﻿ PCA-PSO-ELM配网供电可靠性预测模型
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 哈尔滨工程大学学报  2018, Vol. 39 Issue (6): 1116-1122  DOI: 10.11990/jheu.201611088 0

### 引用本文

XU Aidong, LI Haofei, CHENG Lefeng, et al. Prediction model for power supply reliability of distribution network using PCA-PSO-ELM[J]. Journal of Harbin Engineering University, 2018, 39(6), 1116-1122. DOI: 10.11990/jheu.201611088.

### 文章历史

PCA-PSO-ELM配网供电可靠性预测模型

1. 南方电网科学研究院有限责任公司, 广东 广州 510080;
2. 华南理工大学 电力学院, 广东 广州 510640

Prediction model for power supply reliability of distribution network using PCA-PSO-ELM
XU Aidong1, LI Haofei2, CHENG Lefeng2, YU Tao2
1. Electric Power Research Institute, China Southern Power Grid, Guangzhou 510080, China;
2. School of Electric Power, South China University of Technology, Guangzhou 510640, China
Abstract: To enhance the predictive precision of power supply reliability in a distribution grid, a prediction model of power supply reliability in a distribution grid was proposed via principal component analysis (PCA) and particle swarm optimization extremity learning machine (PSO-ELM). First, the impact factors of power supply reliability were analyzed from various aspects. The linear combinations of the original variables were used to obtain the comprehensive variables for realizing the dimension reduction of the data. On the basis of data pretreatment, the artificial neural network was established, and PSO was applied to optimize the input weights and threshold values of ELM to complete model training. Finally, 30 kinds of impact factors of power supply reliability of the samples, which were obtained from 47 power supply bureaus of a large power grid, were used for simulative analysis. The PCA-PSO-ELM algorithm was compared with three kinds of regressive fitting algorithms to verify the validity of the method. The prediction model could fully consider the impact factors of power supply reliability in many aspects. It is applicable for multiple input variables and can provide a scientific and effective reference to guide power supply enterprises in working out a reliability lifting strategy.
Key words: power supply reliability of distribution network    principal component analysis    extreme learning machine    particle swarm optimization    evaluation index of power supply reliability    prediction model

1 配网供电可靠性预测模型 1.1 主成分分析

1) 构成变量采样的原始数据矩阵Xn×p:

 ${\mathit{\boldsymbol{X}}_{n \times p}} = \left[ {\begin{array}{*{20}{c}} {{x_{11}}}&{{x_{12}}}& \cdots &{{x_{1p}}}\\ {{x_{21}}}&{{x_{22}}}& \cdots &{{x_{2p}}}\\ \cdots&\cdots&\cdots&\cdots \\ {{x_{n1}}}&{{x_{n2}}}& \cdots &{{x_{np}}} \end{array}} \right]$ (1)

2) 对变量采样原始数据矩阵进行标准化处理得到标准化矩阵Xn×p*

3) 对标准化矩阵Xn×p*求解相关系数矩阵R

 ${r_{ij}} = \frac{{\sum\limits_{k = 1}^n {\left( {{x_{ki}} - {{\bar X}_i}} \right)\left( {{x_{kj}} - {{\bar X}_j}} \right)} }}{{\sqrt {\sum\limits_{k = 1}^n {{{\left( {{x_{ki}} - {{\bar X}_i}} \right)}^2}} \sum\limits_{k = 1}^n {{{\left( {{x_{kj}} - {{\bar X}_j}} \right)}^2}} } }}$ (2)

4) 求解样本相关系数矩阵R的特征方程得到特征值和特征向量。求解特征方程与特征向量，首先计算特征方程|λE-R|=0，λi(i=1, 2, …, p)，将p个特征值按由大到小的顺序排列，即λ1λ2λ3…≥λp≥0。然后计算(λiE-R)X=0，分别λi求出对应的X

5) 求出累计贡献率，初步估计主成分个数，所选取的主成分个数应使累计贡献率达到85%~95%。选取主成分的个数取决于主成分的累积贡献率，主成分的贡献率Qi和累计贡献率Q(m)的计算公式分别为

 ${Q_i} = \frac{{{\lambda _i}}}{{\sum\limits_{k = 1}^p {{\lambda _k}} }} \times 100\% \left( {i = 1,2, \cdots ,p} \right)$ (3)
 ${Q_\Sigma }\left( m \right) = \sum\limits_{k = 1}^m {{Q_k}\left( {m = 1,2, \cdots ,p} \right)}$ (4)

6) 计算主成分载荷以及主成分得分。

 ${l_{ij}} = \sqrt {{\lambda _i}} {e_{ij}}\left( {i,j = 1,2, \cdots ,p} \right)$ (5)

