1 pmuBAGE The Benchmarking Assortment of Generated PMU Data for Power System Events

2025-04-30 0 0 2.83MB 13 页 10玖币

侵权投诉

pmuBAGE: The Benchmarking Assortment of

Generated PMU Data for Power System Events

Brandon Foggo, Member, IEEE, Koji Yamashita, Member, IEEE, Nanpeng Yu, Senior Member, IEEE,

Abstract—This paper introduces pmuGE (phasor measure-

ment unit Generator of Events), one of the ﬁrst data-driven

generative model for power system event data. We have trained

this model on thousands of actual events and created a dataset

denoted pmuBAGE (the Benchmarking Assortment of Generated

PMU Events). The dataset consists of almost 1000 instances

of labeled event data to encourage benchmark evaluations on

phasor measurement unit (PMU) data analytics. PMU data are

challenging to obtain, especially those covering event periods.

Nevertheless, power system problems have recently seen phenom-

enal advancements via data-driven machine learning solutions. A

highly accessible standard benchmarking dataset would enable

a drastic acceleration of the development of successful machine

learning techniques in this ﬁeld. We propose a novel learning

method based on the Event Participation Decomposition of Power

System Events, which makes it possible to learn a generative

model of PMU data during system anomalies. The model can

create highly realistic event data without compromising the

differential privacy of the PMUs used to train it. The dataset

is available online for any researcher or practitioner to use at

the pmuBAGE Github Repository.

Index Terms—Generative Adversarial Network, Generative

Model, Phasor Measurement Unit, Power System Event.

I. INTRODUCTION

SOLUTIONS to any power system dynamic study require

realistic dynamic response data. Obtaining realistic phasor

measurement unit (PMU) data that are used by the transmis-

sion system operator (TSO) or electric utilities has always

been a bottleneck in academia. Large-scale IEEE dynamic

test cases, such as the 145-bus system [1], have been widely

leveraged to cope with this. However, generally accepted dy-

namic models, such as combined cycle gas turbine models, and

renewable energy sources (RES), are missing in such dynamic

test cases. Although generic dynamic models for turbine-

governors [2] have been publicly available and implemented

in many commercial dynamic simulation software, the widely

accepted model parameters are not fully provided.

The power system engineering research center has begun to

create synthetic dynamical data by simulating more realistic

North American Eastern and Western Interconnection models

[3]. Many non-data driven modelling approaches to create

synthetic data can be found in literature. Much of this research

builds on each other in a modular way. For example, refer-

ence [4] uses geographic properties to automatically generate

synthetic networks. Reference [5] automatically adjusts the

parameters of the generators according to fuel type and the

statistics of real generators in the same geographic region. Ref-

erence [6] focuses on improving load properties in synthesized

grids. Reference [7] focuses on integrating synthetic trans-

mission systems with synthetic distribution systems. Finally,

reference [8] performs dynamic simulations on a synthetic

Texas power grid to generated synthetic PMU data.

The results of these attempts surely help demonstrate some

particular dynamic aspects of power system events more

accurately - such as poorly damped oscillations and fre-

quency drop following disturbances. However, we have no all-

encompassing or one-size-ﬁts-all dynamic model. Besides, the

parameterization of the aforementioned generic model, specif-

ically RES models, becomes more difﬁcult due to its acceler-

ating spatiotemporal dispersion, which results in insufﬁcient

simulation accuracy (i.e., less credible simulation results),

especially for the future grid analysis with high penetration of

RES. Superimposing realistic noise to the simulated response

is also not trivial [9]. Therefore, real-world measurement data

is craved by both academics and industry engineers.

However, access to real-world PMU data is quite limited.

