IEEE Electrification Magazine - December 2019 - 60

There are several
alternatives for
providing virtual
inertia through
power converters.

One of the most widespread solutions to cope with a weak inertial
response is simply to mimic the
behavior of a classical synchronous
machine by integrating its characteristic equations into the controller of
grid-connected converters. As illustrated in Figure 3, the emulation of
inertia can improve the transient
response of the frequency under a
power perturbation by reducing its RoCoF.
Following the equivalences already highlighted, the
concept can be extended to a dc system by emulating
the behavior of a dc machine or a capacitor directly connected to the grid. In dc systems, such emulation will
decrease the RoCoV at the point of coupling, giving more
time for higher-level controllers to restore the voltage to
its rated value.
This analogy shows that the control philosophy,
including lower-level controllers for the emulation of inertia, can be kept equal regardless of the nature of the

RoCoF

Classical Grid
Converter-Dominated
Grid
Converter-Dominated
Grid With Inertia Emulation

Primary
Inertia
Control
Emu.
5s

Secondary
Control

30 s

Mech.
Inertia

Tertiary
Control

15 min
Time

75 min

Figure 3. A graph showing the evolution of the frequency (f ) under a
demand power perturbation and the role of the mechanical (Mech.) inertia and the hierarchical control in its restoration for a modern power system dominated by power electronic converters. Emu.: emulation.

io
idc

pq
+
vo
-

+
vdc
-

ac or dc
Grid

vc∗
Controller
"

vdcref ωn vref pref qref
Refs.
Figure 4. A diagram showing an electronic converter connected to a
grid. Refs.: references.

Control Techniques for
the Emulation of Inertia

There are several alternatives for providing virtual inertia through power
converters. Even though most of these techniques are
intended especially for converters connected to ac systems, we can see an accelerating trend to apply this control philosophy to converters connected to dc systems.
The following sections provide a brief overview of the
most relevant strategies for the emulation of inertia in ac
and dc systems. Figure 4 illustrates a power converter connected to an ac or dc grid and highlights the most relevant
variables of the system. The references in this case refer to
the voltage at the dc bus (v dc ), frequency (~ n), voltage
amplitude (vt ref ), and active and reactive power setpoints
( p ref and q ref ).
ref

Converters Connected
to ac Systems

Power Perturbation

system current (ac or dc). If the frequency and voltage signals are normalized to per-unit quantities, the
inertia can be equally emulated in ac
and dc systems.

I E E E E l e c t r i f i cati o n M agaz ine / DECEMBER 2019

There are several control techniques for emulating inertia
in devices connected to ac systems. The necessity to
develop such controllers is twofold: first, such controllers
can improve the dynamic behavior of the grid when
power is perturbed; second, some of these techniques
make it possible to do without a synchronization unit in
the converter. Such units are often the source of performance and stability problems.
Despite the high number of approaches proposed in
the literature, most can be categorized as either an inertiaemulation (IE) technique, a synchronverter (SV) technique,
a current-controlled virtual synchronous machine
(CCVSM) technique, or a voltage-controlled VSM (VCVSM)
technique (Figure 5).

IE Technique
The IE technique [Figure 5(a)] relies on the swing equation that describes the mechanical behavior of synchronous machines. This is illustrated in the block diagram in
Figure 2(a). Unlike other controllers that emulate the
behavior of synchronous machines, those using the IE
technique provide an additional power component,
depending on the derivative of the grid frequency. This
frequency is usually estimated with a synchronization
unit, such as a phase-locked loop (PLL).
The concept of this technique is simple and has been
widely applied for different applications because the
additional power component calculated from the IE
loop can be easily added to the power reference coming
from other regulators. However, the use of PLLs and
derivative terms in the controllers can be problematic,

IEEE Electrification Magazine - December 2019

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