# pmuBAGE: The Benchmarking Assortment of Generated PMU Data for Power System
Events - Part I: Overview and Results

Brandon Foggo, Koji Yamashita, Nanpeng Yu B. Foggo, K. Yamashita, and N. Yu
are with the Department of Electrical and Computer Engineering, University of
California, Riverside, CA 92501 USA. E-mail<EMAIL_ADDRESS>
###### Abstract

We present pmuGE (phasor measurement 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. The dataset is
available online for use by any researcher or practitioner in the field. PMU
data are challenging to obtain, especially those covering event periods.
Nevertheless, power system problems have recently seen phenomenal advancements
via data-driven machine learning solutions - solutions created by researchers
who were fortunate enough to obtain such PMU data. 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 to use at the pmuBAGE
Github Repository.

Part I - This is part I of a two part paper. In part I, we describe a high
level overview of pmuBAGE, its creation, and the experiments used to test it.
Part II will discuss the exact models used in its generation in far more
detail.

###### Index Terms:

Generative Adversarial Network, Generative Model, Phasor Measurement Unit,
Power System Event.

pmuBAGE

Actual Data

Figure 1: (Left) A generated frequency event in pmuBAGE. (Right) A real
frequency event of similar type. Different colors represent different PMUs
(100 signals). The interval between two time indices is 1 / 30 seconds. The
full window corresponds to $20$ seconds of data. The presented data is scaled
to per unit values and each timeseries is shifted to have a mean of zero. The
four sub-figures represent real power, reactive power, voltage magnitude, and
frequency from top to bottom.

pmuBAGE

Actual Data

Figure 2: (Left) A generated voltage event in pmuBAGE. (Right) A real
frequency event of similar type. Different colors represent different PMUs
(100 signals). The interval between two time indices is 1 / 30 seconds. The
full window corresponds to $20$ seconds of data. The presented data is scaled
to per unit values and each timeseries is shifted to have a mean of zero. The
four sub-figures represent real power, reactive power, voltage magnitude, and
frequency from top to bottom.

##  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 transmission system operator (TSO), regional system operator (RTO) or
electric utilities has always been a bottleneck in academia. Large-scale IEEE
dynamic test cases, such as the 50-generator (145-bus) system [1], have been
widely leveraged to cope with this. However, generally accepted dynamic
models, such as combined cycle gas turbine models, and nontraditional power
components, such as 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 into many commercially available
dynamic simulation software, the widely accepted model parameters are not
fully provided.

The power system engineering research center (PSERC) 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, reference [4]
uses geographic properties to automatically generate synthetic networks, and
reference [5] focuses on the placement of generator substations and assignment
of transmission line parameters to an existing topology. Reference [6]
automatically adjusts the parameters of the placed generators according to
fuel type and the statistics of real generators in the same geographic region.
References [7] and [8] focus on improving load properties in synthesized
grids. Reference [9] automatically adds realistically placed voltage
controllers onto an existing synthetic grid. Finally, reference [10] focuses
on integrating synthetic transmission systems with synthetic distribution
systems. References [11] and [12] describe statistical properties that can be
checked to ensure that a synthetic grid is realistic to its geographical
region.

The results of these attempts surely help demonstrate some particular dynamic
aspects of power system events more accurately - such as poorly damped
natural/forced oscillations and frequency drop following disturbances.
However, we have no all-encompassing or one-size-fits-all dynamic model.
Besides, the parameterization of the aforementioned generic model,
specifically RES models, becomes more difficult mainly due to its accelerating
spatiotemporal dispersion, which results in insufficient simulation accuracy
(i.e., less credible simulation results), especially for the future grid
analysis with high penetration of the RES. Superimposing realistic noise to
the simulated response is also not trivial. 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
TSO/RTOs 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 research teams will go through several
steps to setup small collaborations with the utility companies who own this
PMU data. This will result in a small amount of data spanning a somewhat
random time-span, and will be accessible by that research team for about the
length of time that it requires to perform one or two innovative research
projects.

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. Suppose,
for example, that two research teams developed a data-driven algorithm with
data from the same geographical location for the same problem. However, the
first team used spring data, and the second used summer data. The first team’s
algorithm then reports a $2\%$ improvement in performance over the second
team. However, summer data is more unwieldy than spring data. Thus, some
improvement must have come from using a more well-behaved dataset. In no way
can we reliably determine the size of this contribution, so we are left in a
scenario in which we do not honestly know which algorithm has better
performance.

