﻿ 电晕电流时间序列时域特性的分析及预测
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 应用科技  2018, Vol. 45 Issue (3): 39-43  DOI: 10.11991/yykj.201709013 0

### 引用本文

CHEN Chenyu, LIU Yuanqing, LYU Jianxun, et al. Analysis and prediction on the time domain characteristics of corona current time series[J]. Applied Science and Technology, 2018, 45(3), 39-43. DOI: 10.11991/yykj.201709013.

### 文章历史

1. 北京航空航天大学 自动化科学与电气工程学院，北京 100191;
2. 中国电力科学研究院，北京 100192

Analysis and prediction on the time domain characteristics of corona current time series
CHEN Chenyu1, LIU Yuanqing2, LYU Jianxun1, YUAN Haiwen1, LIU Yingyi1
1. School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China;
2. China Electric Power Research Institute, Beijing 100192, China
Abstract: The local discharge in an ultra high voltage direct current (UHV DC) transmission line may cause corona current, leading to power loss, audible noise and electromagnetic interference, while too intense electromagnetic radiation threatens the ecological health. By effectively monitoring corona current, the safe and economical operation of transmission lines can be ensured. Aiming at this problem, an autoregressive integrated moving average (ARIMA) model was established for rolling prediction, both the measurement indices on the predicted errors and the time-domain statistic indices of corona current complied with the requirements. The method can be applied to the fit and prediction of the signal of corona current at different transmission levels and it has a certain applicability. The results laid a solid foundation for the subsequent research of corona properties in different measurement environments.
Key words: corona current    UHV    DC transmission    time series analysis    ARIMA    rolling prediction    fitting    time domain index

1 时间序列分析 1.1 自回归滑动平均(autoregressive integrated moving average，ARMA)模型

 ${x_t} = \mathop \sum \limits_{i = 1}^p {\phi _i}{x_{t - i}} - \mathop \sum \limits_{j = 1}^q {\theta _j}{\varepsilon _{t - j}} + {\varepsilon _t}$ (1)

 $\varPhi \left( B \right){x_t} = \varTheta \left( B \right){\varepsilon _t}$

ARMA(p, q)模型中，当q=0时，即为AR(p)模型；当p=0时，即为MA(q)模型。

1.2 求和自回归积分滑动平均(ARIMA)模型

ARIMA(p, d, q)模型具有如下结构：

 $\varPhi \left( B \right){\nabla ^d}{x_t} = \varTheta \left( B \right){\varepsilon _t}$

ARIMA模型实际上是ARMA模型与差分运算的结合。对非平稳信号进行差分处理，将其转化为平稳信号，后对平稳信号建立ARMA模型[9]

2 ARIMA模型的建立过程

ARIMA模型的建模过程如图1所示，模型定阶是建模最主要的部分[10]

2.1 数据预处理

 \begin{aligned}& \Delta {x_t} = \delta {x_{t - 1}} + \mathop \sum \limits_{i = 1}^m {\beta _i}\Delta {x_{t - i}} + {\varepsilon _t}\\& \Delta {x_t} = \alpha + \delta {x_{t - 1}} + \mathop \sum \limits_{i = 1}^m {\beta _i}\Delta {x_{t - i}} + {\varepsilon _t}\\& \Delta {x_t} = \alpha + \beta t + \delta {x_{t - 1}} + \mathop \sum \limits_{i = 1}^m {\beta _i}\Delta {x_{t - i}} + {\varepsilon _t}\end{aligned}

2.2 模型识别

 $\begin{array}{l}{\rm{AIC}} = - 2{\rm{ln}} \; \mu + 2\sigma \\{\rm{BIC}} = - 2{\rm{ln}} \; \mu + \left( {{\rm{log}} \; N + 1} \right) \times \sigma \end{array}$

2.3 参数估计及诊断检验

ARIMA(13, 1, 5)模型系数如表3所示。

3 结果及分析

 \begin{aligned}& {\varepsilon _{{\rm{MSE}}}} = \frac{{\mathop \sum \nolimits_{i = 1}^N {{({y_i} - \hat{y_i})}^2}}}{N}\\& {\varepsilon _{{\rm{NMSE}}}} = \frac{{\mathop \sum \nolimits_{i = 1}^N {{({y_i} - \hat{y_i})}^2}}}{{\mathop \sum \nolimits_{i = 1}^N {{({y_i} - \hat{y_i} )}^2}}}\end{aligned}

+800 kV输电等级下，模型预测度量结果如表4所示，对比分析可得，M=50ARIMA(13, 1, 5)滚动模型预测效果略优于M=100ARIMA(13, 1, 5)滚动模型，但总体效果相差不大。

8个时域指标[13]，均方根xrms、幅度平方根xsra、峰度值xkv、偏态值xsv、峰峰值xppv、波峰因子xcf、脉冲因子xif和边际因子xmf，用于描述电晕电流信号，其计算公式如下：

 \begin{aligned}& {x_{{\rm{rms}}}} = {(\frac{1}{N}\mathop \sum \limits_{i = 1}^N x_i^2)^{1/2}}\\& {x_{{\rm{sra}}}} = {(\frac{1}{N}\mathop \sum \limits_{i = 1}^N \sqrt {|{x_i}|} )^2}\\& {x_{{\rm{kv}}}} = \frac{1}{N}\mathop \sum \limits_{i = 1}^N {\left( {\frac{{{x_i} - \bar x}}{\sigma }} \right)^4}\\& {x_{{\rm{sv}}}} = \frac{1}{N}\mathop \sum \limits_{i = 1}^N {\left( {\frac{{{x_i} - \bar x}}{\sigma }} \right)^3}\\& {x_{{\rm{ppv}}}} = \max \left( {{x_i}} \right) - {\rm{min}}\left( {{x_i}} \right)\\& {x_{{\rm{cf}}}} = \frac{{\max \left( {|{x_i}|} \right)}}{{{{(\displaystyle\frac{1}{N}\mathop \sum \nolimits_{i = 1}^N x_i^2)}^{1/2}}}}\\& {x_{{\rm{if}}}} = \frac{{\max \left( {|{x_i}|} \right)}}{{\displaystyle\frac{1}{N}\mathop \sum \nolimits_{i = 1}^N \left| {{x_i}} \right|}}\\& {x_{{\rm{mf}}}} = \frac{{\max \left( {|{x_i}|} \right)}}{{{{(\displaystyle\frac{1}{N}\mathop \sum \nolimits_{i = 1}^N \sqrt {|{x_i}|} )}^2}}}\end{aligned}

4 结论

1) 本文对特高压直流输电线路下的电晕电流进行时间序列分析，对+800 kV输电等级下信号建立ARIMA(13, 1, 5)模型。

2) 对+800 kV输电电压下的信号波形进行步长M=50及100的滚动预测。预测误差度量指标NMSE、MSE较小。同时设立8个时域统计指标，电晕实际波形与预测波形指标计算结果相似，预测效果良好。

3) 经建模计算表明，ARIMA(13, 1, 5)模型也同样适用于+1 000 kV输电等级下电晕电流信号的预测，本文所建模型具有较强的适用性。

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