CN114357373A - Optimized configuration method of micro synchronous phasor measurement unit considering state estimation error - Google Patents

Optimized configuration method of micro synchronous phasor measurement unit considering state estimation error Download PDF

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CN114357373A
CN114357373A CN202111642882.8A CN202111642882A CN114357373A CN 114357373 A CN114357373 A CN 114357373A CN 202111642882 A CN202111642882 A CN 202111642882A CN 114357373 A CN114357373 A CN 114357373A
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陈腾鹏
刘方岩
任和
李璐
李钷
张景瑞
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Abstract

A method for optimizing and configuring a micro synchrophasor measurement unit (PSCU) by considering state estimation errors comprises the following steps: 1) forming a node admittance matrix and a node-branch model according to the node connection mode and branch impedance of the power distribution network; 2) installing mu PMUs at all nodes of the formed admittance matrix and node branch models to read measurement values and obtain measurement models; 3) carrying out t distribution fitting on the measurement noise according to the measurement value historical data; 4) constructing a maximum likelihood estimator based on the measurement model, and obtaining a state estimation error calculated based on the maximum likelihood estimator according to the influence function IF; 5) and incorporating the sum of the state estimation errors and the maximum value of the state estimation variance into the constraint condition of the mu PMU optimization configuration. The invention considers the precision of the subsequent link (state estimation result) in the optimized configuration, is beneficial to the design and the upgrade of the measurement system and has good application prospect.

Description

考虑状态估计误差的微型同步相量测量单元优化配置方法Optimal configuration method of miniature synchrophasor measurement unit considering state estimation error

技术领域technical field

本发明涉及传感器布局技术领域，特别是指一种考虑状态估计误差的微型同步相量测量单元优化配置方法。The invention relates to the technical field of sensor layout, in particular to a method for optimizing the configuration of a miniature synchrophasor measurement unit considering state estimation errors.

背景技术Background technique

智能配电网具有实现协调优化管理的控制中心，电网响应速度快，可以友好地接入分布式可再生能源，提高可再生资源的消纳水平，提高供电的可靠性和电能质量。但是，智能配电网协调优化控制和快速决策的基础在于先进的量测装置。配电网使用微型同步相量测量单元(Micro-Synchronous Phasor Measurement Unit，μPMU)也得到业界越来越多的关注。μPMU量测值精度较高，但因其成本也相对较高，不可能在所有节点都安装。为了推行在智能配电网大规模部署μPMU，对μPMU布局进行优化配置是一个既节约成本又保证系统全局可观的重要手段。另外，状态估计作为配电管理系统(Distribution ManagementSystem，DMS)的基础功能，作为“态势感知工具”的核心板块，主要对μPMU原始量测值进行处理，是获取准确全网状态量的关键技术。μPMU的布局结果，对状态估计的结果起决定性的作用。现有μPMU配置方法，只保证全网是否达到可观，却忽视了状态估计这一环节，割裂了μPMU配置与状态估计之间的关系。因此，在μPMU优化配置阶段，应该考虑状态估计误差所带来的影响。The smart distribution network has a control center that realizes coordinated and optimized management. The grid responds quickly, and it can connect to distributed renewable energy in a friendly manner, improve the consumption level of renewable resources, and improve the reliability and power quality of power supply. However, the basis for coordinated optimal control and rapid decision-making in smart distribution networks lies in advanced measurement devices. The use of Micro-Synchronous Phasor Measurement Unit (μPMU) in distribution network has also received more and more attention in the industry. The measurement accuracy of μPMU is high, but because of its relatively high cost, it is impossible to install it in all nodes. In order to promote the large-scale deployment of μPMUs in the smart distribution network, optimizing the layout of μPMUs is an important method to save costs and ensure the overall sizing of the system. In addition, as the basic function of the distribution management system (Distribution Management System, DMS), state estimation, as the core part of the "situational awareness tool", mainly processes the original measurement values of the μPMU, and is the key technology to obtain accurate network-wide state quantities. The layout result of the μPMU plays a decisive role in the state estimation result. The existing μPMU configuration method only guarantees whether the entire network can reach considerable value, but ignores the link of state estimation, which separates the relationship between μPMU configuration and state estimation. Therefore, in the optimal configuration stage of μPMU, the influence of state estimation error should be considered.

