IEEE Power Electronics Magazine - June 2020 - 54

idc

Lbr
Vdc

isA

isB Branch

isC

Leg

C
(a)

+
vbr

vbr

Lbr

Lbr
(b)

FIG 1 (a) An MMC. (b) As every branch provides the possibility
for high-quality voltage generation, it can be modeled with an
ideal voltage source.

M
i∗

Power (p.u.)

OP4
3

OP3
OP2

2
1
0

2i ∗ 3i ∗

OP1

AD
0

0.5

OP5

1
1.5
Voltage (p.u.)

Legend
AD

10 × {1 kV/1 kA}

OP1

15 × {1 kV/1 kA}

OP2

Unfeasible

OP3

15 × {1 kV/2 kA}

FIG 2 The MMC power scalability depending on the available SM
design. The availability of an SM with rated voltage and current
equal to 1 kV and 1 kA was assumed, whereas the normalization
basis for the operating voltage of an observed converter was
adopted as 10 kV. As the OP2 cannot be reached unless additional
modifications of the SMs are performed, it was characterized as
the unfeasible operating point (concerning the existing SM design).

IEEE POWER ELECTRONICS MAGAZINE

z June 2020

rating implies its current capacity boost, which may not
always be trivial to accomplish.
Let one observe an exemplary case with the MMC being
connected to a 10-kV dc network while employing the SMs
designed to withstand the voltage and current equal to 1 kV
and 1 kA, respectively. This SM design will be referred to as
the available design (AD), while 10 kV represents the normalization basis regarding the converter dc voltage.
In the analyzed case and using simplified calculation, the number of SMs per branch can be determined as
N = 10 kV/1 kV = 10. In the power-voltage (P-V) diagram
from Figure 2, such an operating point was labeled with
the yellow star [v ) = 1 per unit (p.u.) and p ) = 1 p.u.]. If, for
example, five SMs are added into every branch of the analyzed MMC, the voltage it can interface at its dc terminals
increases to 15 kV ^v ) = 1.5 p.u. h . As the SM current rating
is unchanged, the rated power of the converter gets scaled
linearly. In other words, changing the number of series-connected SMs within a branch causes the converter operating
point (OP) to slide along the green line in Figure 2. Hence,
the point OP 1 indicates an increased number of series-connected SMs ^ N = 15 h with respect to the converter operating at voltage equal to 1 p.u. ^ N = 10 h, yet with the same
current rating.
However, to meet the requirements of any application
with an OP residing above the green line, the current handling capabilities of the converter must be increased. If
an application operates at the OP 2 (15 kV, 1.5 kA), reusing
the available SMs is not possible owing to the current rating insufficiency, even if the application's voltage requirements are met. A new SM could be designed to meet the
application needs; however, this comes with an additional
research and development cost. Providing that a new SM
with twice the initial current rating is available, the newly
designed system ratings allow OP 3 to be reached. However, the system operating voltage remains unchanged, as
indicated in Figure 2.
While the OP 2 can be served now, the actual MMC has
significantly higher ratings than required and is likely to
be more expensive than needed. A further increase of the
SM current rating (e.g., three times the initial current) gives
another capability line in the P-V plane and provides insight
into the MMC scalability. It is noteworthy that reaching the
power-scaling plot corner points (e.g., OP 4: high power−
low voltage or OP 5: low power−high voltage) would likely
not be reasonable economy-wise or practical in engineering terms. In other words, despite many advantages, the
MMC has its own limitations regarding the span of OPs that
can be served with satisfactory economic and technical
efficiency. Moreover, the current, and simultaneously the
power, capacity boost is rather a nontrivial task with several technical challenges as described next.

MMC Scalability Options
The parallel connection of power modules (PMs), as shown
in Figure 3(a), is widely used for monolithic converters such

IEEE Power Electronics Magazine - June 2020

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