IEEE Electrification - March 2021 - 78

in IBRs, a condition that severely limits the applicability
of generic models; manufacturers of IBRs generally do
not provide white-box EMT models, to avoid disclosing
intellectual property. Therefore, the complex dynamic
behavior of IBRs due to the large number of nonlinearities, such as PLLs, limiters in different control loops, and
special control modes during transient events, is more
challenging to predict and understand. Stability analysis
tools for island power systems that have high levels of
IBRs should be able to accept user-defined, black-box
EMT models of IBRs from manufacturers to accurately
evaluate stability issues, including the fundamental frequency and voltage stability, control interactions and
control stability, systemwide oscillations, and different
types of subsynchronous and supersynchronous resonance problems. Impedance methods are increasingly
used for analyzing IBR stability impacts because they do
not depend on open-box models and, instead, characterize IBRs by using their impedance responses, which can
be obtained by performing sweeps on black-box EMT
simulation models and experimentally on hardware
devices (see Shah et al. 2020).
Cosimulation via phasor-based models of conventional generation and the transmission network in transient
stability programs, such as Power System Simulator for
Engineering (PSSE) and Positive Sequence Load Flow as
well as EMT models of IBRs in Power Systems CAD
(PSCAD), can be used for simulating bulk power system
networks, as detailed in another article in this magazine.

Magnitude (dBΩ)

50
40
30
20
10
0
1 Hz

10 Hz

100 Hz

1 kHz

100 Hz

1 kHz

(a)
200

Phase (°)

100
0
-100
-200
-300
1 Hz

10 Hz
(b)

Figure 2. Validating an EMT (PSCAD) model of a 4-MW wind turbine
by comparing its positive-sequence impedance response magnitude
(a) and phase (b) to experimental measurements. The blue lines represent experimental measurements, and the red dots indicate the
response from PSCAD model.

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I E E E E l e c t r i f i cati o n M agaz ine / MARCH 2021

Stability analysis can be performed through the cosimulation platform by combining state-space modal analysis
and impedance analysis approaches to respectively capture the stability characteristics of a transmission network with synchronous generators that are represented
by open-box phasor models and IBRs that are represented by black-box EMT models. However, as demonstrated
through several case studies in subsequent sections,
most island power systems are sufficiently small to be
completely simulated in an EMT environment by using
PSCAD, and their stability can be analyzed through
impedance methods. Experimentally measured impedance responses can also be used for the validation of
EMT models of IBRs, as shown in Figure 2. Note that
impedance analysis methods and state-space tools use
linearization assumptions and so should be used with
caution in systems that have nonlinearities, such as
inverter controls.

Modeling Application Example: Maui
With the recent procurement of central PV-BESS systems
and a stand-alone BESSs, the dispatch of the Maui system,
in roughly 2023, could include many hours of zero online
synchronous generation, which may make the island the
first to have an interconnected transmission system that
operates with 100% IBRs. [Many smaller island systems
have already operated with 100% instantaneous IBRs,
beginning many years ago with isolated power systems,
for example in Metlakatla, Alaska (see Miller et al. 1996).]
With the recognition of likely shortcomings in positive
sequence simulations at high instantaneous IBR penetrations, substantial effort has been made to develop and validate an EMT model of the system, which has already
achieved instantaneous IBR penetrations exceeding 80%.
The system, with a peak demand of approximately
200 MW on a 69-kV transmission system, consists of a
diverse set of generation sources, with two primary fossil
fuel-based plants (Maalaea and Kahului), type 3 and type 4
wind plants, and more than 100 MW of nameplate distributed generation capacity.
The model was constructed in PSCAD, based on Hawaiian Electric's PSSE model and other information provided
by the utility; it is parallelized on 30 cores to increase its
computational efficiency; the roughly 600-bus model (200
three-phase buses) operates for approximately 10 min of
computation time for 1 s of simulation time, with a 15-ns
time step. All the inverter-based generation includes PLLs
and current loop dynamics. Distributed generation and
loads are aggregated at the distribution substation level.
The model was validated by recreating a specific event
that occurred in 2017, in which a single phase fault on
the low-voltage side of a Maalaea generation station
step-up transformer caused the respective generation unit
to trip offline. The fault and subsequent loss of generation
were simulated in PSCAD, with the resultant frequency
and voltage transients favorably matching up with
IEEE Electrification - March 2021

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