发明内容SUMMARY OF THE INVENTION

本发明的主要目的在于克服现有技术中的上述缺陷，考虑到μPMU的量测误差甚至遭循非高斯分布，得出新的状态估计误差(用方差表示)计算公式，进而提出一种考虑状态估计误差的μPMU优化配置方法。The main purpose of the present invention is to overcome the above-mentioned defects in the prior art. Considering that the measurement error of the μPMU even follows a non-Gaussian distribution, a new calculation formula for the state estimation error (represented by variance) is obtained, and a new calculation formula for considering the state A μPMU optimal configuration method for estimation error.

本发明采用如下技术方案：The present invention adopts following technical scheme:

考虑状态估计误差的微型同步相量测量单元优化配置方法，其包括：1)根据配电网的节点连接方式和支路阻抗，形成节点导纳矩阵和节点支路模型；2)在形成的导纳矩阵和节点支路模型的全部节点安装μPMU来读取量测值并得到量测模型；3)根据量测值历史数据对量测噪声进行t分布拟合；其特征在于，还包括：4)基于量测模型构建一个最大似然估计器，根据影响函数IF得到基于最大似然估计器计算的状态估计误差；5)将状态估计误差之和、状态估计方差的最大值并入μPMU优化配置的约束条件。An optimal configuration method for micro-synchrophasor measurement units considering state estimation error, which includes: 1) forming a node admittance matrix and a node branch model according to the node connection mode and branch impedance of the distribution network; 2) in the formed derivative All nodes of the nano-matrix and the node branch model are installed with μPMU to read the measurement value and obtain the measurement model; 3) According to the historical data of the measurement value, perform t-distribution fitting on the measurement noise; It is characterized in that, it also includes: 4. ) Build a maximum likelihood estimator based on the measurement model, and obtain the state estimation error calculated based on the maximum likelihood estimator according to the influence function IF; 5) Incorporate the sum of the state estimation errors and the maximum value of the state estimation variance into the μPMU optimization configuration constraints.

假设配网节点有b个，V＝[1，...，b]为所有节点的集合，μPMU的配置向量为Assuming that there are b nodes in the distribution network, V=[1,...,b] is the set of all nodes, and the configuration vector of μPMU is

p＝[p1，p2，...，pb]T p=[p 1 , p 2 , ..., p b ] T

其中in

Figure BDA0003443432620000021
Figure BDA0003443432620000021

假设全部节点都安装μPMU，则形成的量测矩阵为Assuming that all nodes are installed with μPMU, the measurement matrix formed is

Figure BDA0003443432620000022
Figure BDA0003443432620000022

其中

Figure BDA0003443432620000023
为对应一个μPMU安装于节点j时候形成的量测矩阵，j＝1，...，b。in
Figure BDA0003443432620000023
In order to correspond to the measurement matrix formed when a μPMU is installed at node j, j=1,...,b.

所述量测模型为z(k)＝Hx(k)-∫(k)，z(k)为量测值，k表示采样时刻，x(k)为配电网在第k时刻的状态量，H是量测矩阵，∫(k)为量测噪声。The measurement model is z(k)=Hx(k)-∫(k), z(k) is the measurement value, k represents the sampling time, and x(k) is the state quantity of the distribution network at the kth time , H is the measurement matrix, ∫(k) is the measurement noise.

步骤3)中，t分布的概率密度函数为：In step 3), the probability density function of the t distribution is:

Figure BDA0003443432620000024
Figure BDA0003443432620000024

其中，∫i表示第i个量测噪声，i＝1，...，m，m是量测个数，Γ(·)是伽马函数，ξi是比例系数，νi是形状系数。Among them, ∫ i represents the i -th measurement noise, i =1, .

