IEEE Power & Energy Magazine - November/December 2017 - 68

It can be shown that, to provide a response closely
approaching true inertia from a converter, it is necessary
to accept that there will be a damped resonance.
The VSM behaves as a voltage source, because both its
rotor dynamics (~2-Hz bandwidth) and AVR dynamics have
bandwidths < 50/60 Hz, and the adjustments to the pulsewidth
modulation patterns are slow relative to the 50/60-Hz fundamental. It therefore does a very good job of "mopping up"
unbalance, and it can provide power to heavily unbalanced
loads. It is also quite good at "mopping up" harmonic voltages, although linear load is also (or more) effective at high
harmonic orders. Because the VSM is a voltage source, during the closest faults, some intervention is needed to protect
the solid-state devices from overcurrent. Viable methods have
been demonstrated in the laboratory, able to sustain >140-ms
full-depth balanced and unbalanced faults, but without compromising the normal "voltage source" capability. Additional
interventions can be made during faults. For example, setting
H = 999 during a fault helps to stop the virtual rotors accelerating while fault ride-through is active and so can potentially
make VSMs more robust than real machines against faults.
Parameters such as damping, inertia, and governor response
can, if needed, be adjusted in real time, remotely via software.
Because the VSM is a voltage source, with frequency and
voltage stabilized by its virtual inertia and AVR, it provides
"synchronizing torque." It also provides inertia. But, crucially,
it is not necessary that inertia be established to provide synchronizing torque; they are not the same thing. Thus, it is possible to
provide synchronizing torque without providing inertia.
This can be achieved by a using a second variety of gridforming (voltage source) converter-control algorithm. This
second variety implements frequency and voltage control
loops that operate on a strict pair of droop slopes: active power
to frequency and reactive power to voltage. There is effectively an "instant" (~10-ms) governor/prime-mover response
time. The converter simply measures its output power over a
short window such as one exact cycle (which provides good
harmonic mitigation) or measures the instantaneous power
output and applies low-pass filtering of the order of <1 cycle
period so that the control-loop bandwidth is <50/60 Hz (normally, perhaps in the ~20-Hz region).
Then, using a simple linear droop slope with configurable frequency and power set points, a target frequency is
determined. This target frequency is within a few percent of
nominal for normal set point and droop slope configurations.
The converter simply advances its virtual rotor at this frequency, and power synchronization is effectively achieved. A
parallel loop operates on reactive power and voltage. Such a
control scheme has acquired various names in the literature,
such as power synchronization or VSM0H. This latter term
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refers to the fact that the response of this architecture can
be shown to be mathematically identical to a VSM but with
H = 0, no direct rotor electrical damping, and an "instantly"
responding (within one cycle) governor/prime mover delivering "instant" droop response.
While rotor electrical damping is proportional to rotor speed
minus electrical stator frequency, droop response is proportional
to electrical frequency minus set point electrical frequency.
While they are different, the "instant" droop response actually
provides a useful damping of grid frequency disturbance and is
extremely effective at limiting frequency nadir during events.
It also provides what would be called "synchronizing torque,"
even though it has zero inertia, because it acts as a stiff, balanced voltage source, with a well-defined frequency close to
nominal, behind a reactance (formed by its filter impedance). A
network powered only by VSM0H converters is entirely viable.
In this scenario, a discrete resistive load step results in a network frequency that transitions from one frequency to another
(defined by the droop slopes and set points) over a period of
aproximately one cycle.
So, while this VSM0H-type controller offers no inertia, it
is entirely viable as a grid-forming solution, as confirmed by
the PSERC analysis, and can also be used in parallel with real
machines and with VSM converters that do offer inertia. No
special time-sensitive communications are required between the
converters as long as sensible configurations of set points and
conventional droop slopes are used to suit the network and connected energy sources. Sufficient energy must also be available
on the dc buses to drive the converters and serve the loads.
In both previously described modes (VSM and VSM0H),
the converters are grid forming, provide synchronizing torque,
serve unbalanced loads and mitigate unbalanced voltages,
and serve nonlinear loads and mitigate harmonic voltages.
The converter contribution to these services is, by default,
inversely proportional to the magnitude of the effective filter impedance-in exactly the same way that a synchronous
machine's contribution to these phenomena is inversely proportional to its transient reactance X´. For a real machine, X´ is
inversely proportional to machine rating, and this is normally
true for a converter filter impedance as well. So the device's
contribution to power quality and synchronization torque is
roughly proportional to its rating because X´ is normally in
the region of 0.1-0.15 pu for both machines and conventional
converters. This presents some further challenges (and perhaps opportunities) for multilevel converters, which may in
the future have much lower inductive filter impedances than
conventional converters.
november/december 2017

Table of Contents for the Digital Edition of IEEE Power & Energy Magazine - November/December 2017