IEEE Electrification Magazine - June 2017 - 61

0
-90

-

3,000

2,800

2,600

2,400

PCC

2,200

-180

2,000

-135
1,800

Phase (°)

ion

-45

1,600

+
von

-50

ioi

+
voi
-

0

1,400

-

Diesel
Generator

1,200

Inverter
Interface

+
vo1

50

1,000

DER
n

...

Inverter
Interface
...

DER
i

...

Inverter
Interface
...

DER
1

Zc

Magnitude (dB)

io1

Frequency (Hz)
Figure 8. Frequency domain analysis results for remote microgrids with

ple inverter-interfaced DERs.

multiple inverter-interfaced DERs.

and a capacitor to form an LCL filter, especially for the
remote microgrids with inverter-interfaced DERs. The
LCL filter can be used to suppress the high-frequency
harmonics imposed by pulsewidth modulation switch-
ing behavior.
As seen in the frequency domain analysis results of a
common LCL filter in Figure 6, its high-frequency range
shows a significant damping characteristic. Hence, the
high-frequency disturbances at the inverter switching fre-
quency and the neighboring side-band frequencies can
be effectively suppressed. However, as shown in Figure 6,
there is a resonance peak in the plot of magnitude-
frequency characteristic, which can amplify the distur-
bances around the resonance frequency and degrade
system stability. When multiple inverter-interfaced DERs
coexist in remote microgrids, the system configuration
can be simplified as depicted in Figure 7. The multiple LCL
filters are coupled at the PCC, which is interconnected to
the backup generators via a large impedance. Because of
the existence of the impedance at the PCC, the resonance
peaks of each LCL filter interact with each other, which
further deteriorates the stability of the remote microgrid.
The results of a frequency domain analysis of the transfer
function from the inverter output voltage to the output
current at the PCC side are shown in Figure 8. An addi-
tional resonance peak and an antiresonance peak appear
in the system. Meanwhile, when the number of inverter-
interfaced DERs increases, the additional resonance peak
moves toward the low-frequency range. Because low-fre-
quency harmonics are commonly found in a microgrids
as a result of the high penetration level of nonlinear
sources and loads, these harmonic components with the
similar frequency of the resonance peaks can be ampli-
fied. System operation is thereby influenced, leading to
even worse overall stability. As mentioned previously, the
basis of the degraded stability in remote microgrids is the

Frequency (kHz)

Figure 7. A simplified configuration of remote microgrids with multi-

2.45
2.4

2.2

2

0

0.5

1
1.5
Inductance (mH)

2

Figure 9. Change of resonance frequencies with different |Zc|.

Additional
L and C

Figure 10. A passive damping approach to improve the stability of
inverter-interfaced DERs.

existence of the relatively large impedance Zc at the PCC.
As shown in Figure 9, the frequency of the additional res-
onance peak changes along with |Zc|. Note that the fre-
quency of the additional resonance peak becomes equal
to the original resonance peak existing in the system
with a single LCL-filtered inverter when |Zc| is reduced
gradually to zero. This demonstrates that the existence of
Zc is the essential reason for the occurrence of multiple
resonance peaks.
IEEE Electrific ation Magazine / j une 2 0 1 7

61



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