步骤4)中，基于量测模型构建一个最大似然估计器，通过最小化下述目标方程实现：In step 4), a maximum likelihood estimator is constructed based on the measurement model, which is achieved by minimizing the following objective equation:

Figure BDA0003443432620000025
Figure BDA0003443432620000025

对J求导，得到：Taking the derivative of J, we get:

Figure BDA0003443432620000026
Figure BDA0003443432620000026

其中，

Figure BDA0003443432620000027
表示状态估计值，Wi是权重对角阵W的第i个元素。in,
Figure BDA0003443432620000027
represents the state estimate, and Wi is the ith element of the weight diagonal matrix W.

步骤4)中，所述状态估计误差表示为：In step 4), the state estimation error is expressed as:

Figure BDA0003443432620000031
Figure BDA0003443432620000031

其中，F(∫)为联合密度函数，且where F(∫) is the joint density function, and

Figure BDA0003443432620000032
Figure BDA0003443432620000032

Figure BDA0003443432620000033
Figure BDA0003443432620000033

Figure BDA0003443432620000034
Figure BDA0003443432620000034

Figure BDA0003443432620000035
Figure BDA0003443432620000035

进一步，根据加权最小二乘法关于状态估计方差的基本形式

Figure BDA0003443432620000036
构造一个对角矩阵
Figure BDA0003443432620000037
符合下述条件：Further, according to the weighted least squares method, the basic form of variance is estimated with respect to the state
Figure BDA0003443432620000036
construct a diagonal matrix
Figure BDA0003443432620000037
Meet the following conditions:

Figure BDA0003443432620000038
Figure BDA0003443432620000038

步骤5)中，所述约束条件为：In step 5), the constraints are:

Figure BDA0003443432620000039
Figure BDA0003443432620000039

其中

Figure BDA00034434326200000310
表示矩阵
Figure BDA00034434326200000311
达到满秩，trace表示各个状态估计方差的和，δt和δm是设定的容许值。in
Figure BDA00034434326200000310
representation matrix
Figure BDA00034434326200000311
When the full rank is reached, trace represents the sum of the estimated variances of each state, and δ t and δ m are the set allowable values.

由上述对本发明的描述可知，现有技术都是基于高斯噪声的假设，但现实中的μPMU噪声经常遵循非高斯噪声分布，因此已有的技术不够准确，本发明考虑到μPMU的量测误差甚至遵循非高斯分布，得出新的用方差表示的状态估计误差计算公式，更加符合实际情况。另外，本发明直接在优化配置中就考虑了后续环节(状态估计结果)的精度，有利于量测系统的设计和升级，应用前景良好。It can be seen from the above description of the present invention that the prior art is based on the assumption of Gaussian noise, but the actual μPMU noise often follows a non-Gaussian noise distribution, so the existing technology is not accurate enough, and the present invention takes into account the measurement error of the μPMU and even Following the non-Gaussian distribution, a new state estimation error calculation formula expressed by variance is obtained, which is more in line with the actual situation. In addition, the present invention directly considers the accuracy of the subsequent links (state estimation results) in the optimized configuration, which is beneficial to the design and upgrade of the measurement system and has a good application prospect.

附图说明Description of drawings

图1是本发明实施例IEEE 14节点测试图。FIG. 1 is a test diagram of an IEEE 14 node according to an embodiment of the present invention.

图2是本发明在IEEE 14节点系统的测试结果，其中状态量估计方差的最大值(MSEEV)和状态估计方差(SEE)的单位：10-5。FIG. 2 is the test result of the present invention in the IEEE 14 node system, wherein the maximum value of state quantity estimation variance (MSEEV) and the unit of state estimation variance (SEE): 10 −5 .

以下结合附图和具体实施例对本发明作进一步详述。The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

具体实施方式Detailed ways

以下通过具体实施方式对本发明作进一步的描述。The present invention will be further described below through specific embodiments.