 $\left\{ \begin{array}{l} {F_1} = {l_{11}}\left( {{X_1} - {{\bar X}_1}} \right) + {l_{12}}\left( {{X_2} - {{\bar X}_2}} \right) + \cdots + \\ \;\;\;\;\;\;\;{l_{1p}}\left( {{X_p} - {{\bar X}_p}} \right)\\ {F_2} = {l_{21}}\left( {{X_1} - {{\bar X}_1}} \right) + {l_{22}}\left( {{X_2} - {{\bar X}_2}} \right) + \cdots + \\ \;\;\;\;\;\;\;{l_{2p}}\left( {{X_p} - {{\bar X}_p}} \right)\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \vdots \\ {F_m} = {l_{m1}}\left( {{X_1} - {{\bar X}_1}} \right) + {l_{m2}}\left( {{X_2} - {{\bar X}_2}} \right) + \cdots + \\ \;\;\;\;\;\;\;{l_{mp}}\left( {{X_p} - {{\bar X}_p}} \right) \end{array} \right.$ (6)
1.2 PSO-ELM预测模型

 $\begin{array}{*{20}{c}} {{v_{i,j}}\left( {t + 1} \right) = {v_{i,j}}\left( t \right) + {c_1}{r_1}\left[ {{p_{i,j}} - {x_{i,j}}\left( t \right)} \right] + }\\ {{c_2}{r_2}\left[ {{p_{g,j}} - {x_{i,j}}\left( t \right)} \right]} \end{array}$ (7)
 ${x_{i,j}}\left( {t + 1} \right) = {x_{i,j}}\left( t \right) + {v_{i,j}}\left( {t + 1} \right),j = 1,2, \cdots ,D$ (8)

PSO-ELM预测评估模型需要初始化粒子群体，即确定粒子群的大小及搜索维度，种群过小容易陷入局部最优，种群过大又会影响优化时间。将每个粒子对应的输入层权值和隐含层阈值代入ELM训练算法中。第i个粒子的适应度函数fi用均方误差的倒数表示。对每个粒子将其当前适应度fif(pbest)对比，若fif(pbest)说明当前的适应度更高，则将用当前位置更新个体历史最佳位置pbest，否则保持pbest不变。同理比较当前适应值fif(gbest)，当fif(gbest)更新全局最佳位置gbest。然后，根据式(7)及(8)更新每个粒子的速度与位置。当迭代次数达到最大迭代次数或最佳适应度达到设定阈值即停止寻优过程。通过PSO算法得到的最优输入权值ω和阈值b后，利用ELM训练算法，代入公式β=H+T，即可计算出模型预测值[12]

1.3 供电可靠性影响因素及评价指标的选取 1.3.1 供电可靠性影响因素

 Download: 图 1 供电可靠性指标分类 Fig. 1 Classification of reliability index of power supply

1.3.2 供电可靠性评价指标

 $\left\{ \begin{array}{l} {p_{ij}} = {V_{ij}}/\sum\limits_{j = 1}^M {{V_{ij}}} \\ {e_i} = - \frac{1}{{\ln M}}\sum\limits_{j = 1}^M {{p_{ij}}\ln {p_{ij}}} \\ {D_i} = 1 - {e_i}\\ {x_i} = {D_i}\sum\limits_{i = 1}^N {{D_i}} \end{array} \right.$ (9)

 ${w_i} = {k_1}{x_i} + {k_2}{y_i}$ (10)

 ${p_i} = \sum\limits_{i = 1}^N {{w_i}{V_{ij}}}$ (11)
1.4 预测模型结构与算法流程

 Download: 图 2 算法求解流程图 Fig. 2 Flow chart of the proposed algorithm
2 PCA-PSO-ELM仿真算例 2.1 仿真分析

2.2 模型对比

 Download: 图 6 多种模型决定系数对比 Fig. 6 Comparison decision coefficients of various model

 Download: 图 7 多种模型训练时间对比 Fig. 7 Comparison of training times of various model

3 结论

1) 可以充分考虑多方面多角度的供电可靠性影响因素，适用于多输入变量的情况，有利于对供电可靠性更加全面的分析预测。

2) 对输入的原始数据进行主成分分析的预处理，有效地实现了输入数据的降维，并去除各指标之间的相关性，提升了极限学习机训练模型的预测精度和稳定性。

3) 利用粒子群优化算法对神经网络的输入权值和阈值进行优化，有效减少预测模型的训练时间和预测精度。

4) 根据训练好的模型对影响供电可靠性指标的相关因素进行灵敏度分析可以获得对供电可靠性指标较敏感的相关特征量。

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