Realistic generated data, on the other hand, is more readily accepted for
release by TSO/RTOs 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 classification 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. We encourage any researcher in this field to
provide benchmarks of their algorithms using this dataset. Two example events
are displayed in Figures 1 and 2.

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 an immediately available dataset, the generative model will be
described in excruciating detail in the following subsections of this two
parts paper. Thus, if some researchers desired 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.

We’d like to note a few preliminary works of this type in literature. In these
works, performed in references [13, 14, 15], a simple Generative Adversarial
Network (GAN) architecture was trained on data simulated via IEEE dynamic test
cases. These 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.

To our knowledge, the present work is the first to attempt a fully data driven
approach to generating synthetic synchrophasor 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, separating dynamic components into inter-event components
and intra-event components, and using state-of-the-art probabilistic
programming methods and deep cascaded convolutional generative models, we are
able to create much more realistic synthetic event data than was previously
possible.

  * •

We introduced a new QR-reorthogonalization trick to reintegrate the inter-
event signatures with intra event signatures and sparse signatures, which are
not typically statistically independent. This significantly increases the ease
of training our model.

  * •

By introducing several feature matching training loss functions to our model,
including a completely new loss function which we denote the “quantile loss”,
we are able to capture the distribution of the aforementioned statistical
component extremely tightly.

  * •

We trained our model on the largest real-world synchrophasor dataset to date.
This has allowed us to capture the PMU-varying and time-varying dynamics of
power system event data more accurately.

  * •

We provide the first comprehensive set of realistic synthetic events covering
many types of event causes, including previously under-modelled event types
such as those involving lightning strikes and renewable generation.

Example applications of pmuBAGE include experimenting/benchmarking for power
system event detection [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], event
classification [27, 28, 29, 30, 31, 32], and missing value replacement
(especially during events) [33, 34, 35, 36, 37, 38, 39, 40]

Part I - This is part I of a two part paper. In part I, we describe a high
level overview of pmuBAGE, its creation, and the experiments used to test it.
Part II will discuss the exact models used in its generation in far more
detail.

pmuBAGE is available online in our Github Repository.

##  II Overall Framework

Figure 3: The High Level Framework of our model.

Our goal is to create a realistic PMU dataset for power system events without
compromising the privacy of the PMUs used to train it. The “Event-
Participation” (EP) decomposition transformation is our primary device for
achieving this. This decomposition separates event tensors into Event
Signatures, shared across all PMUs, and participation factors specific to each
PMU [40]. 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 our dataset that do not vary with PMUs (i.e., the
event signatures) in their exact form. We then need only perform
statistical/generative modeling on the participation factors of this
decomposition.

A very high-level view of our framework is provided in Figure 3. 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 The Event-Participation Decomposition

Figure 4: (Left) An event signature. (Middle) Corresponding Participation
Factor distribution. (Right) Resulting PMU data array (with some white noise
added for realism).

Our generative model uses the Event-Participation (EP) decomposition of PMU
event data. The decomposition was originally used in reference [40] wherein
its time-independent component was leveraged for missing value replacement.
Event-Participation decomposes events into several dynamic components, called
event signatures, and a corresponding set of static components (which vary
over PMUs), called participation factors. Each event signature captures a
distinct component of the overall shape of the event, and the corresponding
participation factor captures how much each PMU undergoes that behavior. This
idea has its roots in the small-signal stability analysis of power systems. A
simple conceptual example of this decomposition is shown in Figure 4.

Before we describe how to compute this decomposition, we will first give some
motivation to its use in the present work. The decomposition makes the
conceptualization of a generative model much simpler. We can think of each
participation factor as a set of samples from an independent identically
distributed distribution that depends on the event signature. We can thus, in
turn, think of each event-participation factor as a composition of two maps -
the first of which takes the event signature and returns a probability
distribution, and the second of which takes the distribution and returns
samples. Since no learning is required to imitate a sampling mechanism, we
need only focus on the former of these maps.