Although some TSOs have started to provide sample PMU

data to researcher, most do not offer to serve them. The

primary factor of hesitation for the release of this data is

the potential risk of exposing any vulnerabilities in the bulk

power system. Most of the time, power system researchers

will go through a lengthy process to setup collaborations with

the utility companies who own this PMU data. However, the

amount of data shared with the researchers is often small and

spanning a somewhat random time-span. There are two meta-

level effects to this process. The ﬁrst effect is that initiating

a project on actual data in this ﬁeld has a considerable time

overhead, limiting the amount of quality research that comes

out. The second effect is signiﬁcant heterogeneity of results

on the same problem.

Realistic generated data, on the other hand, is more readily

accepted for release by TSOs because such data is no longer

treated as real. By generated data, we refer speciﬁcally to

the process of creating synthetic data by sending random

noise through a deep neural network trained on real data.

Such deep generative models promise to boost power system

dynamic studies, speciﬁcally for event detection and classi-

ﬁcation with big data analysis. The dataset presented in this

paper, pmuBAGE, will bring back the advantages of using

standard IEEE dynamic test cases - i.e., the accessibility and

homogeneity of results - while maintaining the realism and

difﬁculty of dealing with real PMU data.

pmuBAGE is the result of training a novel generative model,

called the pmuGE (the phasor measurement unit Generator of

Events), and training it on over 1000 real events gathered over

two years on the bulk U.S. Power Grid. While pmuBAGE is

arXiv:2210.14204v1 [eess.SY] 25 Oct 2022

an immediately available dataset, the generative model will be

described in great detail in this paper. If researchers desire to

create an updated version of pmuBAGE using new PMU data,

the instructions for doing so are readily available in this paper.

The model preserves the privacy of the PMUs used to train it.

There are a few existing papers on this topic. A sim-

ple Generative Adversarial Network (GAN) architecture was

trained on PMU data simulated via 9-bus and 39-bus IEEE

dynamic test cases [10], [11]. These two works are important

in showing the feasibility of training generative models on

PMU data during events. However, the limitations of the

data used to train these models - that the corresponding

training datasets do not come from real synchrophasor data

- resulted in a synthetic datasets with unrealistic noise and

PMU-speciﬁc behaviors. Example applications of pmuBAGE

include experimenting/benchmarking for power system event

detection [12]–[16], event classiﬁcation [17], [18], and missing

value replacement (especially during events) [19]–[24]

To our knowledge, the present work is the ﬁrst to attempt a

fully data driven approach to generating synthetic synchropha-

sor data using large-scale real world PMU data.

The contributions of this paper are as follows:

•By decomposing the PMU data into a static statistical

component and a dynamic physical component, separat-

ing dynamic components into inter-event and intra-event

components, and using probabilistic programming meth-

ods and deep cascaded convolutional generative models,

the proposed model is able to create much more realistic

synthetic event data than was previously possible.

•A new QR-reorthogonalization trick is proposed to reinte-

grate the inter-event signatures with intra event signatures

and sparse signatures, which are not typically statistically

independent. This signiﬁcantly increases the ease of train-

ing the proposed model.

•By introducing several feature matching training loss

functions including a completely new loss function de-

noted as the “quantile loss”, the proposed model is able to

capture the distribution of the aforementioned statistical

component extremely tightly.

•The proposed model is trained on the largest real-world

synchrophasor dataset to date. This enables the proposed

model to capture the PMU-varying and time-varying

dynamics of power system event data more accurately.

•The ﬁrst comprehensive set of realistic synthetic events is

provided covering many types of event causes, including

previously under-modelled event types such as those

involving lightning strikes and renewable generation.

The remainder of the paper is organized as follows. Section

II presents the overall framework of the pmuGE model. Sec-

tion III goes over some notational notes. Section IV details the

event-participation decomposition and its computation. Section

V provides all of the information necessary to replicate the

generative model for participation factors, with subsections

V-A through V-F detailing that of the intra-event signature

generator, and subsection V-G detailing those of the inter-

event signatures. Section VI shows the numerical study results.

Section VII concludes the paper.

Fig. 1: The overall framework of the pmuGE model.

