IEEE Power Electronics Magazine - June 2020 - 57
(+)
idc
idc
(+)
+
+
+
vcA∑
vcB∑
vcC∑
vsA∑
vsB∑
vsC∑
icA
+
+
+
+
+
2Rbr
+
2 vcB∑
vsB∑
vcA∑
vsA∑
vsC∑
+
2 vcC∑
+
isA
2Lbr
+
isB
+
isC
A
+
vcB∑
+
+
=
+
+
(-)
Vdc
vsA∑
icC
Vdc
2 vcA∑
+
icB
vcC∑
vsB∑
Lbr
vsC∑
Rbr
(-)
isA
isB
isC
A
B
C
Lbr/2
B
C
Rbr/2
FIG 6 The simultaneous control of terminal currents requires every branch of the analyzed MMC to synthesize the voltage comprising two components, labeled with v c"A/B/C ,R (the dc component) and v s"A/B/C ,R (the ac component). As can be seen on the right
side of the figure, two circuits, decoupled from each other, can be formed to identify the effect that each of the branch voltage
components has on the control of terminal currents.
However, equal energy distribution among the SBRs is
considered the utmost priority of every MMC-based circuit.
Therefore, in the structures containing parallel SBRs, the
energy balancing must be given priority over the balancing
of currents. Since every SBR produces the dc voltage that is
approximately equal to the voltage of the dc grid the MMC
is connected to (Vdc), the SBR power can be expressed as
Power
Current Sharing Yes No No
Voltage Sharing No Yes No
Power Sharing No No Yes
Voltage
Current
FIG 7 Tradeoffs in the current, power, and voltage sharing of
the parallel SBRs set. If a certain side of the triangle is chosen,
equal sharing of the quantities positioned on the other two
sides of the triangle cannot be achieved. For instance, equal
current sharing requires the SBRs to generate different voltages, causing unequal power sharing. Similar reasoning can be
applied to the other two cases.
br+
+
+
vbr,2
+
+
=
Lbr,1
Lbr,2
Lbr,M
Rbr,1
Rbr,2
Rbr,M
br-
Therefore, balancing of the SBR powers (energies) can
be ensured through the intentional generation of the SBR
+
∗
vbr
vbr,M
M
Σ ∆vbr,i = 0
i=1
+
∗
vbr
ibr,2
(1)
br
2 Vdc T I br,i
br+
∗
ibr = ibr
Identical Voltages
ibr
vbr,1
DC
AC
)
P br,i = P br
+ TP br
+ TP br
.
< depends
<
on TZ
1
+
∆vbr,1
∗
vbr
ibr,2
br+
∆Ibr = 0!
ibr,M
+
br-
+
∆vbr,2
∆Ibr,1
+
∆vbr,M
∆Ibr,2
∆Ibr,M
br-
FIG 8 Balancing the SBR energies can be done through the intentional unbalances generated in the SBR dc currents. Namely,
M voltage disturbances, the sum of which equals zero, result in M current components that sum to zero at the branch terminals
(the right-most circuit). Consequently, the energy distribution among the SBRs can be affected.
June 2020
z IEEE POWER ELECTRONICS MAGAZINE
57
IEEE Power Electronics Magazine - June 2020
Table of Contents for the Digital Edition of IEEE Power Electronics Magazine - June 2020
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