To put this into mathematical terms, suppose we are given an event signature
$e\in\mathbb{R}^{T}$ (where $T$ is the temporal length of each instance of
data). Then we need only find a probability distribution $\mu_{\theta}(e)$ for
that event (where $\theta$ denotes any parameters used to specify that
probability distribution). Once $\mu_{\theta}(e)$ is learned (as a full
function of $e$), we can take any event signature - whether it exists in our
training dataset or not - and create a set of PMU data adhering to that
signature by sampling from it.

Note that we need not be limited to a single event signature and participation
factor. It is, in fact, far more realistic to assume that multiple dynamical
modes (i.e., event signatures) coincide - each with their own set of
participation factors.

Most applications using this decomposition require online use and often deal
with data quality problems. As a result, those applications must use advanced
techniques to compute this decomposition. However, the present work does not
have such limitations. At the end of the day, when given a full tensor of
clean PMU data, event-participation decomposition is nothing more than a
regular tensor decomposition - just with some interpretation added to the
factors.

##  IV Numerical Results

###  IV-A Training Dataset

Our training dataset consists of $PQVF$ data for $620$ Voltage Events and $84$
Frequency Events. Data was collected by Pacific Northwest National Laboratory
from $180$ simultaneous Synchrophasor measurements across the Eastern
Interconnection of the U.S. Transmission Grid at a sampling rate of $30Hz$.
The original Synchrophasor data consisted of Voltage Magnitude, Voltage Angle,
Current Magnitude, Current Angle, and Frequency decomposed as symmetrical
components (as opposed to $A$, $B$, $C$ phase data). Some Synchrophasors
reported all three symmetric components for each data type (Positive Sequence,
Negative Sequence, and Zero Sequence), but most only reported the Positive
Sequence component. Thus only Positive Sequence values were used to train our
model. $PQVF$ data was derived from the values mentioned above.

Each event in our training dataset consists of $20$ seconds ($600$ samples) of
data, with the event’s start placed at the $10$ second mark ($300$-th sample).
The exact event timing was not always reported accurately, so expert analysis
either affirmed or adjusted these start times by a few fractions of a second.
Frequent missing data samples appeared during event windows. PMUs that
exhibited such values were removed from the dataset, but only for the event
where they had missing data. Thus the PMUs used in training for one event are
not necessarily the same as the set of PMUs used to train another.

###  IV-B Training Details

Figure 5: (Left) Discriminator Loss Curve over Epochs. (Right) Generator Loss
Curve over Epochs.

The parameters of our model were trained for $500$ epochs with a batch size of
$50$ events per batch. The Adam optimizer was employed, and an $l_{2}$ weight
regularization term with a coefficient of $0.25$ was applied. Generative
Adversarial Networks are known to have notorious training difficulties. The
most common difficulty occurs when the discriminator converges too quickly.
This forces the discriminator’s feedback to the generator to have vanishing
gradients. To avoid this, the learning rates set for the discriminator’s
parameters were significantly lower than that of all other parameters.
Expressly, we set the learning rate of discriminator parameters to $1\times
10^{-5}$ while all other parameters used a learning rate of $1\times 10^{-3}$.

Training this model proceeds relatively smoothly. Training curves are shown in
Figure 5. Both loss functions dip to low values quickly during training,
followed by a somewhat slow-moving period in which both curves converge to
their near-optimal values. Here we have plotted the GAN loss used in training,
not the slew of feature matching losses described earlier. Loss curves for
those feature matching losses are similarly stable but converge much more
quickly.

###  IV-C Similarity Analysis

While we want the resulting generated events to be similar to the training
set, we certainly do not want them to be identical. If identicality were our
goal, then there would have been no problem to solve in the first place - we
would have just copied and pasted the dataset.

To ensure some level of non-similarity to the original dataset, we performed a
correlation analysis. To do so, we partitioned the datasets in two different
ways - first, by Event ID, and second, by PMU ID. For the Event ID partition,
we went through each event and computed the full tensor inner product of the
synthetic event tensor and the measured event tensor (recall that the means
and standard deviations of these datasets are already equal to zero and one
respectively). For the PMU ID partition, we went through each PMU and
calculated the full tensor inner product for that PMU after concatenating all
events that the PMU is in.

