IEEE Power & Energy Magazine - May/June 2022 - 65

T
THIS ARTICLE INTRODUCES WAYS TO IDENTIFY
dynamic system models using measurement data. In power
system analysis, a static model represents the time-invariant
input-output relationship of a system, while a dynamic
model describes the behavior of the system over time. For
example, how will a system transit from one steady-state
operation point to another?
In the control community, learning dynamic models is a
system identification problem. Essentially, machine learning
and system identification are all about inferring models
from data. Both rely on optimization. The exact processes
of the inference may vary from statistical modeling to deep
learning neural networks. This article focuses on presenting
unique applications for deriving power system dynamic models
from measurement data.
Dynamic behaviors are difficult to capture, especially for
applications that lack analytic models. That is where datadriven/machine
learning techniques can play a critical role.
Indeed, there is a long history of power system engineers building
dynamics models using data-driven approaches, well
before machine learning was a popular term. The integration
of inverter-based resources (IBRs) adds more complexity
to the existing modeling framework because of the underlying
complex physics of IBR systems and the strict nondisclosure
requirements from original equipment manufacturers
(OEMs). Thus, data-driven-based system identification methods
are playing an increasingly important role, especially
for systems where physical models are elusive. For example,
when representing aggregated distributed energy resources
at a transmission and distribution interface, one popular
approach is to use the interface measurement data to produce
a distributed energy resource model that can map the inputs
(e.g., the voltage and frequency) to the outputs (real and reactive
power generation).
We begin by introducing the classification of measurement
data and models. We then review five commonly used datadriven
dynamic modeling applications in power systems:
1) synchronous generator model parameter identification
2) aggregated load model parameter identification
3) reduced-order model identification for control design
4) admittance model identification for subsynchronous
resonance (SSR) screening
5) electromechanical oscillation mode identification from
phasor measurement unit (PMU) data.
The first two applications are different from the last
three in terms of the outcomes of the estimation. The first
two applications estimate model parameters. This means
that the model structure is prior knowledge, and the estimation
leads to model parameters. Compared to the last three
applications, partial information of the estimation model is
known; i.e., the model is a gray-box model. Thus, dynamic
model parameter estimation problems are indeed examples
of gray-box model identification. On the other hand, if the
model structure is not imposed, the estimation leads to
black-box models.
may/june 2022
Next, we discuss IBR model identification. The current
practice of which focuses mainly on obtaining frequencydomain
admittance/impedance measurements using frequency
scans. The resulting models are black-box models
that reflect input-output relations. There are many ways to
structure IBR dynamic models to map the same input-output
relation. A more challenging question is: Can we guess
model structures and figure out the model parameters based
on measurements? The follow-up discussions attempt to
address those questions. Figure 1 summarizes the six applications
discussed in this article.
A Brief Classification of
Measurement Data and Models
Measurement data can be expressed in the time domain or
frequency domain. In power grids, digital fault recorders
and PMUs capture time-stamped (time-domain) dynamic
response data. Frequency-domain data are usually produced
via frequency scans; this is also known as the harmonic
injection method. To measure the admittance of a device,
a test circuit is first built to connect the device to a controllable
voltage source. A sinusoidal perturbation is injected
into the input portal: the voltage source. The output port (the
current)'s steady-state time-domain responses are processed
via Fourier transform to extract the frequency components.
Thus, the frequency response of the input-output system is
measured at that frequency. This experiment can be repeated
for a varying frequency.
We use a simple example of a series-connected resistorinductor-capacitor
(RLC) circuit to illustrate the types of measurement
data and the identified models. Figure 2 presents the
procedure of estimating the parameters of the resistor R, the
inductor L, and the capacitor C from time-domain dynamic
response data. The time-domain dynamic response data are
generated by a step change in the source voltage with the
capacitor voltage measured at a sampling period of 0.001 s.
Aggregated
Load Model
Identification
Synchronous
Generator
Model
Identification
IBR Model
Identification
PMU-Based
Oscillation
Mode Analysis
Data-Driven
Dynamic
Modeling
Reduced-Order
Model
Identification
for Control
Design
Admittance
Model
Identification
for SSR
Screening
figure 1. Measurement-based dynamic modeling: six
applications.
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65
IEEE Power & Energy Magazine - May/June 2022

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