IEEE Power Electronics Magazine - June 2018 - 59

34
5
0.
35
0.
35
5
0.
36

900

symbol

Arm inductor

7 mH

400 µH

L filter

3.3 mH

Time (s)
Larm = 7 mH

traditional
Design with
Design
Optimized Inductors

Parameter

32
5
0.
33
0.
33
5
0.
34
0.
34
5
0.
35
0.
35
5
0.
36

850

Table 3. The specifications of the traditional
design and the proposed design with optimized
inductors for the MMC AFE.

950

Fig 3 The equivalent circuit derived for the MMC AFE from (6).

1,000

31
5

MMC AFE

1,050

Udc

ivj

Filter inductor

1,100

Lfilter L /2 ej

Cell Voltage (V)

uvj

Input Voltage (V) and Current (A)

inductors features smaller ripple
Thevenin inductance of the MMC
across the cells.
AFE is considered as L filter + L/2.
The main harmonics
According to [8], the main harTherefore, 1 pu of installed filter
contributing to the
monics contributing to the voltage
inductance will have the same effect
ripple across the cell capacitors are
on the attenuating input current harvoltage ripple across
the first and second harmonics. At
monics as 4 pu of an installed arm
the cell capacitors are
unity power factor operation of the
inductance (since for each filter
converter and for the design case
inductance there are two arm inducthe first and second
with 7-mH arm inductors (traditional
tances in the structure of the MMC).
harmonics.
design), the equations for the first and
Also, in the case of a fault in the
second harmonic of voltage across the
converter structure, the amount of
cell capacitors are shown in (7) and
fault current flowing from the grid
(8), respectively:
side will be similar when having
equal Thevenin inductances.
m a I dc
I va
ma I2
D
Considering these facts, the first step in reducing the
(7)
Tv c~ = : 6~
C - 4~C - 4~C cos ~t,
size of passive elements is to move the majority of the
m I va
I
inductance from the arms to the ac side. Two designs
(8)
Tv 2c ~ = : 16a~C
+ 4~2C D sin 2~t,
are used to investigate the feasibility of the proposed
method. In the first (traditional) design, the arm inducwhere I va is the magnitude of the input ac current from the
tance is selected to be 7 mH (point E in Figure 2), which
grid to the MMC AFE. On the other hand, for the design
has the minimum L/L res,second ratio according to the survey results from Table 2. The second design (the design
with optimized inductances) uses 400 nH of arm inductance (point C in Figure 2). To make the Thevenin inducGrid Voltage
2,000
Larm = 7 mH
tances of the two designs similar, three 3.3-mH filter
1,500
Larm = 400 µH
inductances are added to the second design between the
1,000
converter and grid. The performed designs are summa500
rized in Table 3.
0
To compare the designed converters, simulations are
-500
performed in the MATLAB/Simulink environment.
-1,000
Figure 4 shows the grid voltage and input current to the
-1,500
MMC AFE. According to this figure, in the case of both
-2,000
designs, the input current to the converter has the same
total harmonic distortion value. This is predictable
Time (s)
since the Thevenin inductors in both designs are the
same. The cell capacitor voltages for both of the designs
Fig 4 The simulated grid voltage and input current to the
are shown in Figure 5, where it can be seen that, with
MMC AFE under the traditional design and the proposed
similar cell capacitors, the design with the optimum
design with optimized inductors.

Larm = 400 µH

Fig 5 The simulated voltage fluctuation across the cell capacitors under the traditional design (193.3-V ripple) and the proposed design with optimized inductors (84.6-V ripple).

June 2018

z IEEE POwEr ElECtrOnICs MAGAzInE

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