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Harmonic State Estimation of Oilfield Distribution Based on Least Squares
DOI: 10.12677/TDET.2018.74010, PDF, HTML, XML, 下载: 1,027  浏览: 2,262  科研立项经费支持

Abstract: With the increasing number of nonlinear power electronic devices such as inverters in oilfield power grids, the number and types of harmonic sources in oilfield power grids continue to increase. Therefore, it is very meaningful to study the mechanism of harmonic transfer in oilfield power grids. Harmonic state estimation can provide an effective means for analyzing and mastering the harmonic transfer law of oilfield power grid. Based on the structural characteristics of oilfield distribution network and the working characteristics of typical production equipment, this paper takes node voltage as the state variable and branch current, bus voltage and node injection current as the measurement variable. The node voltage measurement equation, branch current measurement equation and node injection measurement equation are established. A mathematic model of harmonic state estimation for distribution network of oilfield is established and solved by least square method; the error caused by underdetermined equation is corrected by taking into account the correlation between the current ratio of branch wave and the harmonic current ratio. Simulation results demonstrate the effectiveness of the proposed method.

1. 引言

2. 配电网谐波状态估计方法

2.1. 网络谐波模型的数学描述

${y}_{f}=\left(\begin{array}{cccc}{y}_{11}& {y}_{12}& \cdots & {y}_{1b}\\ {y}_{21}& {y}_{22}& \cdots & {y}_{2b}\\ ⋮& ⋮& \ddots & ⋮\\ {y}_{b1}& {y}_{b2}& \cdots & {y}_{bb}\end{array}\right)$ (1)

Figure 1. Node-to-branch incidence matrix A

$Y=A{y}_{b}{A}^{\text{T}}$ (2)

2.2. 谐波状态估计的数学模型

$Z=HX+\epsilon$ (3)

2.3. 谐波状态估计相量量测方程

1) 电压量测方程

${\stackrel{˙}{U}}_{m,i}\left(h\right)=I{\stackrel{˙}{U}}_{T,i}\left(h\right)+{\eta }_{i}\left(h\right)$ (4)

${\stackrel{˙}{U}}_{T,i}\left(h\right)$ 表示i节点h次谐波电压状态量；

I表示适当维数的单位矩阵；

${\eta }_{i}\left(h\right)$ 表示i节点h次谐波电压量测误差。

2) 节点注入电流量测方程

${\stackrel{˙}{I}}_{m,i}\left(h\right)=\underset{j=1}{\overset{n}{\sum }}{Y}_{ij}\left(h\right){\stackrel{˙}{U}}_{T,j}\left(h\right)+{\eta }_{i}\left(h\right)$ (5)

${\stackrel{˙}{U}}_{T,j}\left(h\right)$ 表示j节点h次谐波电压状态量；

${Y}_{ij}$ 表示节点导纳矩阵中对应节点i和j的分块导纳矩阵元素；

n表示网络节点总数。

3) 支路量测方程

${\stackrel{˙}{I}}_{i,j}={Y}_{i,j}\left({\stackrel{˙}{U}}_{i}-{\stackrel{˙}{U}}_{j}\right)+{\eta }_{i,j}$ (6)

4) 考虑基波电流比值的节点注入电流量测方程

$\begin{array}{l}{\stackrel{˙}{I}}_{m,i}\left(h\right)={\stackrel{˙}{I}}_{m,j}\left(h\right)+{\stackrel{˙}{I}}_{m,k}\left(h\right)\\ \frac{{\stackrel{˙}{I}}_{m,j}\left(h\right)}{{\stackrel{˙}{I}}_{m,i}\left(h\right)}=\frac{{\stackrel{˙}{I}}_{m,j}\left(1\right)}{{\stackrel{˙}{I}}_{m,i}\left(1\right)}\\ \frac{{\stackrel{˙}{I}}_{m,k}\left(h\right)}{{\stackrel{˙}{I}}_{m,i}\left(h\right)}=\frac{{\stackrel{˙}{I}}_{m,k}\left(1\right)}{{\stackrel{˙}{I}}_{m,i}\left(1\right)}\end{array}$ (7)

2.4. 谐波状态估计求解方法

$Z=Hx+\epsilon$ (8)

$J\left(X\right)={\left(Z-HX\right)}^{\text{T}}\left(Z-HX\right)$ (9)

$\frac{\partial J\left(X\right)}{\partial X}=0$ (10)

1) 矩阵H正定；有唯一解

${x}_{*}={H}^{-1}z$ (11)

2) 矩阵H超定；最小二乘误差解有唯一表示

${x}_{*}={\left({H}^{\text{T}}H\right)}^{-1}{H}^{\text{T}}z={H}^{+}z$ (12)

3) 矩阵H欠定，最小2-范数 ${‖x‖}_{2}^{2}$ 的唯一解：

${x}_{*}={H}^{\text{T}}{\left(H{H}^{\text{T}}\right)}^{-1}z={H}^{+}z$ (13)

Figure 2. The flow chart of modeling and solving of Harmonic State Estimation

3. 算例分析

Figure 3. Simplified schematic of Oilfield distribution network line

3.1. 监测装置的布点

Table 1. Measuring equipment configuration

3.2. 数据处理

Table 2. The parameter of field line

Table 3. Measurement of node 5th harmonic voltage

Table 4. Measurement of 5th branch harmonic current

3.3. 结果对比

Table 5. 5th harmonic voltage amplitude error comparison

Table 6. 5th harmonic voltage phase error comparison

Table 7. The 5th harmonic voltage ampitude of the node obtained by underdetermined equation

Table 8. The 5th harmonic voltage phase of the node obtained by underdetermined equation

Table 9. Fundamental wave current ratio

Table 10. The 5th harmonic voltage ampitude of the node obtained by positive definite matrix

Table 11. The 5th harmonic voltage phase of the node obtained by positive definite matrix

4. 结论

1) 基于油田负荷运行监测系统数据，某些支路虽然没有安装谐波量测装置，但可以获取基波电流。利用各支路基波电流与节点注入基波电流之比等于各支路谐波电流与节点注入谐波电流之比，建立考虑基波电流比值的节点注入电流量测方程，将量测方程由欠定转为正定。

2) 对油田配电网某馈线进行建模，在6个节点安装谐波量测装置，进行谐波状态估计。通过最小二乘法得出的计算值和仿真出的结果误差较小，并且建立欠定方程求解了4个不精确的状态估计点，并在线路基波量测量基础上将欠定方程转化成了正定方程，减小了不精确点的误差。

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