最新「计算机体系结构和系统的机器学习」综述论文

计算机系统结构

机器学习

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Abstract—Deep neural networks have revolutionized many

machine learning tasks in power systems, ranging from pattern

recognition to signal processing. The data in these tasks is

typically represented in Euclidean domains. Nevertheless, there is

an increasing number of applications in power systems, where

data are collected from non-Euclidean domains and represented

as the graph-structured data with high dimensional features and

interdependency among nodes. The complexity of

graph-structured data has brought significant challenges to the

existing deep neural networks defined in Euclidean domains.

Recently, many studies on extending deep neural networks for

graph-structured data in power systems have emerged. In this

paper, a comprehensive overview of graph neural networks

(GNNs) in power systems is proposed. Specifically, several

classical paradigms of GNNs structures (e.g., graph convolutional

networks, graph recurrent neural networks, graph attention

networks, graph generative networks, spatial-temporal graph

convolutional networks, and hybrid forms of GNNs) are

summarized, and key applications in power systems such as fault

diagnosis, power prediction, power flow calculation, and data

generation are reviewed in detail. Furthermore, main issues and

some research trends about the applications of GNNs in power

systems are discussed.

Index Terms—Machine learning, Power systems, Deep neural

networks, Graph neural networks.

I. INTRODUCTION

After several decades of developments, the smart grid has

evolved into a typical dynamic, non-linear, and large-scale

control system, known as the power system. The

multi-directional information makes it hard to find optimal

solutions that coordinate all participants such as distribution

systems operators, producers, demand response aggregators,

and consumers [1]. For example, the high penetration of

renewable energy sources (RES) such as photovoltaic (PV)

systems and wind turbines, brings fluctuation and intermittence

to distribution networks, which requires more reserve capacity

to avoid power outage. The integration of flexible sources (e.g.,

electric vehicles) poses revolutionary changes to radial

distribution networks, such as relay protection, bidirectional

power flow, and voltage regulation [2]. Moreover, the

deregulation of electricity markets makes it difficult to find a

strategy that is beneficial to both customers and producers. In

_____________________________________

W. Liao, B. Jensen, and J. Pillai are with the Department of Energy

Technology, Aalborg University, Aalborg, Denmark (e-mail: weli@et.aau.dk;

[email protected].dk; jrp@et.aau.dk).

Y. Wang is with the State Grid Tianjin Chengxi Electric Power Supply

Branch, Tianjin, China (e-mail: yuelong.wang@tj.sgcc.com.cn).

Y. Wang (corresponding author) is with the School of Electrical

Engineering and Computer Science, KTH Royal Institute of Technology,

Stockholm, Sweden (e-mail: yusenw@kth.se).

these cases, traditional model-based methods are hard to fully

meet the control and analysis requirements of power systems

because of their uncertainty and complexity. For example,

traditional model-based methods for scenario generation of

RES aren’t able to accurately capture the probability

distribution characteristics and fluctuations of power curves [3],

since they need to artificially assume the probability density

function of power curves. Furthermore, traditional model-based

methods are not universal, since the probability distributions of

power curves vary from regions and times.

The outstanding performances of deep neural networks

(DNNs) in computer vision bring new opportunities to these

problems that cannot be solved by traditional model-based

methods in power systems. Many challenging tasks, such as

time series prediction of loads and RES, fault diagnosis,

scenario generation, and operational control, which is highly

dependent hand-made feature engineering to extract

information-rich feature sets, have recently been completely

changed by various DNNs such as recurrent neural networks

(RNNs), convolutional neural networks (CNNs), generative

adversarial networks (GANs), and automatic encoders (AEs)

[4]. The successful applications of DNNs in many tasks of

power systems are due in part to the rapid development of

advanced sensors, smart meters, computing resources, and the

effectiveness of DNNs that mines potential representations

from various Euclidean data such as power curves of RES,

dissolved gas of power transformers, and images of insulators.

Taking the detection of power line insulator defects as an

example, the image can be considered as a regular grid in

Euclidean domains as shown in Fig 1(a). To accurately identify

different states of insulators, convolutional filters of CNNs are

used to extract locally latent features due to their advantages in

processing compositionality, local connectivity, and

shift-invariance of 2-D data [5]. However, there are some data

of power systems collected from non-Euclidean domains, such

as the graph-structured data with nodes and edges. For instance,

the input data of power flow calculation includes the loads of

each node and an adjacency matrix, which is a kind of

graph-structured data as shown in Fig 1(b) [6]. The complexity

of graph-structured data has brought huge challenges to

existing DNNs defined in Euclidean domains [7]. Specifically,

the graph-structured data may have unordered nodes of

different sizes, and these nodes may have a different number of

neighbors, since the graph-structured data may be irregular.

Although some important operations (e.g., convolution) are

easy to calculate in Euclidean domains, they are hard to be

generalized to graph domains. In this case, the existing DNNs

in Euclidean domains such as CNNs and RNNs are not suitable

for processing the graph-structured data [8], since they stack

the features of nodes by a specific order and ignore the

topological information.

