IEEE Electrification - September 2021 - 15

30 min, 2) (S2) islanded mode due to
planned disconnection for 30 min, 3)
(S3) reconnecting to the grid-connected
mode for 30 min, 4) (S4) islanded mode
due to unplanned disconnection for
30 min, and 5) (S5) reconnecting to the
grid-connected mode for 30 min. The
five contingencies are 1) major synchronous
generator fault, 2) major renewable
energy generator fault, 3) distributed
energy storage fault, 4) main line fault,
and 5) communication system fault.
In summary, the tests last a total of
150 min, with a total of 25 contingencies.
A load loss is counted every time
that the system falls outside of the
voltage/frequency area, demarcated by
" Zone B " in Figure 9, as defined by the
IEC 60034-1 standards, or every time
that the system does not satisfy the
requirements of the IEEE Standard
1547-2018, Power Quality in Voltage and
Frequency, including 1) rapid voltage
change, 2) voltage flicker, 3) total ratedcurrent
distortion, 4) transient overvoltage,
5) voltage ridethrough, and 6)
frequency ridethrough.
According to some initial evaluations,
current microgrids suffer
approximately four losses out of the
25 contingencies proposed here (initial
case = 20%). In this context, a
potential target could be roughly one
loss out of the 25 contingencies (target
case = 4%), and a maximum/optimal
case of zero losses out of the 25
contingencies (maximum case = 0%).
Additionally, the dynamic factor Dy
of the M1 metric represents the decay
of the oscillation, or relative damping
of the microgrid, when a disturbance
enters the network and the control
system reacts to reject it. This is measured
both in voltage Dv and frequency
Df under the same contingencies
defined previously and as shown in
(5)-(7), with
0050## ##
.,
DD Dyv f
D . nn Ok
Ok
v 05 1 11 npo
nco
=+
e
D .,n r=1
co
f=- /
05 1
d
=- //
1 cmn
co
r=1
nco
e
po
O
O
f
f
1
2
k=1
r
v
v
2
1
^
^
DD .,
vf 05
(5)
h
h o o (6)
r
(7)
Disturbance
Figure 10. The frequency and voltage oscillations.
IEEE Electrification Magazine / SEPTEMBER 2021
15
Time
where npo is the number of test
points and nco is the number of contingencies.
The relative damping is
defined as the second overshoot O2
(or undershoot) divided by the first
overshoot O1 (or undershoot), O2/O1,
for both frequency (Of1, Of2) and voltage
(Ov1, Ov2), considering always
(/ )OO
## (see Figure 10).
Typically, with a PID controller
tuned using a classical Ziegler-Nichols
method, the relative damping
(O2/O1) is 25%. In this context, an
01
21
initial relative damping of about 20%,
a potential target of 5% and a maximum
of 0% are defined.
Based on all of these cases (initial,
target, and maximum) for both availability
Ay and dynamics Dy, and to
have a well-balanced M1 metric
according to the expressions given by
(1), the parameters of the polynomials
of (2) and (3) are
a =-71 ., a =
1
a = 46 .,
2
875
875
10 300 and b =2 50 ,0
b =-775, and b = 0 325 . The contributions
of the availability and
Voltage (p.u.)
1.08
1.05
1.03
Zone A,
0.95
0.98
Continuous
Operation
1.02 1.03
Frequency (p.u.)
60 Hz
57 Hz
58.8 Hz
Zone B,
Temporary
Operation/
Reduced
Performance
0.92
Figure 9. The voltage-frequency limits for power generators and transformers according
to IEC 60034-1.
0.97
0.95
61.8 Hz
61.2 Hz
f or V
O1
O2
IEEE Electrification - September 2021

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