II. OVERALL FRAMEWORK

The goal of this research is to create a realistic PMU dataset

for power system events without compromising the privacy of

the PMUs used to train it. The proposed “Event-Participation”

(EP) decomposition transformation is the primary device for

achieving this. This decomposition separates event tensors

into event signatures, shared across all PMUs, and participa-

tion factors speciﬁc to each PMU [24]. By using the Event

Participation Decomposition, the data properties that could

compromise PMUs are extracted into the participation factors,

while the parts that cannot are extracted into event signatures.

This allows us to maintain the properties of the dataset that do

not vary with PMUs (i.e., the event signatures) in their exact

form. Then, a statistical/generative modeling can be performed

on the participation factors of this decomposition.

A very high-level view of the proposed framework is

provided in Figure 1. Standardized PQVF (real power, reactive

power, voltage magnitude, frequency) data tensors are ﬁrst

fed into a module denoted “EP” (short for Event-Participation

Decomposition). The EP module decomposes each tensor

into four building blocks - inter-event signatures, intra-event

signatures, inter-event participation factors, and intra-event

participation factors. No generative modeling is required for

either of the event-signature components. On the other hand,

the participation factor components cannot be used directly

since they carry all of the PMU speciﬁc information.

The synthetic Intra-Event components are created via a

deep generative probabilistic program resembling a Generative

Adversarial Network (GAN). The inter-event participation

factors, being much less nuanced in their distributions, are

modelled via a statistical simulation.

III. IMPORTANT NOTATIONAL NOTES

Most of the tensors that appear in this text will have

three axes. The ﬁrst axis will typically denote the datatype

- indexing, in order, “real power,” “reactive power,” “voltage

magnitude,” and “frequency.” The meaning of the latter two

axes will differ by context. However, the products of these

tensors will be written with the standard matrix multiplication

notation. If Aand Bare both tensors with three axes, then

AB is a new three-axis tensor given by contracting the third

axis of Awith the second axis of B. Put another way, AB

is the tensor obtained by looping through and holding each

index of the ﬁrst axis of Aand B(resulting in 4standard

matrices each), performing matrix multiplication on each of

the holds, and then re-stacking the resulting matrices back

into a 3-tensor. For further reference, this is the convention

used in the “matmul” function in both NumPy and PyTorch.

IV. THE EVENT-PARTICIPATION DECOMPOSITION

A. Decomposition Properties and Transformation Tricks

In this subsection, we give a set of desired properties

that the event-participation decomposition ought to have, and

present some general tips to obtain such properties. A full

description of the decomposition steps will be provided in the

next subsection.

1) Algorithmic Requirements: There are a myriad of tensor

decomposition methods available for use. Selecting which to

use depended on two key design constraints. First, the method

must have guaranteed convergence over a widely varying

set of tensors. Second, the method should yield independent

participation factors.

The reason for this ﬁrst constraint is that the dataset used

for training the model involves almost 1000 power system

event tensors, with event causes ranging from downed lines,

generator tripping, lightning strikes, and more. A wide variety

of dynamic phenomena can be observed in this dataset. Thus,

uniform convergence of the chosen tensor decomposition

technique is critical.

The second constraint is not as straightforward as the ﬁrst.

Recall that each participation factor is a set of samples from

an event-dependent distribution. Orthogonality means that the

distributions corresponding to each co-occurring event signa-

ture are statistically uncorrelated. In the “PMUs-as-samples”

viewpoint, this is the only variable observed in multiple

instances. Unlike participation factors, event signatures are

viewed holistically, not as samples of a random variable. Thus,

the independence of event-participation pairs from one another

can only be tested by the independence of participation factors.

Independence of event-participation pairs has three impor-

tant outcomes:

1) The distributions are less taxed by the curse of dimen-

sionality, and are therefore easier to learn.

2) An outlying or otherwise unrealistic sample of one

participation factor has no effect on the realism of the

other participation factors.