A Review of Graph Neural Networks and Their

Applications in Power Systems

Wenlong Liao, Birgitte Bak-Jensen, Jayakrishnan Radhakrishna Pillai, Yuelong Wang, and Yusen Wang

Fig. 1. Euclidean convolution versus graph convolution. (a) Detection of

insulators defects in Euclidean domains. (b) Power flow calculation of the

IEEE 14-bus system in graph domains.

Recently, the generalization of DNNs from Euclidean

domains to graph domain has received more and more attention.

Various new paradigms and definitions of DNNs in graph

domains have been rapidly developed over the past few years to

deal with the complicated graph-structured data. The classical

graph neural networks (GNNs) mainly include graph

convolutional networks (GCNs), graph recurrent neural

networks (GRNNs), graph attention networks (GATs), graph

generative networks (GGNs), spatial-temporal graph neural

networks (STGNNs), and hybrid forms of GNNs such as graph

reinforcement learning (GRL) and graph transfer learning

(GTL) [9], which have shown outstanding performance for the

graph-structured data.

There is a limited number of existing review articles related

to GNNs or deep learning in power systems. These reviews

either focus on the structures of GNNs and their applications in

computer vision, or analyze the applications in power systems

of traditional DNNs defined in Euclidean domains. For

example, the training strategies and model architectures related

to five different types of GNNs are discussed in [10]. A few

review articles pay close attention to the application for

non-structural scenarios, such as image classification [11] and

natural language processing [12]. Some methods for how much

various models can be trained on large-scale knowledge graphs

are reviewed in [13]. The theoretical background of GNNs and

some geometric data such as social networks and point clouds

are introduced in [14]. Reinforcement learning (RL) is

becoming increasingly popular because of its success in dealing

with challenging decision-making problems in power systems.

The recent combinations of RL and DNNs in Euclidean

domains, and their application in power systems are critically

reviewed in [15],[16]. A comprehensive review of the

advantages of deep representation learning is conducted in [17],

which covered several large ranges, including supervised,

unsupervised, and semi-supervised applications. In general, a

part of the existing articles only focus on the application of

GNNs in the computer science (e.g., Recommendation systems,

link prediction, and protein structure classification), but do not

review the applications in power systems. Another part of the

articles investigate the advantages of traditional DNNs in

power systems, but does not involve GNNs. Relatively, this

paper provides a comprehensive review of classical GNNs and

their applications in power systems for interested researchers

who major in electrical engineering, machine learning, and

energy.

This paper focuses on providing a comprehensive review of

the GNNs and their applications in power systems, and

identifies future challenges. The contributions of this paper are

summarized as follows.

1) Introducing several classical paradigms of GNNs

structures. Each paradigm provides detailed structure and

descriptions of representative applications, and interested

researchers can easily apply it to different fields.

2) Conducting a comprehensive survey of GNNs on power

systems with the newest developments (e.g., fault diagnosis,

power prediction, power flow calculation, data generation, and

so forth), particularly over the past three years.

3) Discussing the limitations of existing models, the

theoretical advantage of GNNs, and possible future research

directions in power systems.

The remainder of this paper is organized as follows. Section

II introduces the definitions of graph-structured data and

several classical paradigms of GNNs structures. Section III

presents a comprehensive survey of GNNs on power systems

with the newest developments. Section IV shows the current

challenges and suggests application directions. Section V

summarizes conclusions.

II. DEFINITION AND PARADIGMS

A. Definitions of Graph-Structured Data

Normally, the graph-structured data can be represented as

 

,G V E

, where

is the set of edges and

is a set of

nodes [18]. Specifically,

is the i

node and

is the edge

from the j

node to the i

node. For the i

node, its

neighborhood can be denoted as

 

 

( ) ,

i i i i

N v u V v u E  

The graph-structured data generally has a nodal feature matrix

node

of n×f scales, and a feature matrix

edge

of m×c scales

for edges. The adjacency matrix

is a matrix of n×n scales

where

is equal to 0 if

eE

and

is equal to 1 if

eE

For the spatial-temporal graph, it is an attributed graph where

the features of nodes change with times [19]. A

spatial-temporal graph can be represented as

 

( ) ( )

G V E X

. For the directed graph, it has an asymmetric

adjacency matrix, since these edges are directed from one node

to another. Relatively, edges of the undirected graph are all

undirected, i.e. the adjacency matrix is symmetric, and its

normalized Laplacian matrix can be defined as:

L I D AD





(1)

where

denotes the diagonal matrix of node degrees with

ii ij





; and

is an identity matrix. Since the normalized

graph Laplacian matrix is real symmetric positive semi-definite,

it can be factored as:

L U U

(2)

where





denotes the corresponding eigenvectors

ordered by eigenvalues



; and



denotes the diagonal matrix

with

ii i





Before going further into next sections, Table I lists the

(a)

(b)

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