计算机系统应用  2001, Vol. 29 Issue (9): 131-135 PDF

1. 中国科学院大学 计算机与控制学院, 北京 100049;
2. 中国科学院 沈阳计算技术研究所, 沈阳 110168;
3. 国网辽宁省电力有限公司, 沈阳 110168

Accident Prediction of Power Distribution Network Based on Graph Neural Network
YANG Hua1,2, LI Xi-Wang2, SI Zhi-Jian2,3, ZHANG Xiao1,2
1. School of Computer and Control Engineering, University of Chinese Academy of Sciences, Beijing 100049, China;
2. Shenyang Institute of Computing Technology, Chinese Academy of Sciences, Shenyang 110168, China;
3. State Grid Liaoning Electric Power Co. Ltd., Shenyang 110168, China
Foundation item: National Science and Technology Major Program of China (2017ZX01030-201)
Abstract: Power distribution network accident in actual application scenarios account for more than 80% of total grid accident, and the prediction of power distribution network accident has always been a difficult issue. This study, under the call of “Ubiquitous IoT” proposed by the State Grid, analyzes the research results of scholars on this issue, and proposes an accident prediction method for power distribution network based on graph neural network with the idea of graph neural network. Referring to the commonly used graph neural network design framework, the node information aggregation function, prediction function, and loss function are designed in detail, and reasonable depth parameters are selected according to the algorithm flow test. The algorithm fully considers the mutual influence between connected nodes, and uses the real grid operation data to compare the two other algorithms commonly used in this field. Experiments show that the proposed algorithm improves the accuracy by 3.0% and is more robust.
Key words: graph neural network     power distribution network     Ubiquitous IoT     deep learning     back propagation

1 配电网结构分析

 图 1 配电网局部拓扑图

2 算法模型 2.1 算法框架概述

 图 2 配电网简化拓扑图

 $\left\{\begin{array}{l} h_v^k = {f_v}({l_v},h_v^{k - 1},h_{ne[v]}^k) \\ {o_v} = {g_v}(h_v^k,{l_v}) \\ \end{array} \right.$ (1)

 图 3 图模型计算结构

2.2 关键算法流程

 $h_v^k \leftarrow \sigma (W_{agg}^k \cdot {{MEAN(\{ h}}_v^k{\rm{\} }} \cup {{\{ h}}_n^k{{,}}\forall {{n}} \in {{Ne[v]\} )}})$ (2)

1　　 $\scriptstyle h_v^0 \leftarrow {x_v},\forall v \in V$

2　　for $\scriptstyle K$ to 0 do

3　　　for $\scriptstyle v \in V$ do

4　　 $\scriptstyle h_v^k \leftarrow f_w^k(\{ h_v^{k - 1},\forall v \in Ne[v]\} )$

5　　　end

6　　　 $\scriptstyle h_v^k \leftarrow h_v^k/{\left\| {h_v^k} \right\|_2},\forall v \in V$

7　　end

8　　 $\scriptstyle {t_v} \leftarrow h_v^k,\forall v \in V$

 ${o_v} = \sigma ({W_o} \times h_v^k)$ (3)

 $L = {y_t}\log ({o_t}) + (1 - {y_t})\log (1 - {o_t})$ (4)

2.3 优化方法

 图 4 网络展开图

 \left\{ \begin{aligned} \dfrac{{\partial L}}{{\partial {W_o}}}\;\;& = \left(\dfrac{{{y_t}}}{{{o_t}}} + \dfrac{{1 - {y_t}}}{{1 - {o_t}}}\right) \cdot \dfrac{{\partial {o_t}}}{{\partial {W_o}}}\\ & = \left(\dfrac{{{y_t}}}{{{o_t}}} \!+\! \dfrac{{1 - {y_t}}}{{1 - {o_t}}}\right)\! \cdot \! \sigma ({W_o}h_v^k\! +\! {b_o})(1 - \sigma ({W_o}h_v^k \!+ \!{b_o})) \cdot h_v^k \\ & = ({y_t} - {o_t}) \cdot h_v^k\\ \dfrac{{\partial L}}{{\partial {b_o}}} \;\;\; &= {y_t} - {o_t}\\ \dfrac{{\partial h_v^k}}{{\partial {W_{agg}}}}\! &= \sigma ({W_{agg}} \! \cdot \! h_v^{k \! - \! 1} \! + \! {b_{agg}}) \! \cdot \! (1 \! - \! \sigma ({W_{agg}} \! \cdot \! h_v^{k - 1} \! + \! {b_{agg}})) \! \cdot \! h_v^{k - 1}\\ \dfrac{{\partial h_v^k}}{{\partial {b_{agg}}}} &= \sigma ({W_{agg}} \cdot h_v^{k - 1} + {b_{agg}}) \cdot (1 - \sigma ({W_{agg}} \cdot h_v^{k - 1} + {b_{agg}})) \end{aligned}\right. (5)

Different aggregator functions $\scriptstyle f_v^k$ ; iteration $\scriptstyle Epoch$

$\scriptstyle Main$ :

for $\scriptstyle epoch$ =1 to $\scriptstyle Epoch$ do

$\scriptstyle L = Forward$

$\scriptstyle Backward$

End

$\scriptstyle Forward$ :

$\scriptstyle {t_v} = aggregation(G(V,\varepsilon ),{x_v},k,W_{agg}^k,f_v^k)$

$\scriptstyle {o_t} = \sigma ({W_o} \times h_v^{})$

$\scriptstyle L = \sum\limits_{t \in T} {{y_t}\log ({o_t}) + (1 - {y_t})\log (1 - {o_t})}$

return $\scriptstyle L$

$\scriptstyle Backward$ :

For 2 to $\scriptstyle k$ do:

$\scriptstyle {W_o} = {W_o} - \lambda ({y_t} - {o_t}) \cdot h_v^k$

$\scriptstyle {b_o} = {b_o} - \alpha \cdot ({y_t} - o{}_t)$

$\scriptstyle{ {W_{agg}} = {W_{agg}} - \beta ({y_t} - {o_t}) \cdot \sigma ({W_{agg}} \cdot h_v^{k - 1} + {b_{agg}}) \times }$

$\scriptstyle(1 - \sigma ({W_{agg}} \cdot h_v^{k - 1} + {b_{agg}})) \cdot h_v^{k - 1}$

$\scriptstyle {b_{agg}} = {b_{agg}} - \delta \cdot ({y_t} - o{}_t)\sigma ({W_o}h_v^k + {b_o})(1 - \sigma ({W_o}h_v^k + {b_o}))$

3 仿真实验

3.1 网络深度的取值与分析

 图 5 不同k值的损失对比

3.2 模型对比

4 结论与展望

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