The Event ID partition will help us identify if any of the synthetic events in
our dataset are too similar to the corresponding measured event (the event
with the same set of event signatures as the synthesized tensor). The PMU ID
partition will help us identify if any PMUs have been compromised by the
synthetic dataset.

Two histograms of correlation values are plotted in Figure 6. On the left,
each datapoint used in calculating the histogram was an Event ID partitioned
correlation value. There is a peak at correlation $0.25$, but this is the
maximum of such correlation. As such, we deem that no events are too similar
to their original incarnation. On the right of Figure 6, each datapoint used
in calculating the histogram was a PMU ID partitioned correlation value. No
correlation exceeds $0.21$, so we deem that no PMU has been compromised.

###  IV-D Inception-Like Scoring

One of the most well-accepted ways to analyze the quality of generated data
samples is through a measure called the “Inception Score.” A universally
agreed-upon third-party classification model, called the Inception Model, is
trained on a set of measured data to calculate an inception score. Generated
samples are then fed into the Inception Model, and the classification accuracy
of the Inception Model on those generated images is reported. A high
classification accuracy indicates that the generated images are of high
quality.

Unfortunately, we can use no standard Inception Model for our generated Event
Samples. This is not surprising since, to our knowledge, this paper represents
the first attempt to create such data. We will thus assess the quality of
these event samples with an approximation of the Inception Score. To do this,
we took a relatively standard ResNext [41] Model (equivalent to each of the
“Feature Extraction Maps” presented above) and trained it to classify event
types with class labels “Frequency”, and “Voltage”. Training of this
classification model was performed over $200$ epochs with a batch size of $50$
using the Binary Cross Entropy loss function. Training was performed with the
Adam optimizer with a learning rate of $1\times 10^{-3}$. Training proceeded
smoothly with near monotonically-decreasing loss.

Training was performed twice - once with the synthetic data and once with the
measured data. Each training data point was 20 second event window - either
synthetic or real depending on the experiment - unmodified from its original
form. We then tested each trained model on the synthetic and measured PMU
data. This gives us four different train-test scenarios:

  1. 1.

Train on Synthetic, test on Synthetic

  2. 2.

Train on Synthetic, test on Measured

  3. 3.

Train on Measured, test on Synthetic

  4. 4.

Train on Measured, test on Measured

We are interested in the difference between the Synthetic-Synthetic, Measured-
Measured scores and the Synthetic-Measured, Measured-Synthetic Scores. Suppose
the cross scores (Synthetic-Measured, Measured-Synthetic) are not
significantly degraded from the self scores (Synthetic-Synthetic, Measured-
Measured). In that case, we deem the quality of the generated samples to be
high.

In terms of interpretation of these scores, the Synthetic-Measured score
indicates how well a model trained on these generated events will perform in
practice. In contrast, the Measured-Synthetic score indicates how well a model
trained on measured data would benchmark against pmuBAGE.

Results are reported in Table I. Since our measured and synthetic datasets are
imbalanced (with a ratio of about ${7:1}$ in favor of voltage events), we
report F1 and F2 scores alongside classification accuracy. In training each
classification scenario, we multiplied each training loss for voltage events
by $1/7$ so that their back-propagation gradient descents would be weighted
equally to those of frequency events.

Training-Testing | Acc. | F1 | F2
---|---|---|---
Synthetic-Synthetic | $99.9\%$ | $94.3\%$ | $93.3\%$
Synthetic-Measured | $\mathbf{94.3\%}$ | $\mathbf{94.2\%}$ | $\mathbf{92.8\%}$
Measured-Measured | $99.8\%$ | $94.4\%$ | $91.2\%$
Measured-Synthetic | $\mathbf{93.2\%}$ | $\mathbf{94.3\%}$ | $\mathbf{92.7\%}$
TABLE I: Self Scores and Cross Scores across different train-test scenarios.
Accuracy, F1 scores, and F2 scores are reported.

Figure 6: Correlation histograms between the synthetic and measured PMU
datasets partitioned by (Left) Event ID (Right) PMU ID.

There appears to be no significant degradation in $F1$ or $F2$ scores in
cross-comparisons compared to self comparisons, but there is a notable drop in
accuracy. However, this drop is less than $7\%$, and all values are still
greater than $90\%$. However, since the dataset is very imbalanced for this
problem, the $F$ scores are more relevant since the accuracy measure is far
less sensitive to the correct identification of frequency events than they are
to voltage events (even if we misclassified every frequency event, we would
still obtain an accuracy of $85\%$).

