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
1
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
2
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
3
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)
+
N
X
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.
摘要:

1pmuBAGE:TheBenchmarkingAssortmentofGeneratedPMUDataforPowerSystemEventsBrandonFoggo,Member,IEEE,KojiYamashita,Member,IEEE,NanpengYu,SeniorMember,IEEE,Abstract—ThispaperintroducespmuGE(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!
分类:图书资源 价格:10玖币 属性:13 页 大小:2.83MB 格式:PDF 时间:2025-04-30

开通VIP享超值会员特权

  • 多端同步记录
  • 高速下载文档
  • 免费文档工具
  • 分享文档赚钱
  • 每日登录抽奖
  • 优质衍生服务
/ 13
客服
关注