IEEE Electrification - June 2021 - 76

respective time scale of the relevant process, creating a
" natural " separation among the time processes.
On the other hand, inverter-based generation is dominated
by dynamics induced by logic and controls, such as
a phase-locked loop (PLL), voltage and current controllers,
and power controllers. In the control block diagram of the
virtual synchronous machine (VSM) inverter model presented
in Figure 4, the only states defined by physical phenomena
are the six resistor-inductor-capacitor (RLC) filter
states. As a result, the inverter dynamics can span a wide
range of time scales and interact with existing controls or
physical components.
These two dynamic behavior sources can interact
unexpectedly, and the guidance of time scale separation
may not apply. Hence, when studying the massive integration
of converter-interfaced sources, it is impossible to
know a priori if and at which time scales the interactions
may occur and requiring dynamic simulations that capture
fast electromagnetic phenomena, such as electromagnetic
transients (EMT), on a large scale introduces
computational challenges.
From an analytical perspective, RMS and EMT modeling
approaches are similar: They both use differentialalgebraic
equations (DAEs) to represent system dynamics.
The dynamic models used in the power industry tend to
be stiff because they represent phenomena at multiple
rates. Depending on the model's time constants, the
required integrator time steps can impose substantial
computational requirements. In RMS models, the maximum
time step is ~1-10 ms. Simultaneously, EMT time
step usually is about ~1-50 μs. As a result, RMS simulations
are typical when modeling large, interconnected
areas like continental Europe or the Eastern Interconnection
in the United States. They are typically used to study
the transient response of different disturbances and
require significant simplifications. On the other hand,
EMT simulations have a smaller scope. They are commonly
used to analyze a single device's dynamic behavior
against infinite buses.
The difference in modeling complexity also means that
the RMS and EMT simulations' solution methods differ in
important ways. The commercial tools for RMS modeling
typically implement Adams-Bashforth-2 and use explicit
formulation through mass matrix representations. On
the other hand, EMT software tools use the trapezoidal
rule and directly model the electromagnetic differential
equations (also known as the Dommel method) in the solution
process.
In large systems with detailed models, the calculation
of Jacobian matrices and eigenvalues can require significant
computational effort. There are multiple opportunities
available from the recent advances in AD thanks to
the machine learning community that obtain exact Jacobians
in this area. Exact Jacobians have myriad uses in
dynamic modeling, from algorithmic design to parameter
evaluation.
Three States: [θoc, ωoc, qoc]
rt
p∗
q∗
w∗
v∗
idq
o
Outer
Control
Loop
ωpll
Four States:
[vpll , εpll, θpll]
dq
PLL
θoc
v~
ωoc
ωoc
Virtual
Impedance
v
Inner
Control
Loop
[ξdq, γdq, φdq]
Six States:
ic ic ic
vdc
v
PWM
iabc
cnv
m
rf
If
cf
vdq
o
idq
cnv
abc
dq
iabc
vabc
o
o
RLC Filter
Six States:
[icnv, iri, vri]
ri
oo
It
To
Grid
Figure 4. A block diagram of a commonly used 19-state grid-supporting inverter for simulation experiments. This architecture features the
main components of inverter models: the outer control that uses a VSM model, the PLL, the inner controls, and the filter. PWM: pulsewidth
modulation.
76
IEEE Electrification Magazine / JUNE 2021
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IEEE Electrification - June 2021

Table of Contents for the Digital Edition of IEEE Electrification - June 2021