IEEE Electrification - June 2021 - 75

numerical solution of the models'
differential equations. For
instance, Euler, backwards differentiation
formulas, and RungeKutta,
among others.
x Linear algebra libraries: In this
layer, low-level algorithms are
used to perform numerical linear
algebra calculations for system
solutions, a lower-upper (LU)
decomposition, or eigenvalue
calculations.
Novel research needs improvements
at all levels of the software
stack; however, progress requires that
the computational experiments be
replicated under many conditions.
Free and open source-validated models that provide a
benchmark for the development of algorithms are a critical
step that is not currently available. Stable and reliable
implementations of integration algorithms usually require
tremendous development efforts and limit the scope of
the models to small systems.
More tools are emerging to address each of these modeling
needs, thanks to the advent of code-sharing repositories,
broad access to software development tools, and
the popularity of open source programming languages
like R, Julia, and Python. However, without a deliberate
effort to develop a platform that can be reused by many
researchers, we risk limiting the
scope and scale of power system
research or duplicating efforts. In
this context, the Julia programming
language offers a host of
unique features that significantly
reduce the effort to implement scientific
computing practices to simulate
low-inertia power systems.
Before discussing Julia, we first
highlight some key challenges of
low-inertia systems.
Computational Challenges
of Low-Inertia Systems
The dynamic analysis of power systems
resorts to mainly two computational
numerical methods: 1)
time-domain simulations and)
small-signal stability analysis. For
many decades, there has been a
focus on reducing time-domain
simulations' computational complexity
through model order re -
ductions. Some of the modeling
practices and analytical assumptions
currently in use derive from
From an analytical
perspective, RMS
and EMT modeling
approaches are
similar: They both
use differentialalgebraic
equations
to represent system
dynamics.
the singular perturbation theory popularized
in the 1980s. The seminal
papers showed that a simplified
model is still a valid representation of
certain system dynamics under the
premise of time scale separation.
Traditionally, time-domain simulations
assume that the fundamental
frequency of the system dominates
current and voltage waveforms. As a
result, the network can be simplified
to a voltage and current phasor representation,
known as the root mean
square (RMS) or quasi-static phasor
modeling approach. Additionally,
synchronous generator stator fluxes
relationships reduce to algebraic
equations, further simplifying RMS modeling ap -
proaches. However, this representation cannot capture
some of the converters' high-frequency dynamics. Figure
3 displays the dependency between frequency phenomena
and modeling requirements to capture the
system's behavior.
In power systems dominated by synchronous
machines, the source of dynamics is physical phenomena
with a behavior described by physics laws. These include,
for instance, magnetic fluxes, electromechanics, mechanical
control reaction times, or thermodynamic processes.
Moreover, the control logic is commonly tuned to the
How to model?
Phasor representation
or full waveform?
Lightning Propagation
Switching Surges
Inverter-Based Controls
Stator Transients and
Subsynchronous Resonance
Thermodynamic
Phenomena
Rotor-Angle Dynamics
Governor and Load
Frequency Control
Voltage Control
Boiler Dynamics
Wave
Phenomena
10-7
10-5
Electromagnetic
Phenomena
10-3
10-1
Time (s)
Figure 3. The time scales used for power systems' dynamic behavior. Current power systems
have dynamic behaviors dominated by physical laws. New inverter dynamics introduces new
dynamics from logical components and poses new challenges in model complexity for time-domain
simulations. (Adapted from Hatziargyriou et al. 2020).
IEEE Electrification Magazine / JUNE 2021
75
101
103
105
Electromechanical
Phenomena

IEEE Electrification - June 2021

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