Environmental Engineering Reference
In-Depth Information
where
E
2
2
I
1
|
|
2
EI
1
|
|
V
1
=
+
Z
o
(
j
ω
)
−
Z
o
(
j
ω
)
cos(
φ
1
+
θ
−
δ
)
,
arctan
I
1
|
Z
o
(
j
ω
)
|
sin(
φ
1
+
θ
−
δ
)
β
=
.
I
1
|
Z
o
(
j
ω
)
|
cos(
φ
1
+
θ
−
δ
)
−
E
The sum of all harmonic components in the output voltage is
√
2
h
=
2
I
h
|
v
H
=
Z
o
(
jh
ω
)
|
sin(
h
ω
t
+
φ
h
+
∠
Z
o
(
jh
ω
))
.
It is clear that
v
1
is determined by the clean reference
voltage, the fundamental current and the output impedance at the fundamental frequency.
v
1
and
v
H
do not affect each other.
v
H
is determined by the harmonic current components and the output impedance at the harmonic
frequencies. This is an important feature and enables the design of the impedance to meet
different requirements.
According to the definition of THD, the THD of the output voltage is
2
h
=
2
I
h
|
Z
o
(
jh
ω
|
)
THD
=
×
100%
.
(2.1)
V
1
Hence, the THD is mainly affected by the output impedance at the harmonic frequencies. As
a result, it is feasible to optimise the design of the output impedance at high frequencies to
minimise the THD of the output voltage, without affecting the impedance at the fundamental
frequency. In other words, the design of the output impedance can be decoupled to meet two
different requirements in the frequency domain. For example, the output impedance at the
fundamental frequency can be designed to meet the requirements of the droop controller for
proportional load sharing, as shown in Chapter 19, and the output impedance at harmonic
frequencies can be designed to reduce the THD of the voltage, as shown in Chapter 7. Hence,
one parameter can be used to meet two requirements at the same time (one qualitatively and
the other quantitatively).
2.2 Repetitive Control
2.2.1 Basic Principles
One of the main objectives of a control system is to asymptotically track a reference signal
while rejecting disturbances. According to the well-known internal model principle (Francis
and Wonham, 1975), there is a need to include a model of the reference signal or the disturbance
signal in the closed loop in order to achieve perfect tracking or disturbance rejection. For
example, when the reference signal and/or the disturbances are step signals, it is necessary to
include an integrator
1
s
in the closed loop to achieve zero static error. Similarly, for periodic
signals (such as those in the case of controlling inverters), there is a need to include a pair
of conjugate imaginary poles at the frequency
ω
of the signal in the closed loop. A pair of
1
conjugate imaginary poles can be provided by
2
, as used in the proportional-resonant
s
2
+
ω
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