3) A given power system event signature can be perturbed

independently without sacriﬁcing the realism of the

others.

The ﬁrst two of these outcomes depend only on the in-

dependence of participation factors. The last outcome relies

on assuming that this independence also carries over to the

independence of event signatures.

These latter outcomes are expanded upon next. For the sec-

ond outcome, suppose there are several coinciding event sig-

natures e1, e2,· · · , er. These event signatures are sent through

the learned functions µθto obtain µθ(e1, e2,· · · , er) =

µθ1(e1)µθ2(e2)· · · µθr(er). Then Nvalues are sampled from

this joint distribution and stacked in vectors to obtain partici-

pation factors p1, p2,· · · , pr. If there is an immense outlying

value in p1, then only the outlier in p1needs to be resampled.

If they are not independent, then all rparticipation factors

need to be resampled. As the number of co-occurring event

signatures increases, the likelihood of one of these participa-

tion factors being an outlier increases as well.

For the third outcome, suppose there are rcoinciding

event signatures {ei}i=1,···r, which can be used to obtain

the distributions {µθ(ei)}i=1,··· ,r, and participation factors

{pi}i=1,··· ,r. If the ﬁrst event signature is perturbed by a small

amount ∆e1, then the log-likelihood of the full event tensor

changes by the following expression:

∆P(x) = log P(e1+ ∆e1)−log P(e1)

i=1

log P(pi

1(e1+ ∆e1)|e1+ ∆e1)−log P(pi(e1)|e1),

where the index iruns over the sampled participation factors.

The ﬁrst two terms only depends on the perturbed event

signature and the latter two depend only on the adaptability of

the ﬁrst participation factor map (the terms in the sum, which

should be near zero for a well trained participation factor map).

Independent Component Analysis (ICA) [25] seems to ﬁt

the tensor decomposition method best given this latter algorith-

mic requirement. In ICA, the independent vector components

can be interpreted as participation factors and view the mixing

matrix as event signatures. Unfortunately, ICA fails to con-

verge on about 10% of the data tensors. As such, uncorrelated

(orthogonal) participation factors instead of truly independent

ones will be used in this study. A variant of Singular Value

Decomposition (SVD) was applicable. While SVD does yield

orthogonal event signatures, this property is not required since

distinct event signatures may overlap in time while still being

statistically independent in the PMU space. Removing this

requirement means that it is appropriate to either perturb event

signatures or replace them entirely - so long as any changes

made preserve the orthogonality of the participation factors.

2) The QR Re-Orthogonalization Trick: The participation

factors can always be re-orthogonalized with a QR factor-

ization. To be speciﬁc, suppose there is an existing Event-

Participation decomposition X=P ET. If Eis changed to

E, then a change in participation factor is induced resulting

in ˜

P(to maintain the equality). If a QR decomposition is

performed on ˜

P, then X=QR ˜

ET. Denoting Qas the new

set of participation factors and R˜

ETas the new set of event

signatures, then we have a new orthogonal-satisfying event

participation decomposition. This does mix the event signa-

tures. However, since Ris upper-triangular, some subspace

uniqueness can be kept by placing signatures that should be

preserved at the bottom of the event-signature matrix.

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

1pmuBAGE:TheBenchmarkingAssortmentofGeneratedPMUDataforPowerSystemEventsBrandonFoggo,Member,IEEE,KojiYamashita,Member,IEEE,NanpengYu,SeniorMember,IEEE,AbstractThispaperintroducespmuGE(phasormeasure-mentunitGeneratorofEvents),oneoftherstdata-drivengenerativemodelforpowersystemeventdata.Wehavetraine...

展开>> 收起<<

1 pmuBAGE The Benchmarking Assortment of Generated PMU Data for Power System Events.pdf

共13页,预览3页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

1 pmuBAGE The Benchmarking Assortment of Generated PMU Data for Power System Events

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: