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From the above analysis and discussion, it is known that the discretization
effect on discrete resonance controller is exactly the same by using virtual LC
method and step response invariant method. However reference [14] pointed out
that virtual LC method makes the transfer function of step response invariant
method expand
ω
n
times in number, which obviously ignores the influence on
discrete-time transfer function of rewriting formula (4) into formula (5). Using
the discrete-time transfer function of reference [10] to analyze the stability of
the system is very desirable. Therefore, the method of reference [7-10] will be
employed to the design of PR controller discretization.
4 Analysis of Control Strategy and Design of Parameters
4.1 Current Inner Loop
The transfer function of inverter unit can be deduced from Fig. 2, which is shown
as follows:
1
LCs
2
+
Crs
+1
G
(
s
)=
(11)
The specific parameters of the experimental prototype are as the following:
L
=
680
μH
,
C
= 100
μF
,
r
=0
.
2
Ω
, and sampling period
T
=0
.
1ms.Usingthe
ZOH with the step response invariant method to discrete transfer function
G
(
s
),
which can be transformed to
G
(
z
) in Z - domain.
G
(
z
)=
Z
1
=
e
−Ts
s
·
−
1
LCs
2
+
Crs
+1
0
.
1448
z
+0
.
1419
z
2
(12)
−
1
.
655
z
+0
.
9412
The design parameters of current inner loop's harmonic PR controller are based
upon discrete method in formula (10). After a beat delay and LC filter, the 3rd,
5th and 7th harmonics phase angle lag respectively are about 42.5
◦
45
◦
and 47.5,
then
θ
3
=42
.
5
◦
,
θ
5
=45
◦
and
θ
7
=47
.
5
◦
. Transfer functions of the harmonic
resonant controller respectively are
R
3
(
z
),
R
5
(
z
)and
R
7
(
z
) in the Z-domain as
follows:
R
3
(
z
)=
0
.
0664
z
−
0
.
0724
1
942
.
4778
1
.
9912
z
+1
·
(13)
z
2
−
R
5
(
z
)=
0
.
1019
z
−
0
.
1193
1
1570
.
8
1
.
9754
z
+1
·
(14)
z
2
−
R
7
(
z
)=
0
.
1296
z
+0
.
1652
z
2
1
2199
.
1
1
.
9518
z
+1
·
(15)
−
References [15, 16] brought forth the principle of priority to system stability,
DVR control system has a good stability at
K
ph
=0
.
9.
4.2 Voltage Outer Loop
Similar to the current inner loop, the parameters design of voltage outer loop
adopt the virtual LC discrete method in formula (10). After a beat delay and LC
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