IEEE Power & Energy Magazine - May/June 2022 - 69

This application of admittance model identification is to
identify a black-box model describing the terminal voltage
and current relationship only. The resulting model does not
lead to further information on the generator model structure.
Application 5: PMU Data-Basedt
Oscillation Mode Identification
PMU data have been used for oscillation mode identification
where the black-box modeling approach is usually applied.
In 2012, the IEEE Power and Energy Task Force of Identification
of Electromechanical Modes published a report,
" Identification of Electromechanical Modes in Power Systems. "
The electromechanical modes are in the range of a
fraction of to several hertz. This report presents a perspective
on using different identification methods for finding the
oscillation mode frequency, damping ratio, and mode shape
based on PMU data with a sampling rate of 30-60 Hz.
If time-domain dynamic response data are viewed as
the impulse responses of a dynamic system describing the
entire power grid, the Laplace transform of the time-domain
data represents the resulting input-output model. Oscillation
modes are associated with the poles of the Laplace domain
expression, or the eigenvalues. Subspace methods, e.g., the
eigensystem realization algorithm, may be used to form a
Hankel data matrix, further extract the system matrices for
eigenvalue computing. From the eigenvalues, the oscillation
modes, damping ratio, and frequencies are found. PMUbased
oscillation mode identification is a mature technology.
For example, several utilities have real-time mode analyzers
available to process PMU data.
Summary of the Five Applications
and Recent Progress in Gray-Box
Model Identification
To summarize, for the five applications, three of them, i.e.,
finding reduced-order models for control design, finding dq
admittance for SSR stability analysis, and PMU-based electromechanical
oscillation mode identification, are related to
identifying black-box models from measurement data. Those
models describe the input-output relationship only. The internal
structure and parameters of the system under investigation
are not imposed as for a gray-box model. The technology
of black-box model identification is mature as we have seen
real-world applications in these areas. The black-box models
are all linear models.
On the other hand, gray-box model identification is actively
under investigation. The first two applications-identifying
generator reactance and time constants and identifying parameters
for load modeling-belong to the category of gray-box
model identification. For those applications, a prior knowledge
of internal physics must be combined with measurement-based
learning to achieve the goal of model identification.
The models can be nonlinear.
The main issue of gray-box identification is that the measurement
data may not contain sufficient information on the
may/june 2022
parameters. This leads to ill-conditioned estimation problems.
If this is the case, the estimation problem can be formulated
to estimate a subset of the parameters. Algorithm-wise, convergence
and local optimum are the main issues for nonlinear
optimization problems. For parameter estimation, a local
optimum means the identified parameters may be far from the
true parameters. The resulting estimated output may have a
poor matching degree with the measured output. Therefore,
much effort has been devoted to refining the optimization
problem formulation.
Optimization is one of the key technologies in gray-box
identification. A significant achievement in recent years is
the adoption of convex programming techniques into optimization
problem formulation and solving. A benefit is that
the solution to a convex optimization problem is the global
optimum, which ensures that the identified parameters produce
the best matching results.
IBR Modeling: A Forward Look
The sixth application is data-driven IBR modeling. We use a
2.3-MVA inverter as an example to demonstrate the state-ofthe-art
technology in black-box IBR model identification,
and we give our perspective on challenges to be tackled in
IBR modeling.
dq Admittance Model Identification
For IBRs, dq admittance measurement technology is a
mature technology. The measurement capability can be realized
in software as well as hardware experiments with the
availability of advanced high-power converters and mediumvoltage
sensors.
Figure 4 shows a measurement testbed set up at the National
Renewable Energy Laboratory's Flatirons Campus in Colorado,
United States. A critical component of the testbed
is the 7-MVA, 13.2-kV controllable grid interface (CGI).
The CGI essentially works as a grid-forming converter. It
draws electricity from a utility grid and acts as a controllable
voltage source. When an IBR is connected through
a step-up transformer to a CGI, it can be configured to
operate at a certain operating condition. The CGI can produce
a harmonic voltage source superimposed to its 60-Hz
voltage source. This harmonic voltage source's frequency
may vary. Thus, frequency scans can be conducted using
the CGI.
For this testbed, the model to be identified describes
the relationship between the two inputs (the dq-axis voltages)
and the two outputs (the dq-axis currents), as shown
in Figure 4. This model is called dq admittance and it
is a two-by-two matrix in the Laplace domain. The four
components of the dq admittance matrix are Ydd, Ydq, Yqd,
and Yqq. Figure 5 presents photos of the CGI and mediumvoltage
sensing equipment at the National Renewable
Energy Laboratory.
The resulting dq admittance of the IBR viewed at the
measurement point is shown in Figure 6. The measurement
ieee power & energy magazine
69
IEEE Power & Energy Magazine - May/June 2022

Table of Contents for the Digital Edition of IEEE Power & Energy Magazine - May/June 2022