考虑状态估计误差的微型同步相量测量单元优化配置方法，其包括如下步骤：An optimal configuration method for a micro-synchrophasor measurement unit considering the state estimation error, which includes the following steps:

1)根据配电网的节点连接方式和支路阻抗，形成节点导纳矩阵和节点-支路模型即配电网拓扑结构，如图1所示，假设配网节点有b个，V＝[1，...，b]为所有节点的集合，则μPMU的配置向量为1) According to the node connection mode and branch impedance of the distribution network, the node admittance matrix and the node-branch model are formed, that is, the distribution network topology structure. As shown in Figure 1, assuming that there are b nodes in the distribution network, V = [ 1,...,b] is the set of all nodes, then the configuration vector of μPMU is

p＝[p1，p2，...，pb]T p=[p 1 , p 2 , ..., p b ] T

其中in

Figure BDA0003443432620000041
Figure BDA0003443432620000041

2)在形成的导纳矩阵和节点支路模型的全部节点安装μPMU来读取量测值并得到量测模型。2) Install μPMU on all nodes of the formed admittance matrix and node branch model to read the measurement value and obtain the measurement model.

该步骤中，假设全部节点都安装μPMU，则形成的量测矩阵为In this step, assuming that all nodes are installed with μPMU, the measurement matrix formed is

Figure BDA0003443432620000042
Figure BDA0003443432620000042

其中

Figure BDA0003443432620000043
为对应一个μPMU安装于节点j时候形成的量测矩阵，j＝1，...，b。in
Figure BDA0003443432620000043
In order to correspond to the measurement matrix formed when a μPMU is installed at node j, j=1,...,b.

假设配电网在第k时刻的状态x(k)与量测值存在如下关系式即量测模型为：z(k)＝Hx(k)+∫(k)，z(k)为量测值，k表示采样时刻，x(k)为配电网在第k时刻的状态量，H是量测矩阵，∫(k)为量测噪声。该量测模型将用于状态估计方差的计算。It is assumed that the state x(k) of the distribution network at the k-th moment has the following relationship with the measured value, that is, the measurement model is: z(k)=Hx(k)+∫(k), z(k) is the measurement value, k represents the sampling time, x(k) is the state quantity of the distribution network at the kth time, H is the measurement matrix, and ∫(k) is the measurement noise. This measurement model will be used in the calculation of the variance of the state estimate.

3)根据量测值历史数据对量测噪声进行t分布拟合。3) t-distribution fitting of the measurement noise according to the historical data of the measurement value.

本发明中，基于t分布和高斯分布，对量测值历史数据分别进行t分布和高斯分布的拟合，并比较得到t分布拟合量测数据的结果更好，故采用的量测噪声模型为t分布模型。则t分布的概率密度函数为：In the present invention, based on t distribution and Gaussian distribution, t distribution and Gaussian distribution are respectively fitted to the historical data of measurement values, and the results obtained by comparing the t distribution to the measurement data are better. Therefore, the measurement noise model is adopted. is the t-distribution model. Then the probability density function of the t distribution is:

Figure BDA0003443432620000051
Figure BDA0003443432620000051

其中，∫i表示第i个量测噪声，i＝1，...，m，m是量测个数，Γ(·)是伽马函数，ξi是比例系数，νi是形状系数。当形状系数νi趋于无穷时，t分布变成高斯分布；所以，t分布具有很大的灵活性，可以方便地模拟高斯噪声或非高斯噪声。t分布的概率密度函数将用于状态估计方差的计算。Among them, ∫ i represents the i -th measurement noise, i =1, . When the shape coefficient ν i tends to infinity, the t distribution becomes Gaussian; therefore, the t distribution has great flexibility and can easily simulate Gaussian noise or non-Gaussian noise. The probability density function of the t-distribution will be used in the calculation of the variance of the state estimate.

4)基于量测模型构建一个最大似然估计器，根据影响函数IF得到基于最大似然估计器计算的状态估计误差。4) Build a maximum likelihood estimator based on the measurement model, and obtain the state estimation error calculated based on the maximum likelihood estimator according to the influence function IF.

