304A (en) * 2023-05-16 2023-12-29 上海交通大学 Gaussian mixture model method for analyzing overall sensitivity of power flow of power distribution network
CN117313304B (en) * 2023-05-16 2024-03-08 上海交通大学 Gaussian mixture model method for analyzing overall sensitivity of power flow of power distribution network

Similar Documents

Publication Publication Date Title
Liu et al. Solving power system differential algebraic equations using differential transformation
CN108390393B (en) Multi-objective reactive power optimization method and terminal equipment for distribution network
CN110120670B (en) DPV-containing power distribution network reactive voltage optimization method, terminal equipment and storage medium
CN113361176B (en) Nonlinear characteristic value topology optimization method and system considering frequency-dependent material
US11175641B2 (en) Processing platform with holomorphic embedding functionality for power control and other applications
CN115833147A (en) Reactive voltage optimization method, device, equipment and medium based on reinforcement learning
CN111463793B (en) Analytic probabilistic power flow calculation method and system
CN107994567B (en) A Generalized Fast Decomposition State Estimation Method
WO2019184132A1 (en) Data driving-based grid power flow equation linearization and solving method
CN110518591B (en) A Power Flow Calculation Method for Uncertain Power Systems
WO2025112776A1 (en) Parameter adjustment method and apparatus for photovoltaic simulation model, device and storage medium
CN103915840B (en) A kind of bulk power grid method for estimating state based on the line translation of Givens orthogonal increment
CN111181166B (en) An Uncertainty Affine Power Flow Method for Prediction and Correction
CN106532712B (en) Compensation Method Cartesian Coordinate Newton's Method of Power Flow Calculation Method for Power Networks with Small Impedance Branch
CN114421483A (en) An analytical probabilistic power flow calculation method, device and storage medium
CN102780220A (en) Power flow calculation method for electric distribution network comprising PV constant distributed generation
CN114091623A (en) A method and device for transient voltage partitioning based on multi-binary table-AP clustering
CN112597649B (en) A Numerical Calculation Method of Meshless Electrostatic Field with Strong and Weak Coupling
CN112600200B (en) Harmonic power flow calculation method, device and equipment of power grid node and storage medium
CN111697575A (en) Flexibility-improved quantitative analysis method, device and system
CN117495153A (en) Method and system for quickly correcting regional power grid line loss influence factors
CN114188945A (en) Method and device for calculating short-circuit current of distribution network with photovoltaic power source
CN106021191A (en) Network equivalence algorithm based on decomposition filtering
CN116432541B (en) New energy station modeling method and system based on optimization clustering algorithm
Mahmoudi et al. A direct matrix inversion-less analysis for distribution system power flow considering distributed generation

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
点击 这是indexloc提供的php浏览器服务，不要输入任何密码和下载