###  IV-E Synthetic Event Images

Sample images of Voltage Events in pmuBAGE are demonstrated in Figures 7
through 10. Here, we have increased the granularity of our event labels into
further groups of “lightning strikes”, “line trips”, “wind”, and “equipment
failures”.

Sample images of Frequency Events in pmuBAGE are demonstrated in Figures 11
and 12. Here, we have increased the granularity of our event labels into
further groups of “generator trips”, and “on premises generator equipment
failures”.

Each color in these figures represents a different PMU, while each group of
four figures comprises one event (where $P$ is real power data, $Q$ is
reactive power data, $V$ is voltage magnitude data, and $F$ is frequency
data).

##  V Conclusion

The synthesized PMU dataset created in this work, pmuBAGE, is highly realistic
to the human eye and does not significantly degrade important training
evaluation metrics compared to the original measured PMU dataset from which it
was trained. Thus, pmuBAGE may serve the scientific community as a standard
benchmarking tool for algorithms which need PMU dynamic event data to train
and validate on.

Researchers should be aware of some pitfalls to this synthesized dataset.
Four, in particular, are notable. First, there is a lack of realistic banding
for frequency data - that is, the tendency for several PMUs to have the same
frequency behavior, especially during a frequency event. Instead, as a direct
result of the method used to train it, pmuBAGE tends to have PMUs act
similarly in frequency data but with a slight spread in their exact values.
Second, there is a small “wrong direction” effect in voltage events voltage
data. Actual voltage data undergoing a voltage event will primarily have PMUs
drop their voltage values, while pmuBAGE will have a small amount of PMUs
raise their values very slightly. Third, pmuBAGE occasionally displays Inter-
Area Oscillations that do not dampen as quickly as actual data; however, the
difference is relatively small. Finally, the generated events are a little
more similar to each other than one would expect from a real dataset.

While we wish to eliminate these problems in future versions of this dataset,
we believe that the current incarnation is sufficiently realistic to serve its
purpose to the community - as a training, validating, and benchmarking
dataset. We encourage any researcher to utilize this synthetic PMU dataset for
these purposes.

##  VI Acknowledgements

We sincerely thank James Follum at the Pacific Northwest National Laboratory
for reviewing the generated event dataset in detail.

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Figure 7: Samples of generated full event tensors designated as “voltage
events” caused by lightning strikes. All time stamps on the horizontal axis
correspond to $1/30$ seconds, and the full event window comprises $20$ seconds
of synthetic event data. The presented data is scaled to per unit values and
each timeseries is shifted to have a mean of zero.

Figure 8: Samples of generated full event tensors designated as “voltage
events” caused by line trips. All time stamps on the horizontal axis
correspond to $1/30$ seconds, and the full event window comprises $20$ seconds
of synthetic event data. The presented data is scaled to per unit values and
each timeseries is shifted to have a mean of zero.

Figure 9: Samples of generated full event tensors designated as “voltage
events” caused by wind. All time stamps on the horizontal axis correspond to
$1/30$ seconds, and the full event window comprises $20$ seconds of synthetic
event data. The presented data is scaled to per unit values and each
timeseries is shifted to have a mean of zero.

Figure 10: Samples of generated full event tensors designated as “voltage
events” caused by equipment failures. All time stamps on the horizontal axis
correspond to $1/30$ seconds, and the full event window comprises $20$ seconds
of synthetic event data. The presented data is scaled to per unit values and
each timeseries is shifted to have a mean of zero.

Figure 11: Samples of generated full event tensors designated as “frequency
events” caused by generator trips. All time stamps on the horizontal axis
correspond to $1/30$ seconds, and the full event window comprises $20$ seconds
of synthetic event data. The presented data is scaled to per unit values and
each timeseries is shifted to have a mean of zero.

Figure 12: Samples of generated full event tensors designated as “frequency
events” caused by on-premises generator equipment failures. All time stamps on
the horizontal axis correspond to $1/30$ seconds, and the full event window
comprises $20$ seconds of synthetic event data. The presented data is scaled
to per unit values and each timeseries is shifted to have a mean of zero.