该步骤中，最大似然估计器具有鲁棒性，可通过最小化下述目标方程实现In this step, the maximum likelihood estimator is robust and can be achieved by minimizing the following objective equation

Figure BDA0003443432620000052
Figure BDA0003443432620000052

对J求导，得到：Taking the derivative of J, we get:

Figure BDA0003443432620000053
Figure BDA0003443432620000053

其中，

Figure BDA0003443432620000054
表示状态估计值，Wi是权重对角阵W的第i个元素。根据影响函数IF，可以得到基于最大似然估计器计算的状态估计误差(用方差表示)为：in,
Figure BDA0003443432620000054
represents the state estimate, and Wi is the ith element of the weight diagonal matrix W. According to the influence function IF, the state estimation error (represented by variance) calculated based on the maximum likelihood estimator can be obtained as:

Figure BDA0003443432620000061
Figure BDA0003443432620000061

其中，F(∫)为联合密度函数，且where F(∫) is the joint density function, and

Figure BDA0003443432620000062
Figure BDA0003443432620000062

Figure BDA0003443432620000063
Figure BDA0003443432620000063

Figure BDA0003443432620000064
Figure BDA0003443432620000064

Figure BDA0003443432620000065
Figure BDA0003443432620000065

根据加权最小二乘法关于状态估计方差的基本形式

Figure BDA0003443432620000066
构造一个对角矩阵
Figure BDA0003443432620000067
符合下述条件：Basic Form of Estimated Variance with respect to State according to Weighted Least Squares
Figure BDA0003443432620000066
construct a diagonal matrix
Figure BDA0003443432620000067
Meet the following conditions:

Figure BDA0003443432620000068
Figure BDA0003443432620000068

5)将状态估计误差之和、状态估计方差的最大值并入μPMU优化配置的约束条件。5) Incorporate the sum of the state estimation errors and the maximum value of the state estimation variance into the constraints of the optimal configuration of the μPMU.

该步骤中，考虑状态估计误差，本发明同时考虑了状态估计误差之和，同时考虑状态估计方差的最大值，当做约束条件，并入μPMU优化配置问题。即约束条件为：In this step, the state estimation error is considered, and the present invention also considers the sum of the state estimation errors and the maximum value of the state estimation variance as constraints, which are incorporated into the μPMU optimal configuration problem. That is, the constraints are:

Figure BDA0003443432620000069
Figure BDA0003443432620000069

其中

Figure BDA00034434326200000610
表示矩阵
Figure BDA00034434326200000611
达到满秩，trace表示各个状态估计方差的和，δt和δm是设定的容许值。in
Figure BDA00034434326200000610
representation matrix
Figure BDA00034434326200000611
When the full rank is reached, trace represents the sum of the estimated variances of each state, and δ t and δ m are the set allowable values.

其中p的元素为0或者1，其中1表示对应节点位置应该安装μPMU，δt和δm用于设置状态估计方差的容许值，代表对状态估计精度的限制，这也是本发明的优点，即直接在优化配置中就考虑了后续环节(状态估计结果)的精度，有利于量测系统的设计和升级，应用前景良好。图2说明了本申请μPMU优化配置方法能充分考虑到状态估计方差的约束，得到最佳μPMU配置方案，最终的MSEEV和SEE结果都在所添加的约束范围之内。The element of p is 0 or 1, where 1 indicates that the μPMU should be installed at the corresponding node position, and δt and δm are used to set the allowable value of the variance of the state estimation, which represents the limitation on the accuracy of the state estimation, which is also an advantage of the present invention, that is, The accuracy of the subsequent links (state estimation results) is considered directly in the optimized configuration, which is beneficial to the design and upgrade of the measurement system, and has a good application prospect. Figure 2 illustrates that the μPMU optimal configuration method of the present application can fully consider the constraints of state estimation variance to obtain the optimal μPMU configuration scheme, and the final MSEEV and SEE results are within the added constraints.

上述仅为本发明的具体实施方式，但本发明的设计构思并不局限于此，凡利用此构思对本发明进行非实质性的改动，均应属于侵犯本发明保护范围的行为。The above are only specific embodiments of the present invention, but the design concept of the present invention is not limited to this, and any non-substantial modification of the present invention by using this concept should be regarded as an act of infringing the protection scope of the present invention.

Claims (8)

1. The optimized configuration method of the micro synchronous phasor measurement unit considering the state estimation error comprises the following steps: 1) forming a node admittance matrix and a node-branch model according to the node connection mode and branch impedance of the power distribution network; 2) installing mu PMUs at all nodes of the formed admittance matrix and node branch models to read measurement values and obtain measurement models; 3) carrying out t distribution fitting on the measurement noise according to the measurement value historical data; it is characterized by also comprising: 4) constructing a maximum likelihood estimator based on the measurement model, and obtaining a state estimation error calculated based on the maximum likelihood estimator according to the influence function IF; 5) and incorporating the sum of the state estimation errors and the maximum value of the state estimation variance into the constraint condition of the mu PMU optimization configuration.
2. The method of claim 1, wherein the optimal configuration of the micro synchrophasor measurement unit considering the state estimation error comprises: assuming that there are b nodes in the distribution network, V ═ 1.. and b ] is the set of all nodes, the configuration vector of μ PMU is
p＝[p1，p2，...，pb]T
Wherein
Figure FDA0003443432610000011
3. The method of claim 2, wherein the optimal configuration of the micro synchrophasor measurement unit considering the state estimation error comprises: assuming that all nodes are installed with mu PMUs, the measurement matrix is formed
Figure FDA0003443432610000012
Wherein
Figure FDA0003443432610000013
J is 1.. and b is a measurement matrix formed when a PMU is installed at node j.
4. The method of claim 1, wherein the optimal configuration of the micro synchrophasor measurement unit considering the state estimation error comprises: the measurement model is z (k) ═ hx (k) ++ (k), z (k) is a measurement value, k represents a sampling time, x (k) is a state quantity of the power distribution network at the k-th time, H is a measurement matrix, and ^ k is measurement noise.
5. The method of claim 1, wherein the optimal configuration of the micro synchrophasor measurement unit considering the state estimation error comprises: in step 3), the probability density function of t distribution is:
Figure FDA0003443432610000014
wherein ^ niRepresents the ith measurement noise, i is 1iIs the proportionality coefficient viIs the form factor.
6. The method of claim 5, wherein the optimal configuration of the SSPMTUs considering the state estimation error comprises: in step 4), a maximum likelihood estimator is constructed based on the measurement model, and the maximum likelihood estimator is realized by minimizing the following objective equation:
Figure FDA0003443432610000021
taking the derivative of J to obtain:
Figure FDA0003443432610000022
wherein,
Figure FDA0003443432610000023
represents a state estimate, WiIs the ith element of the weight diagonal matrix W.
7. The method of claim 6, wherein the optimal configuration of the micro synchrophasor measurement unit considering the state estimation error comprises: in step 4), the state estimation error is expressed as:
Figure FDA0003443432610000024
wherein F ([ integral ] F) is a joint density function, an
Figure FDA0003443432610000025
Figure FDA0003443432610000026
Figure FDA0003443432610000027
Figure FDA0003443432610000028
Further, the basic form of the variance is estimated with respect to the state according to a weighted least squares method
Figure FDA0003443432610000029
Constructing a diagonal matrix
Figure FDA00034434326100000210
The following conditions are met:
Figure FDA00034434326100000211
8. the method of claim 7, wherein the optimal configuration of the micro synchrophasor measurement unit considering the state estimation error comprises: in step 5), the constraint conditions are as follows:
Figure FDA0003443432610000031
wherein
Figure FDA0003443432610000032
Representation matrix
Figure FDA0003443432610000033
Up to full rank, trace represents the sum of the variances of the estimates of the various states, δtAnd deltamIs a set tolerance value.
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